{"id":2630,"date":"2015-03-10T22:12:36","date_gmt":"2015-03-11T01:12:36","guid":{"rendered":"https:\/\/www.antonioguilherme.web.br.com\/blog\/?page_id=2630"},"modified":"2023-04-24T07:45:15","modified_gmt":"2023-04-24T10:45:15","slug":"equacao-de-schrondinger","status":"publish","type":"page","link":"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/fisica-quantica\/equacao-de-schrondinger\/","title":{"rendered":"Equa\u00e7\u00e3o de Schr\u00f6dinger"},"content":{"rendered":"\r\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\r\n<div class=\"wp-block-group__inner-container\">\r\n<p style=\"text-align: right;\"><em><span style=\"font-family: verdana, geneva, sans-serif;\">&#8220;<strong><span style=\"font-size: 14pt;\">Deus controla o eletromagnetismo pela teoria das ondas nas segundas, quartas e sextas-feiras, e o Diabo o controla pela teoria qu\u00e2ntica na ter\u00e7a, quinta e s\u00e1bado&#8221;.<\/span><\/strong><\/span><\/em><\/p>\r\n<p style=\"text-align: right;\"><span style=\"font-size: 14pt;\"><b>Sir William Bragg &#8211; <\/b>F\u00edsico Brit\u00e2nico<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A <a href=\"https:\/\/en.wikipedia.org\/wiki\/Schr\u00f6dinger_equation\" target=\"_blank\" rel=\"noopener\">equa\u00e7\u00e3o de Schr\u00f6dinger<\/a> consiste na equa\u00e7\u00e3o diferencial parcial que descreve a fun\u00e7\u00e3o de onda da mec\u00e2nica qu\u00e2ntica.\u00a0<\/span><span style=\"font-family: verdana, geneva, sans-serif;\">Por\u00e9m, entre Bohr e Schr\u00f6dinger muita coisa aconteceu.<\/span><\/p>\r\n<p><span style=\"letter-spacing: -0.015em;\"><span style=\"font-family: verdana, geneva, sans-serif;\">Conforme visto <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/mecanica-quantica\/\">anteriormente<\/a>, <\/span><a href=\"https:\/\/pt.wikipedia.org\/wiki\/Max_Planck\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: verdana, geneva, sans-serif;\">Planck<\/span><\/a><span style=\"font-family: verdana, geneva, sans-serif;\"> prop\u00f4s, ao estudar a <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-termicas\/radiacao-termica\/\">radia\u00e7\u00e3o t\u00e9rmica,<\/a> que a emiss\u00e3o de luz ocorria em quantidades discretas de energia. <\/span><\/span><\/p>\r\n<p><span style=\"letter-spacing: -0.015em;\"><span style=\"font-family: verdana, geneva, sans-serif;\">Logo a seguir em 1905, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Albert_Einstein\" target=\"_blank\" rel=\"noopener\">Einstein <span id='easy-footnote-1-2630' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/fisica-quantica\/equacao-de-schrondinger\/#easy-footnote-bottom-1-2630\" title=\"&lt;\/a&gt;\u00a0em seu artigo &lt;span style=&quot;letter-spacing: normal;&quot;&gt;&amp;#8220;On a Heuristic Point &lt;\/span&gt;&lt;span style=&quot;letter-spacing: normal;&quot;&gt;of View about the Creation and Conversion of Light&amp;#8221;\"><sup>1<\/sup><\/a><\/span> <\/span><\/span><\/span><span style=\"letter-spacing: -0.015em; font-family: verdana, geneva, sans-serif;\">expandiu este conceito afirmando que a luz tamb\u00e9m se propagava, era absorvida e emitida em quantidades discretas de energia. <\/span><span style=\"letter-spacing: -0.015em; font-family: verdana, geneva, sans-serif;\">Planck recebeu o Pr\u00eamio Nobel de F\u00edsica em 1918 e Einstein em 1921.<\/span><br \/><br \/><span style=\"letter-spacing: -0.015em; font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 1 sintetiza o conceito revolucion\u00e1rio de que a energia da luz se tornou discreta com degraus iguais \u00e0 constante de Planck.<\/span><br \/><br \/><\/p>\r\n<figure id=\"attachment_22457\" aria-describedby=\"caption-attachment-22457\" style=\"width: 220px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/Einstein_Planck_2.png\"><img decoding=\"async\" class=\"wp-image-22457 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/Einstein_Planck_2.png\" alt=\"\" width=\"220\" height=\"180\" \/><\/a><figcaption id=\"caption-attachment-22457\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Equa\u00e7\u00e3o 1. Equa\u00e7\u00f5es Planck-Einstein<\/span><\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">E \u00e9 a energia;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">h \u00e9 a constante de Planck;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">f \u00e9 a frequ\u00eancia;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">p \u00e9 o momento;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">c \u00e9 a velocidade da luz;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03bb \u00e9 o comprimento de onda.<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h2 id='de-broglie'  id=\"boomdevs_1\"><span style=\"font-family: verdana, geneva, sans-serif;\">De Broglie<\/span><\/h2>\r\n<p><a href=\"http:\/\/pt.wikipedia.org\/wiki\/Louis_de_Broglie\" target=\"_blank\" rel=\"noopener noreferrer\"><span style=\"font-family: verdana, geneva, sans-serif;\">Louis de Broglie<\/span><\/a><span style=\"font-family: verdana, geneva, sans-serif;\"><span id='easy-footnote-2-2630' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/fisica-quantica\/equacao-de-schrondinger\/#easy-footnote-bottom-2-2630\" title=\" ganhou o pr\u00eamio &lt;a href=&quot;http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1929\/&quot; target=&quot;_blank&quot; rel=&quot;noopener noreferrer&quot;&gt;Nobel de F\u00edsica de 1929&lt;\/a&gt; com este conceito\"><sup>2<\/sup><\/a><\/span> deu um passo \u00e0 frente ao estender aos el\u00e9trons o comportamento de ondas, at\u00e9 ent\u00e3o restrito \u00e0 luz. <\/span><span style=\"font-family: verdana, geneva, sans-serif;\">As figuras 1 e 2 mostram a ideia de substituir a part\u00edcula por uma onda.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Ondas podem permanecer est\u00e1veis em orbitais, mas isto n\u00e3o ocorre com qualquer frequ\u00eancia. O n\u00famero de ciclos da onda necessita ser m\u00faltiplo inteiro do caminho percorrido para que seja uma onda estacion\u00e1ria. Se isto n\u00e3o ocorrer, aparece uma descontinuidade na onda, que a torna inst\u00e1vel.<\/span><\/p>\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter\">\r\n<figure id=\"attachment_2614\" aria-describedby=\"caption-attachment-2614\" style=\"width: 716px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/quantica_3.png\"><img decoding=\"async\" class=\"wp-image-2614 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/quantica_3.png\" alt=\"Frequ\u00eancia adequada\" width=\"716\" height=\"712\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/quantica_3.png 716w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/quantica_3-150x150.png 150w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/quantica_3-300x298.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/quantica_3-624x621.png 624w\" sizes=\"(max-width: 716px) 100vw, 716px\" \/><\/a><figcaption id=\"caption-attachment-2614\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Figura 1. Frequ\u00eancia Adequada<\/span><\/figcaption><\/figure>\r\n<\/figure>\r\n<\/div>\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter\">\r\n<figure id=\"attachment_2615\" aria-describedby=\"caption-attachment-2615\" style=\"width: 716px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/quantica_4.png\"><img decoding=\"async\" class=\"wp-image-2615 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/quantica_4.png\" alt=\"Frequ\u00eancia inadequada\" width=\"716\" height=\"712\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/quantica_4.png 716w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/quantica_4-150x150.png 150w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/quantica_4-300x298.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/quantica_4-624x621.png 624w\" sizes=\"(max-width: 716px) 100vw, 716px\" \/><\/a><figcaption id=\"caption-attachment-2615\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Figura 2. Frequ\u00eancia Inadequada<\/span><\/figcaption><\/figure>\r\n<\/figure>\r\n<figure><\/figure>\r\n<figure><span style=\"font-family: verdana, geneva, sans-serif; letter-spacing: -0.015em;\">A hip\u00f3tese de De Broile considera o <\/span><strong style=\"font-family: verdana, geneva, sans-serif; letter-spacing: -0.015em;\">el\u00e9tron uma onda plana com comprimento de onda<\/strong><span style=\"font-family: verdana, geneva, sans-serif; letter-spacing: -0.015em;\"> relacionado ao seu momento e energia de acordo com a Equa\u00e7\u00e3o 2. Apesar das equa\u00e7\u00f5es serem semelhantes \u00e0s de Planck-Einstein, De Broile estabeleceu que o el\u00e9tron se comporta de forma &#8220;qu\u00e2ntica&#8221; e, consequentemente, a mat\u00e9ria se tornou qu\u00e2ntica. Essa teoria causou muita pol\u00eamica na comunidade cient\u00edfica, mas suportava o postulado de estabilidade dos orbitais dos el\u00e9trons \u00a0de Bohr.<\/span><\/figure>\r\n<\/div>\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter is-resized\">\r\n<figure id=\"attachment_22460\" aria-describedby=\"caption-attachment-22460\" style=\"width: 306px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/De_broile_1.png\"><img decoding=\"async\" class=\"wp-image-22460 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/De_broile_1.png\" alt=\"\" width=\"306\" height=\"134\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/De_broile_1.png 306w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/De_broile_1-300x131.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><\/a><figcaption id=\"caption-attachment-22460\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Equa\u00e7\u00e3o 2. Equa\u00e7\u00e3o De Broile<\/span><\/figcaption><\/figure>\r\n<figure class=\"aligncenter is-resized\">\r\n<p style=\"text-align: left;\"><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li style=\"text-align: left;\"><span style=\"font-family: verdana, geneva, sans-serif;\">E \u00e9 a energia do el\u00e9tron;<\/span><\/li>\r\n<li style=\"text-align: left;\"><span style=\"font-family: verdana, geneva, sans-serif;\">\u03bb \u00e9 o comprimento de onda do el\u00e9tron;<\/span><\/li>\r\n<li style=\"text-align: left;\"><span style=\"font-family: verdana, geneva, sans-serif;\">h \u00e9 a constante de Planck;<\/span><\/li>\r\n<li style=\"text-align: left;\"><span style=\"font-family: verdana, geneva, sans-serif;\">h cortado \u00e9 a constante de Planck dividida por 2\u03c0;<\/span><\/li>\r\n<li style=\"text-align: left;\"><span style=\"font-family: verdana, geneva, sans-serif;\">p \u00e9 o momento do el\u00e9tron.<\/span>\u00a0<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h2 id='schr\u00f6dinger'  id=\"boomdevs_2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Schr\u00f6dinger<\/span><\/h2>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 3 representa uma onda unidimensional.<\/span><\/p>\r\n<figure id=\"attachment_9363\" aria-describedby=\"caption-attachment-9363\" style=\"width: 162px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/onda_plana_1.png\"><img decoding=\"async\" class=\"wp-image-9363 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/onda_plana_1.png\" alt=\"\" width=\"162\" height=\"56\" \/><\/a><figcaption id=\"caption-attachment-9363\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 3. Onda plana<\/figcaption><\/figure>\r\n<p>&nbsp;<\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Este tipo de onda \u00a0se origina de uma equa\u00e7\u00e3o diferencial tipo <\/span><a style=\"font-family: verdana, geneva, sans-serif;\" href=\"http:\/\/en.wikipedia.org\/wiki\/Helmholtz_equation\" target=\"_blank\" rel=\"noopener noreferrer\">Helmholtz<\/a><span style=\"font-family: verdana, geneva, sans-serif;\">. No caso de coordenadas cartesianas, a solu\u00e7\u00e3o desta equa\u00e7\u00e3o consiste numa fun\u00e7\u00e3o senoidal.<\/span><\/p>\r\n<p><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/helmholtz.png\"><img decoding=\"async\" class=\"size-full wp-image-1994 aligncenter\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/helmholtz.png\" alt=\"\" width=\"242\" height=\"47\" \/><\/a><\/p>\r\n<figure id=\"attachment_22570\" aria-describedby=\"caption-attachment-22570\" style=\"width: 162px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/k.png\"><img decoding=\"async\" class=\"wp-image-22570 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/k.png\" alt=\"\" width=\"162\" height=\"85\" \/><\/a><figcaption id=\"caption-attachment-22570\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 4. Equa\u00e7\u00e3o de Helmholtz<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c8 \u00e9 a fun\u00e7\u00e3o de onda;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u2207<sup>2\u00a0<\/sup>\u00e9 o operador Laplaciano<span id='easy-footnote-3-2630' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/fisica-quantica\/equacao-de-schrondinger\/#easy-footnote-bottom-3-2630\" title=\"&lt;a href=&quot;https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/nabla.png&quot;&gt;&lt;img class=&quot;aligncenter size-full wp-image-9364&quot; src=&quot;https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/nabla.png&quot; alt=&quot;&quot; width=&quot;414&quot; height=&quot;101&quot; \/&gt;&lt;\/a&gt; \"><sup>3<\/sup><\/a><\/span>;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">k \u00e9 o autovalor da equa\u00e7\u00e3o ou n\u00famero de onda.<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Aplicando a Equa\u00e7\u00e3o 1 na Equa\u00e7\u00e3o 4, teremos que:<\/span><\/p>\r\n<figure id=\"attachment_22573\" aria-describedby=\"caption-attachment-22573\" style=\"width: 116px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/k_1.png\"><img decoding=\"async\" class=\"size-full wp-image-22573\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/k_1.png\" alt=\"\" width=\"116\" height=\"78\" \/><\/a><figcaption id=\"caption-attachment-22573\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 5. n\u00famero de onda<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Substituindo a Equa\u00e7\u00e3o 5 na Equa\u00e7\u00e3o 4 e dividindo todos os termos por duas vezes a massa da part\u00edcula obtem-se a seguinte express\u00e3o:<\/span><\/p>\r\n<figure id=\"attachment_9371\" aria-describedby=\"caption-attachment-9371\" style=\"width: 501px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/schrondinger_2.png\"><img decoding=\"async\" class=\"size-full wp-image-9371\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/schrondinger_2.png\" alt=\"\" width=\"501\" height=\"94\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/schrondinger_2.png 501w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/schrondinger_2-300x56.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/a><figcaption id=\"caption-attachment-9371\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 6.<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">m \u00e9 a massa da part\u00edcula;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">p \u00e9 o momento da part\u00edcula;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">h cortado \u00e9 a constante de Planck dividida por 2\u03c0;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c8 \u00e9 a fun\u00e7\u00e3o de onda.<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O fator do segundo termo da Equa\u00e7\u00e3o 6 representa a energia cin\u00e9tica da part\u00edcula. Como a soma da energia cin\u00e9tica e potencial fornece a energia total do sistema, pode-se transformar a Equa\u00e7\u00e3o 6 na Equa\u00e7\u00e3o 7, denominada de Equa\u00e7\u00e3o de Schr\u00f6ndiger invariante no tempo. <span id='easy-footnote-4-2630' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/fisica-quantica\/equacao-de-schrondinger\/#easy-footnote-bottom-4-2630\" title=\" A literatura representa a energia potencial por V porque o campo el\u00e9trico normalmente gera a energia potencial \"><sup>4<\/sup><\/a><\/span><\/span><\/p>\r\n<figure id=\"attachment_22592\" aria-describedby=\"caption-attachment-22592\" style=\"width: 557px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/schrondinger.png\"><img decoding=\"async\" class=\"wp-image-22592 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/schrondinger.png\" alt=\"\" width=\"557\" height=\"94\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/schrondinger.png 557w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/schrondinger-300x51.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/a><figcaption id=\"caption-attachment-22592\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 7. Equa\u00e7\u00e3o de Schr\u00f6dinger invariante no tempo<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Ep \u00e9 a energia potencial da part\u00edcula;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">E \u00e9 a energia total da part\u00edcula.<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Em 1926, <\/span><a style=\"font-family: verdana, geneva, sans-serif;\" title=\"http:\/\/en.wikipedia.org\/wiki\/Erwin_Schr\u00f6dinger\" href=\"https:\/\/en.wikipedia.org\/wiki\/Erwin_Schr%C3%B6dinger\" target=\"_blank\" rel=\"noopener\">Erwin Schr\u00f6ndinger<\/a><span style=\"font-family: verdana, geneva, sans-serif;\"> publicou sua famosa equa\u00e7\u00e3o que passou a representar, para a mec\u00e2nica qu\u00e2ntica, o que a segunda lei de Newton significa para a mec\u00e2nica cl\u00e1ssica. Ele ganhou em conjunto com Dirac o pr\u00eamio <a href=\"http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1933\/\" target=\"_blank\" rel=\"noopener noreferrer\">Nobel de F\u00edsica em 1933<\/a>.<\/span><\/p>\r\n<h2 id='fun\u00e7\u00e3o-de-onda'  id=\"boomdevs_3\"><span style=\"font-family: verdana, geneva, sans-serif;\">Fun\u00e7\u00e3o de onda<\/span><\/h2>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">As leis de conserva\u00e7\u00e3o s\u00e3o extremamente fortes e poderosas e, por isso, os cientistas procuram sempre encontrar novas teorias que as respeitem. <\/span><span style=\"font-family: verdana, geneva, sans-serif;\">A conserva\u00e7\u00e3o da energia e do momento representam casos particulares destas leis.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif; letter-spacing: -0.015em;\">A solu\u00e7\u00e3o da equa\u00e7\u00e3o de Helmholtz<span id='easy-footnote-5-2630' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/fisica-quantica\/equacao-de-schrondinger\/#easy-footnote-bottom-5-2630\" title=\" Equa\u00e7\u00e3o 5\"><sup>5<\/sup><\/a><\/span> j\u00e1 previa uma fun\u00e7\u00e3o de onda \u03a8 <span id='easy-footnote-6-2630' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/fisica-quantica\/equacao-de-schrondinger\/#easy-footnote-bottom-6-2630\" title=\" cap.12 do Kreyszig\"><sup>6<\/sup><\/a><\/span>. Contudo, a grande contribui\u00e7\u00e3o de Schr\u00f6dinger consistiu em definir uma equa\u00e7\u00e3o de ondas planas com a energia total do sistema e sua energia potencial. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif; letter-spacing: -0.015em;\">Por\u00e9m, n\u00e3o existe uma dedu\u00e7\u00e3o para esta equa\u00e7\u00e3o porque ela foi postulada assim como diversas outras coisas na mec\u00e2nica qu\u00e2ntica.<\/span><\/p>\r\n<p><strong><span style=\"font-family: verdana, geneva, sans-serif;\">Mas qual o significado f\u00edsico da fun\u00e7\u00e3o de onda &#8211; \u03a8(r)?<\/span><\/strong><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">No caso da Equa\u00e7\u00e3o invariante no tempo, a fun\u00e7\u00e3o de onda depende apenas da posi\u00e7\u00e3o &#8211; r &#8211; da part\u00edcula.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"> Portanto, o <strong>quadrado do m\u00f3dulo desta fun\u00e7\u00e3o representa a probabilidade da part\u00edcula se encontrar pr\u00f3xima ao ponto r<\/strong>.<\/span><span style=\"font-family: verdana, geneva, sans-serif;\"><span id='easy-footnote-7-2630' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/fisica-quantica\/equacao-de-schrondinger\/#easy-footnote-bottom-7-2630\" title=\"Por\u00e9m, as ondas na mec\u00e2nica qu\u00e2ntica n\u00e3o s\u00e3o eletromagn\u00e9ticas, nem ondas de press\u00e3o, nem de qualquer outra grandeza f\u00edsica. Utilizam-se analogias com essas ondas em determinados casos apenas para facilitar o entendimento. \"><sup>7<\/sup><\/a><\/span><\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Na verdade, as solu\u00e7\u00f5es da Equa\u00e7\u00e3o 7 dependem de um conjunto de n\u00fameros discretos, denominados de <a href=\"https:\/\/en.wikipedia.org\/wiki\/Quantum_number\" target=\"_blank\" rel=\"noopener\">n\u00fameros qu\u00e2nticos<\/a>, que determinam as caracter\u00edsticas dos orbitais dos El\u00e9trons nos \u00c1tomos e, matematicamente, s\u00e3o os autovalores da equa\u00e7\u00e3o.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"> Esses quatro n\u00fameros <strong>n, l, m<sub>l<\/sub> e m<sub>s<\/sub><\/strong> caracterizam os orbitais dos el\u00e9trons nos \u00e1tomos, mas apenas os tr\u00eas primeiros resultam da Equa\u00e7\u00e3o de Schr\u00f6ndiger.<span id='easy-footnote-8-2630' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/fisica-quantica\/equacao-de-schrondinger\/#easy-footnote-bottom-8-2630\" title=\"Na verdade a quimica j\u00e1 conhecia esses n\u00fameros experimentalmente\"><sup>8<\/sup><\/a><\/span><\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O \u00faltimo, momento magn\u00e9tico do Spin possui uma outra origem.\u00a0<\/span><\/p>\r\n<h5 id='n\u00famero-qu\u00e2ntico-principal'  id=\"boomdevs_4\"><span style=\"font-family: verdana, geneva, sans-serif;\">N\u00famero Qu\u00e2ntico Principal<\/span><\/h5>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O n\u00famero &#8211; <strong>n<\/strong>, denominado de Principal, determina a energia do orbital do El\u00e9tron e representa as linhas da Tabela Peri\u00f3dica, que variam de 1 a 7. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Bohr j\u00e1 havia previsto este n\u00famero em sua teoria, mas os demais n\u00fameros qu\u00e2nticos n\u00e3o. Adicionalmente, a Tabela Peri\u00f3dica de Mendelev considerava esse n\u00famero de forma emp\u00edrica.<\/span><\/p>\r\n<h5 id='n\u00famero-qu\u00e2ntico-azimutal'  id=\"boomdevs_5\"><span style=\"font-family: verdana, geneva, sans-serif;\">N\u00famero Qu\u00e2ntico Azimutal<\/span><\/h5>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O segundo n\u00famero &#8211; <strong><span style=\"font-family: 'book antiqua', palatino, serif;\"><em>l<\/em><\/span><\/strong>, denominado de <a href=\"https:\/\/en.wikipedia.org\/wiki\/Azimuthal_quantum_number\" target=\"_blank\" rel=\"noopener\"><strong>n\u00famero qu\u00e2ntico azimutal ou angular<\/strong><\/a>, descreve o momento angular do El\u00e9tron e varia entre 0 e n-1. Ele descreve o tipo de \u00f3rbita e subn\u00edvel dos El\u00e9trons no \u00c1tomo, podendo variar entre 0 e 6. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">\u00c9 importante observar que os tr\u00eas primeiros n\u00fameros qu\u00e2nticos se encontram relacionados porque representam os autovalores da Equa\u00e7\u00e3o de Schr\u00f6dinger.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 8 determina o momento angular dos El\u00e9trons.<\/span><\/p>\r\n<figure id=\"attachment_39506\" aria-describedby=\"caption-attachment-39506\" style=\"width: 333px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/L.png\"><img decoding=\"async\" class=\"wp-image-39506 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/L.png\" alt=\"\" width=\"333\" height=\"80\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/L.png 333w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/L-300x72.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/a><figcaption id=\"caption-attachment-39506\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 8. Momento angular dos El\u00e9trons<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">L \u00e9 o momento angular dos El\u00e9trons;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">h cortado \u00e9 constante de Planck dividida por 2\u03c0;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">l \u00e9 o n\u00famero qu\u00e2ntico azimutal.<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Como este n\u00famero qu\u00e2ntico se encontra relacionado ao n\u00famero qu\u00e2ntico principal, a camada eletr\u00f4nica n=1 possui apenas a configura\u00e7\u00e3o s, a camada n=2 possui apenas as configura\u00e7\u00f5es s e p, a camada n=3 as configura\u00e7\u00f5es s, p e d, e a camada n=4 as configura\u00e7\u00f5es s, p, d e f.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Qu\u00edmica j\u00e1 havia descoberto isso experimentalmente atrav\u00e9s da an\u00e1lise espectral dos elementos qu\u00edmicos e as denominou de <strong>S<\/strong>harp, <strong>P<\/strong>rincipal, <strong>D<\/strong>ifusa e <strong>F<\/strong>undamental. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por raz\u00f5es hist\u00f3ricas, esta denomina\u00e7\u00e3o prevaleceu. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por\u00e9m, os n\u00edveis seguintes, que n\u00e3o possu\u00edam denomina\u00e7\u00e3o cl\u00e1ssica, receberam a designa\u00e7\u00e3o de <strong>g, h e i<\/strong> seguindo a ordem alfab\u00e9tica a partir de f.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Este n\u00famero qu\u00e2ntico, possui grande influ\u00eancia na Ci\u00eancia dos Materiais porque determina a forma do orbital dos El\u00e9trons nos \u00c1tomos e, consequentemente, influencia as liga\u00e7\u00f5es qu\u00edmicas e os \u00e2ngulos dessas liga\u00e7\u00f5es.<\/span><\/p>\r\n<h5 id='n\u00famero-qu\u00e2ntico-magn\u00e9tico'  id=\"boomdevs_6\"><span style=\"font-family: verdana, geneva, sans-serif;\">N\u00famero Qu\u00e2ntico Magn\u00e9tico<\/span><\/h5>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O <a href=\"https:\/\/en.wikipedia.org\/wiki\/Magnetic_quantum_number\" target=\"_blank\" rel=\"noopener\">N\u00famero Qu\u00e2ntico Magn\u00e9tico<\/a> &#8211; <strong>m<sub>l<\/sub> <\/strong>&#8211; diferencia os orbitais dentro das subcamadas e varia entre -l e l, incluindo o zero. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por isso, as subcamadas possuem quantidades crescentes de orbitais conforme mostra a Figura 3 e a Tabela abaixo. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Observa-se nesta Figura que somente a subcamada s possui simetria esf\u00e9rica. <\/span><\/p>\r\n<figure id=\"attachment_39509\" aria-describedby=\"caption-attachment-39509\" style=\"width: 1200px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/numeros_quanticos.png\"><img decoding=\"async\" class=\"wp-image-39509\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/numeros_quanticos.png\" alt=\"\" width=\"1200\" height=\"723\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/numeros_quanticos.png 2134w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/numeros_quanticos-300x181.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/numeros_quanticos-1024x617.png 1024w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/numeros_quanticos-768x463.png 768w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/numeros_quanticos-1536x926.png 1536w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/numeros_quanticos-2048x1234.png 2048w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/numeros_quanticos-1200x723.png 1200w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/numeros_quanticos-1980x1193.png 1980w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/a><figcaption id=\"caption-attachment-39509\" class=\"wp-caption-text\">Figura 3. N\u00famero qu\u00e2ntico azimutal. Fonte: Inigo.quilez<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Al\u00e9m disso, o aumento da quantidade de El\u00e9trons nas subcamadas equivale \u00e0 quantidade de valores poss\u00edveis para l multiplicado por dois, a quantidade de spins poss\u00edveis dos El\u00e9trons.<\/span><\/p>\r\n<h2 class=\"wpdt-c\" id=\"wdt-table-title-54\">N\u00fameros Qu\u00e2nticos<\/h2>\n<div class=\"wpdt-c wdt-skin-aqua\">\n    \n    <input type=\"hidden\" id=\"wdtNonceFrontendServerSide_54\" name=\"wdtNonceFrontendServerSide_54\" value=\"10d8d3623c\" \/><input type=\"hidden\" name=\"_wp_http_referer\" value=\"\/blog\/wp-json\/wp\/v2\/pages\/2630\" \/><input type=\"hidden\" id=\"wdtFrontendelementorNonce_54\" name=\"wdtFrontendelementorNonce_54\" value=\"3d02628d1b\" \/>    <input type=\"hidden\" id=\"table_1_desc\"\n           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   <table id=\"table_1\"\n           class=\" scroll responsive display nowrap wdt-no-display data-t data-t wpDataTable wpDataTableID-54 \"\n           style=\"\"\n           data-described-by='table_1_desc'\n           data-wpdatatable_id=\"54\">\n        \n        <!-- Table header -->\n        \n<thead>\n<tr>\n                    <th\n                        class=\" wdtheader sort numdata integer \"\n        style=\"\">        wdt_ID<\/th>        <th\n        data-class=\"expand\"                class=\" wdtheader sort \"\n        style=\"\">        Orbital<\/th>        <th\n                        class=\" wdtheader sort \"\n        style=\"\">        Momento Angular l<\/th>        <th\n                        class=\" wdtheader sort \"\n        style=\"\">        Momento Magn\u00e9tico ml<\/th>        <th\n                        class=\" wdtheader sort \"\n        style=\"\">        N\u00famero de El\u00e9trons nas Subcamadas<\/th>    <\/tr>\n<\/thead>\n        <!-- \/Table header -->\n\n        <!-- Table body -->\n        \n<tbody>\n<!-- Table body -->\n<div data-id=\"54\"\n     class=\"wdt-timeline-item wdt-timeline-table_1\"\n     style=\"\">\n    <div class=\"wdt-table-loader\">\n        <div class=\"wdt-table-loader-row wdt-table-loader-header\">\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n        <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n            <\/div>\n<\/div><!-- \/Table body -->\n                    <tr id=\"table_54_row_0\"\n            data-row-index=\"0\">\n                            <td style=\"\">1<\/td>\n                            <td style=\"\">s<\/td>\n                            <td style=\"\">0<\/td>\n                            <td style=\"\">0<\/td>\n                            <td style=\"\">2<\/td>\n                    <\/tr>\n                            <tr id=\"table_54_row_1\"\n            data-row-index=\"1\">\n                            <td style=\"\">2<\/td>\n                            <td style=\"\">p<\/td>\n                            <td style=\"\">1<\/td>\n                            <td style=\"\">-1,0,1<\/td>\n                            <td style=\"\">6<\/td>\n                    <\/tr>\n                            <tr id=\"table_54_row_2\"\n            data-row-index=\"2\">\n                            <td style=\"\">3<\/td>\n                            <td style=\"\">d<\/td>\n                            <td style=\"\">2<\/td>\n                            <td style=\"\">-2,-1,0,1,2<\/td>\n                            <td style=\"\">10<\/td>\n                    <\/tr>\n                            <tr id=\"table_54_row_3\"\n            data-row-index=\"3\">\n                            <td style=\"\">4<\/td>\n                            <td style=\"\">f<\/td>\n                            <td style=\"\">3<\/td>\n                            <td style=\"\">-3,-2,-1,0,1,2,3<\/td>\n                            <td style=\"\">14<\/td>\n                    <\/tr>\n                            <tr id=\"table_54_row_4\"\n            data-row-index=\"4\">\n                            <td style=\"\">5<\/td>\n                            <td style=\"\">g<\/td>\n                            <td style=\"\">4<\/td>\n                            <td style=\"\">-4,-3,-2,-1,0,1,2,3,4<\/td>\n                            <td style=\"\">18<\/td>\n                    <\/tr>\n            <\/tbody>        <!-- \/Table body -->\n\n        <!-- Table footer -->\n        \n        <!-- \/Table footer -->\n    <\/table>\n\n<\/div><style>\ntable.wpDataTable td.numdata { text-align: right !important; }\n<\/style>\n<style>\n                    \n                                                                                    .wpdt-c .wpDataTablesWrapper table.wpDataTable thead tr:nth-child(2) th {\n        overflow: visible;\n    }\n\n            \/* table font color *\/\n    .wpdt-c.wpDataTablesWrapper table.wpdtSimpleTable,\n    .wpdt-c .wpDataTablesWrapper table.wpDataTable {\n        font-family: Verdana, Geneva, sans-serif !important;\n    }\n\n            \/* table font size *\/\n    .wpdt-c.wpDataTablesWrapper table.wpdtSimpleTable,\n    .wpdt-c .wpDataTablesWrapper table.wpDataTable {\n        font-size: 24px !important;\n    }\n\n            \n                <\/style>\n<style>\n<\/style>\n<style>\n                            \n                                        \n                    \n<\/style>\n\r\n<h5 id='spin'  id=\"boomdevs_7\"><span style=\"font-family: verdana, geneva, sans-serif;\">Spin<\/span><\/h5>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O N\u00famero Qu\u00e2ntico <a href=\"https:\/\/en.wikipedia.org\/wiki\/Spin_quantum_number\" target=\"_blank\" rel=\"noopener\">Spin<\/a> representa o momento angular intr\u00ednseco de determinada part\u00edcula.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"> Inicialmente, <a href=\"https:\/\/en.wikipedia.org\/wiki\/George_Uhlenbeck\" target=\"_blank\" rel=\"noopener\">Uhlenbeck<\/a> e <a href=\"https:\/\/en.wikipedia.org\/wiki\/Samuel_Goudsmit\" target=\"_blank\" rel=\"noopener\">Goudsmit<\/a> associaram este momento angular \u00e0 rota\u00e7\u00e3o da part\u00edcula ao redor de seu eixo. Contudo, essa explica\u00e7\u00e3o possui inconsist\u00eancias f\u00edsicas porque o El\u00e9tron e diversas part\u00edculas elementares se confundem com ondas e n\u00e3o h\u00e1 como determinar seus raios. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por isso, o conceito do Spin se tornou abstrato e definido pela Mec\u00e2nica Qu\u00e2ntica.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Ao contr\u00e1rio dos n\u00fameros qu\u00e2nticos anteriores, o Spin n\u00e3o surgiu com a Equa\u00e7\u00e3o de Schr\u00f6dinger. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Os n\u00fameros qu\u00e2nticos apresentados anteriormente permitiam prever o espectro de emiss\u00e3o ocasionado pela transi\u00e7\u00e3o de El\u00e9trons entre as diversas posi\u00e7\u00f5es orbitais. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Essas transi\u00e7\u00f5es somente deveriam ocorrer quando tr\u00eas n\u00fameros mudam porque a emiss\u00e3o\/absor\u00e7\u00e3o de energia eletromagn\u00e9tica necessita de uma mudan\u00e7a no dipolo eletromagn\u00e9tico do \u00e1tomo.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Todavia, trabalhos experimentais mostraram que esta regra deixava de funcionar na presen\u00e7a de campo magn\u00e9tico externo. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Este fen\u00f4meno, descoberto em 1896, tornou-se conhecido como <a href=\"https:\/\/en.wikipedia.org\/wiki\/Zeeman_effect\" target=\"_blank\" rel=\"noopener\">Efeito Zeeman<\/a>. <a href=\"https:\/\/en.wikipedia.org\/wiki\/Pieter_Zeeman\" target=\"_blank\" rel=\"noopener\">Pieter Zeeman<\/a> <span id='easy-footnote-9-2630' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/fisica-quantica\/equacao-de-schrondinger\/#easy-footnote-bottom-9-2630\" title=\" Ele dividiu o Pr\u00eamio Nobel de F\u00edsica de 1902 com Hendrik Lorentz por esta descoberta\"><sup>9<\/sup><\/a><\/span> mostrou que as linhas espectrais se dividiam em diversas componentes na presen\u00e7a de campos magn\u00e9ticos est\u00e1ticos.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Em 1913, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Johannes_Stark\" target=\"_blank\" rel=\"noopener\">Johannes Stark<\/a> <span id='easy-footnote-10-2630' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/fisica-quantica\/equacao-de-schrondinger\/#easy-footnote-bottom-10-2630\" title=\" Ele recebeu o Pr\u00eamio Nobel de F\u00edsica em 1919 \"><sup>10<\/sup><\/a><\/span> descobriu que o mesmo tipo de fen\u00f4meno ocorria quando \u00e1tomos e mol\u00e9culas sofriam a influ\u00eancia de campos el\u00e9tricos.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"> Este efeito, an\u00e1logo ao Efeito Zeeman, se tornou conhecido como <a href=\"https:\/\/en.wikipedia.org\/wiki\/Stark_effect\" target=\"_blank\" rel=\"noopener\">Efeito Stark<\/a>.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Somente em 1925, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Wolfgang_Pauli\" target=\"_blank\" rel=\"noopener\">Wolfgang Pauli<\/a> <span id='easy-footnote-11-2630' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/fisica-quantica\/equacao-de-schrondinger\/#easy-footnote-bottom-11-2630\" title=\" Ele recebeu o Pr\u00eamio Nobel de F\u00edsica em 1945 \"><sup>11<\/sup><\/a><\/span> prop\u00f4s o quarto n\u00famero qu\u00e2ntico com dois valores poss\u00edveis que ficou conhecido como o Spin, do El\u00e9tron e de outras part\u00edculas.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Considerando este momento angular do Spin similar ao orbital, pode-se aplicar a Equa\u00e7\u00e3o 8, conforme mostra a Equa\u00e7\u00e3o 9.<\/span><\/p>\r\n<figure id=\"attachment_39526\" aria-describedby=\"caption-attachment-39526\" style=\"width: 328px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/spin0.png\"><img decoding=\"async\" class=\"size-full wp-image-39526\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/spin0.png\" alt=\"\" width=\"328\" height=\"80\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/spin0.png 328w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/spin0-300x73.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/a><figcaption id=\"caption-attachment-39526\" class=\"wp-caption-text\">Figura 9. Momento Angular do Spin<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">S \u00e9 o momento angular do Spin;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">s \u00e9 o n\u00famero qu\u00e2ntico spin;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">h cortado \u00e9 constante de Planck dividida por 2\u03c0;<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 10 define o N\u00famero Qu\u00e2ntico Spin.<\/span><\/p>\r\n<figure id=\"attachment_39549\" aria-describedby=\"caption-attachment-39549\" style=\"width: 116px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/s.png\"><img decoding=\"async\" class=\"size-full wp-image-39549\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/s.png\" alt=\"\" width=\"116\" height=\"78\" \/><\/a><figcaption id=\"caption-attachment-39549\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 10. N\u00famero Qu\u00e2ntico Spin<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">s \u00e9 o N\u00famero Qu\u00e2ntico Spin;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">n \u00e9 um n\u00famero inteiro positivo que inclui o zero.<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O N\u00famero Qu\u00e2ntico Spin depende do tipo da part\u00edcula, mas todos os F\u00e9rmions possuem n \u00edmpar, sendo que os elementos que formam a mat\u00e9ria &#8211; Pr\u00f3ton, Neutron, El\u00e9tron, e Quarks possuem n=1. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Al\u00e9m disso, todos os F\u00e9rmions conhecidos possuem n=1.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por outro lado, os Bosons possuem n par, sendo que os associados \u00e0s for\u00e7as respons\u00e1veis pela exist\u00eancia da mat\u00e9ria &#8211; For\u00e7a Eletromagn\u00e9tica, For\u00e7a Fraca e For\u00e7a Forte &#8211; possuem n=2, que resulta em s=1. Lembrando que esses Bosons s\u00e3o o F\u00f3ton, o Gluon, o W e o Z.\u00a0<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O B\u00f3son de Higgs, recentemente descoberto, possui n=0 e nenhuma outro B\u00f3son ainda foi encontrado com n maior que 2.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">No caso dos El\u00e9trons, o <strong>Momento Angular<\/strong> <strong>do Spin<\/strong> se caracteriza pelo n\u00famero qu\u00e2ntico <strong>s<\/strong>, que no caso dos <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/particulas-atomicas\/\">F\u00e9rmions<\/a> vale 1\/2<span id='easy-footnote-12-2630' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/fisica-quantica\/equacao-de-schrondinger\/#easy-footnote-bottom-12-2630\" title=\" O El\u00e9tron \u00e9 um F\u00e9rmion\"><sup>12<\/sup><\/a><\/span>. Desta maneira, o Momento Angular do Spin nos El\u00e9trons vale:<\/span><\/p>\r\n<figure id=\"attachment_39525\" aria-describedby=\"caption-attachment-39525\" style=\"width: 553px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/spin.png\"><img decoding=\"async\" class=\"size-full wp-image-39525\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/spin.png\" alt=\"\" width=\"553\" height=\"125\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/spin.png 553w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/spin-300x68.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/a><figcaption id=\"caption-attachment-39525\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 9. Momento Angular do Spin do El\u00e9tron<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">S \u00e9 o momento angular do Spin;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">h cortado \u00e9 constante de Planck dividida por 2\u03c0;<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O Momento Angular do Spin, analogamente ao momento angular orbital, gera um momento magn\u00e9tico de acordo com a Equa\u00e7\u00e3o 10.<\/span><\/p>\r\n<figure id=\"attachment_39537\" aria-describedby=\"caption-attachment-39537\" style=\"width: 312px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/momento_spin1.png\"><img decoding=\"async\" class=\"wp-image-39537 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/momento_spin1.png\" alt=\"\" width=\"312\" height=\"89\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/momento_spin1.png 312w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/momento_spin1-300x86.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/a><figcaption id=\"caption-attachment-39537\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 10. Momento Magn\u00e9tico do Spin<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ul>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">m<sub>s<\/sub> \u00e9 o momento magn\u00e9tico do spin;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">g<sub>s<\/sub> \u00e9 o fator g;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03bc<sub>B<\/sub> \u00e9 o Magneton de Bohr;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">S \u00e9 o momento angular do Spin;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">h cortado \u00e9 a constante de Plank dividida por 2\u03c0.<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O Magneton de Bohr consiste numa constante f\u00edsica definida de acordo com a express\u00e3o abaixo:<\/span><\/p>\r\n<figure id=\"attachment_39536\" aria-describedby=\"caption-attachment-39536\" style=\"width: 216px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/magneton_Bohr.png\"><img decoding=\"async\" class=\"wp-image-39536 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/02\/magneton_Bohr.png\" alt=\"\" width=\"216\" height=\"92\" \/><\/a><figcaption id=\"caption-attachment-39536\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 11. Magneton de Bohr<\/figcaption><\/figure>\r\n<p>Onde:<\/p>\r\n<p>&nbsp;<\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A configura\u00e7\u00e3o dos El\u00e9trons nos \u00c1tomos obedece a algumas regras b\u00e1sicas.\u00a0<\/span><\/p>\r\n<ul>\r\n<li style=\"list-style-type: none;\">\r\n<ol>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Os El\u00e9trons procuram ocupar os orbitais de menor energia. Isto significa que preferem o n\u00edvel s ao p, mas quando excitados por alguma fonte de energia podem ocupar orbitais com maior conte\u00fado energ\u00e9tico. Por\u00e9m, o estado excitado n\u00e3o \u00e9 est\u00e1vel e o El\u00e9tron tende a retornar ao orbital com menor n\u00edvel energ\u00e9tico emitindo energia- F\u00f3ton &#8211; equivalente a diferen\u00e7a energ\u00e9tica dos orbitais.<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Os El\u00e9trons ocupam orbitais com mesmo n\u00edvel energ\u00e9tico isoladamente antes de aceitarem outro El\u00e9tron. Esta regra se tornou conhecida como <a href=\"https:\/\/en.wikipedia.org\/wiki\/Hund%27s_rules\" target=\"_blank\" rel=\"noopener\"><strong>Regra de Hund<\/strong><\/a>. Hund formulou em 1927 tr\u00eas regras que se tornaram fundamentais para a Ci\u00eancia dos Materiais.\u00a0<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">O maior n\u00famero de El\u00e9trons no mesmo orbital \u00e9 dois, sendo que obrigatoriamente possuem spins opostos. Este \u00e9 o princ\u00edpio de exclus\u00e3o de Pauli.<\/span><\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">As Regras de Hund, formuladas em 1927, utilizam conceitos da Mec\u00e2nica Qu\u00e2ntica para determinar os orbitais dos El\u00e9trons nos \u00e1tomos.<\/span><\/p>\r\n<ol>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A configura\u00e7\u00e3o eletr\u00f4nica do \u00e1tomo, cujo n\u00famero de El\u00e9trons n\u00e3o parelhados for maior possuir\u00e1 a menor energia.<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">No caso de configura\u00e7\u00f5es com o mesmo n\u00famero de El\u00e9trons n\u00e3o parelhados, a configura\u00e7\u00e3o com maior momento orbital L possuir\u00e1 a menor energia.<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">No caso de \u00e1tomos com menos da metade de el\u00e9trons na subcamada mais externa, o n\u00edvel de menor energia corresponde ao que possuir o momento angular total (L+S) menor.<\/span><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<h6 id='material-complementar'  id=\"boomdevs_8\">Material Complementar<\/h6>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Estes v\u00eddeos fornecem uma visualiza\u00e7\u00e3o interessante da fun\u00e7\u00e3o de onda e da mec\u00e2nica qu\u00e2ntica.<\/span><\/p>\r\n<div class=\"wp-block-group\">\r\n<div class=\"wp-block-group__inner-container\">\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter is-resized\">\r\n<p>[wpdevart_youtube width=&#8221;640&#8243; height=&#8221;385&#8243; autoplay=&#8221;0&#8243; theme=&#8221;dark&#8221; loop_video=&#8221;0&#8243; enable_fullscreen=&#8221;1&#8243; show_related=&#8221;1&#8243; show_popup=&#8221;0&#8243; thumb_popup_width=&#8221;213&#8243; thumb_popup_height=&#8221;128&#8243; show_title=&#8221;1&#8243; show_youtube_icon=&#8221;1&#8243; show_annotations=&#8221;1&#8243; show_progress_bar_color=&#8221;white&#8221; autohide_parameters=&#8221;1&#8243; set_initial_volume=&#8221;true&#8221; initial_volume=&#8221;72&#8243; disable_keyboard=&#8221;1&#8243;]p7bzE1E5PMY[\/wpdevart_youtube]<\/p>\r\n<\/figure>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/figure>\r\n<\/figure>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"wp-block-group\">\r\n<div class=\"wp-block-group__inner-container\">\r\n<p>[wpdevart_youtube width=&#8221;640&#8243; height=&#8221;385&#8243; autoplay=&#8221;0&#8243; theme=&#8221;dark&#8221; loop_video=&#8221;0&#8243; enable_fullscreen=&#8221;1&#8243; show_related=&#8221;1&#8243; show_popup=&#8221;0&#8243; thumb_popup_width=&#8221;213&#8243; thumb_popup_height=&#8221;128&#8243; show_title=&#8221;1&#8243; show_youtube_icon=&#8221;1&#8243; show_annotations=&#8221;1&#8243; show_progress_bar_color=&#8221;white&#8221; autohide_parameters=&#8221;1&#8243; set_initial_volume=&#8221;true&#8221; initial_volume=&#8221;72&#8243; disable_keyboard=&#8221;1&#8243;]q7v5NtV8v6I[\/wpdevart_youtube]<\/p>\r\n<hr \/>\r\n<h2 id='refer\u00eancias'  id=\"boomdevs_9\">Refer\u00eancias<\/h2>\r\n<ol>\r\n<li>\r\n<p class=\"p1\"><span style=\"font-family: verdana, geneva, sans-serif;\">EINSTEIN, A. <strong>On a Heuristic Point of View about the Creation and Conversion of Light<\/strong> , Ann. Physik 17,132 <\/span><span style=\"font-family: verdana, geneva, sans-serif;\">(1905), translated by Haar, D. R., The Old Quantum Theory , pg. 91-107, Pergamon Press Ltd, 1967<\/span><\/p>\r\n<\/li>\r\n<li style=\"text-align: left;\"><span style=\"font-family: verdana, geneva, sans-serif;\">KREYSZIG, E. <strong>Advanced Engineering Mathematics<\/strong>, 9 edi\u00e7\u00e3o, John Wiley &amp; Sons, 2006.<\/span><\/li>\r\n<li style=\"text-align: left;\"><span style=\"font-family: verdana, geneva, sans-serif;\">MILLER, D.A.B, <strong>Quantum Mechanics for Scientists and Engineers<\/strong>, Cambridge University Press, 2008.<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">WOLF, H., <strong>Atomic and Quantum Physics<\/strong>, Springer, 1987.<\/span><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n\r\n<p>&nbsp;<\/p>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-inline: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: initial; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; inset-inline: initial; isolation: initial; letter-spacing: initial; lighting-color: initial; line-break: initial; list-style: initial; margin-block: initial; margin: initial; margin-inline: initial; marker: initial; mask: initial; mask-type: initial; max-block-size: initial; max-height: initial; max-inline-size: initial; max-width: initial; min-block-size: initial; min-height: initial; min-inline-size: initial; min-width: initial; mix-blend-mode: initial; object-fit: initial; object-position: initial; offset: initial; opacity: initial; order: initial; origin-trial-test-property: initial; orphans: initial; outline: initial; outline-offset: initial; overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-inline: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: initial; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; inset-inline: initial; isolation: initial; letter-spacing: initial; lighting-color: initial; line-break: initial; list-style: initial; margin-block: initial; margin: initial; margin-inline: initial; marker: initial; mask: initial; mask-type: initial; max-block-size: initial; max-height: initial; max-inline-size: initial; max-width: initial; min-block-size: initial; min-height: initial; min-inline-size: initial; min-width: initial; mix-blend-mode: initial; object-fit: initial; object-position: initial; offset: initial; opacity: initial; order: initial; origin-trial-test-property: initial; orphans: initial; outline: initial; outline-offset: initial; overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-inline: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: initial; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; 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text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; 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max-width: initial; min-block-size: initial; min-height: initial; min-inline-size: initial; min-width: initial; mix-blend-mode: initial; object-fit: initial; object-position: initial; offset: initial; opacity: initial; order: initial; origin-trial-test-property: initial; orphans: initial; outline: initial; outline-offset: initial; overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; 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empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: initial; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; inset-inline: initial; isolation: initial; letter-spacing: initial; lighting-color: initial; line-break: initial; list-style: initial; margin-block: initial; margin: initial; margin-inline: initial; marker: initial; mask: initial; mask-type: initial; max-block-size: initial; max-height: initial; max-inline-size: initial; max-width: initial; min-block-size: initial; min-height: initial; min-inline-size: initial; min-width: initial; mix-blend-mode: initial; object-fit: initial; object-position: initial; offset: initial; opacity: initial; order: initial; origin-trial-test-property: initial; orphans: initial; outline: initial; outline-offset: initial; overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-inline: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: initial; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; inset-inline: initial; isolation: initial; letter-spacing: initial; lighting-color: initial; line-break: initial; list-style: initial; margin-block: initial; margin: initial; margin-inline: initial; marker: initial; mask: initial; mask-type: initial; max-block-size: initial; max-height: initial; max-inline-size: initial; max-width: initial; min-block-size: initial; min-height: initial; min-inline-size: initial; min-width: initial; mix-blend-mode: initial; object-fit: initial; object-position: initial; offset: initial; opacity: initial; order: initial; origin-trial-test-property: initial; orphans: initial; outline: initial; outline-offset: initial; overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-inline: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: initial; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; inset-inline: initial; isolation: initial; letter-spacing: initial; lighting-color: initial; line-break: initial; list-style: initial; margin-block: initial; margin: initial; margin-inline: initial; marker: initial; mask: initial; mask-type: initial; max-block-size: initial; max-height: initial; max-inline-size: initial; max-width: initial; min-block-size: initial; min-height: initial; min-inline-size: initial; min-width: initial; mix-blend-mode: initial; object-fit: initial; object-position: initial; offset: initial; opacity: initial; order: initial; origin-trial-test-property: initial; orphans: initial; outline: initial; outline-offset: initial; overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; 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x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-inline: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; 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text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; 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gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: initial; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; inset-inline: initial; isolation: initial; letter-spacing: initial; lighting-color: initial; line-break: initial; list-style: initial; margin-block: initial; margin: initial; margin-inline: initial; marker: initial; mask: initial; mask-type: initial; max-block-size: initial; max-height: initial; max-inline-size: initial; max-width: initial; min-block-size: initial; min-height: initial; min-inline-size: initial; min-width: initial; mix-blend-mode: initial; object-fit: initial; object-position: initial; offset: initial; opacity: initial; order: initial; origin-trial-test-property: initial; orphans: initial; outline: initial; outline-offset: initial; overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; 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overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-inline: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; 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pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; 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vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; 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overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; 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-webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-inline: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: initial; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; 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pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-inline: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: initial; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; inset-inline: initial; isolation: initial; letter-spacing: initial; lighting-color: initial; line-break: initial; list-style: initial; margin-block: initial; margin: initial; margin-inline: initial; marker: initial; mask: initial; mask-type: initial; max-block-size: initial; max-height: initial; max-inline-size: initial; max-width: initial; min-block-size: initial; min-height: initial; min-inline-size: initial; min-width: initial; mix-blend-mode: initial; object-fit: initial; object-position: initial; offset: initial; opacity: initial; order: initial; origin-trial-test-property: initial; orphans: initial; outline: initial; outline-offset: initial; overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\">\u00a0<\/div>\r\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-inline: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; 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