{"id":1714,"date":"2015-02-22T18:10:20","date_gmt":"2015-02-22T21:10:20","guid":{"rendered":"https:\/\/www.antonioguilherme.web.br.com\/blog\/?page_id=1714"},"modified":"2023-09-06T08:50:03","modified_gmt":"2023-09-06T11:50:03","slug":"fisica-quantica","status":"publish","type":"page","link":"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/fisica-quantica\/","title":{"rendered":"Mec\u00e2nica Qu\u00e2ntica"},"content":{"rendered":"\r\n<p class=\"is-layout-flow wp-block-group-is-layout-flow\" style=\"text-align: right;\"><strong>&#8220;<span style=\"font-family: verdana, geneva, sans-serif; font-size: 14pt;\"><em><strong>S<\/strong>e a Mec\u00e2nica Qu\u00e2ntica ainda n\u00e3o o chocou profundamente, voc\u00ea ainda n\u00e3o a entendeu.&#8221;<\/em><\/span><\/strong><\/p>\r\n<p style=\"text-align: right;\"><span style=\"font-family: verdana, geneva, sans-serif; font-size: 14pt;\">Niels Bohr<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A <a href=\"https:\/\/pt.wikipedia.org\/wiki\/Introdu\u00e7\u00e3o_\u00e0_mec\u00e2nica_qu\u00e2ntica\" target=\"_blank\" rel=\"noopener\">Mec\u00e2nica Qu\u00e2ntica<\/a> estuda a estrutura da mat\u00e9ria nas escalas at\u00f4mica e subat\u00f4micas, e a suas intera\u00e7\u00f5es com a energia. Portanto, ela se tornou a base te\u00f3rica para o estudo dos materiais, principalmente os el\u00e9tricos e magn\u00e9ticos.<\/span><\/p>\r\n<h2 id='hist\u00f3ria-da-mec\u00e2nica-qu\u00e2ntica'  id=\"boomdevs_1\"><span style=\"font-family: verdana, geneva, sans-serif;\">Hist\u00f3ria da Mec\u00e2nica Qu\u00e2ntica<\/span><\/h2>\r\n<p style=\"text-align: left;\"><span style=\"font-family: verdana, geneva, sans-serif;\">Procuramos o sol no inverno para nos aquecer e a sombra no ver\u00e3o para nos refrescar. O sol fornece a energia que atinge a terra atrav\u00e9s do espa\u00e7o.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A brasa brilhante na churrasqueira se encontra muito quente, mas o carv\u00e3o que n\u00e3o brilha tamb\u00e9m pode nos queimar (Figura 1). <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Portanto, os materiais devem estar acima de determinada temperatura para brilhar e a cor muda com a temperatura. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Denomina-se <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-termicas\/radiacao-termica\/\">Radia\u00e7\u00e3o<\/a> este fen\u00f4meno de transfer\u00eancia de calor, que associa temperatura e luz, e ocorre sem a necessidade de existir um meio material.<\/span><\/p>\r\n<figure id=\"attachment_1907\" aria-describedby=\"caption-attachment-1907\" style=\"width: 640px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/brasa.jpg\"><img decoding=\"async\" class=\"wp-image-1907 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/brasa.jpg\" alt=\"Brasa de Carv\u00e3o\" width=\"640\" height=\"480\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/brasa.jpg 640w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/brasa-300x225.jpg 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/brasa-624x468.jpg 624w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/><\/a><figcaption id=\"caption-attachment-1907\" class=\"wp-caption-text\">Figura 1. Brasa de Carv\u00e3o<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Em 1887, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Photoelectric_effect\" target=\"_blank\" rel=\"noopener noreferrer\">Hertz<\/a> observou que uma chapa met\u00e1lica liberava cargas negativas quando recebia luz ultravioleta. Esta corrente el\u00e9trica podia ser interrompida aplicando-se uma tens\u00e3o. O valor desta tens\u00e3o independia do brilho, mas dependia da frequ\u00eancia da luz. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Este fen\u00f4meno ficou conhecido como efeito fotoel\u00e9trico.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A brasa mostra que a energia depende da cor e o <a href=\"http:\/\/en.wikipedia.org\/wiki\/Photoelectric_effect\" target=\"_blank\" rel=\"noopener noreferrer\">efeito fotoel\u00e9trico<\/a> mostra que a energia depende da frequ\u00eancia. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Logo, <strong>cor, frequ\u00eancia, e energia se encontram relacionados.<\/strong><\/span><\/p>\r\n<h3 id='planck'  id=\"boomdevs_2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Planck<\/span><\/h3>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A rela\u00e7\u00e3o entre energia e frequ\u00eancia deu a <a href=\"http:\/\/pt.wikipedia.org\/wiki\/Max_Planck\" target=\"_blank\" rel=\"noopener noreferrer\">Planck<\/a> o <a href=\"http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1918\/\" target=\"_blank\" rel=\"noopener noreferrer\">pr\u00eamio Nobel de F\u00edsica de 1918<\/a>.<\/span><\/p>\r\n<p style=\"text-align: left;\"><span style=\"font-family: verdana, geneva, sans-serif;\">Evidentemente, ningu\u00e9m ganha o pr\u00eamio Nobel sem matem\u00e1tica. Planck estabeleceu que a energia se relacionava com a frequ\u00eancia atrav\u00e9s de uma constante, denominada em sua homenagem de <a href=\"http:\/\/en.wikipedia.org\/wiki\/Planck_constant\" target=\"_blank\" rel=\"noopener noreferrer\">constante de Planck<\/a>, conforme mostra a Equa\u00e7\u00e3o 1.<\/span><\/p>\r\n<p><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/planck_2.png\"><img decoding=\"async\" class=\"aligncenter wp-image-22419 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/planck_2.png\" alt=\"\" width=\"267\" height=\"83\" \/><\/a><\/p>\r\n<figure id=\"attachment_1731\" aria-describedby=\"caption-attachment-1731\" style=\"width: 476px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/planck_4.png\"><img decoding=\"async\" class=\"wp-image-1731 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/planck_4.png\" alt=\"planck_4\" width=\"476\" height=\"83\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/planck_4.png 476w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/planck_4-300x52.png 300w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><\/a><figcaption id=\"caption-attachment-1731\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 1. Equa\u00e7\u00e3o de Planck<\/figcaption><\/figure>\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><span style=\"font-family: verdana, geneva, sans-serif;\">E \u00e9 a energia [J];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">h \u00e9 a constante de Planck [6,626 069 57 E-34 J.s];<\/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;\">f \u00e9 a frequ\u00eancia [Hz];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">c \u00e9 a velocidade da luz [299 792 458 m\/s];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03bb \u00e9 o comprimento de onda [m];<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c9 \u00e9 a frequ\u00eancia angular [rad\/s].<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h3 id='einstein'  id=\"boomdevs_3\"><span style=\"font-family: verdana, geneva, sans-serif;\">Einstein<\/span><\/h3>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Einstein demonstrou que o aumento da energia das cargas retiradas pelo efeito fotoel\u00e9trico depende do aumento da frequ\u00eancia da luz (sua energia). Al\u00e9m disso, a energia da luz deveria ser maior do que a energia que mantinha a carga presa ao metal. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Isto deu a <a href=\"http:\/\/pt.wikipedia.org\/wiki\/Albert_Einstein\" target=\"_blank\" rel=\"noopener noreferrer\">Einstein<\/a> o Pr\u00eamio <a href=\"http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1921\/\" target=\"_blank\" rel=\"noopener noreferrer\">Nobel de F\u00edsica de 1921<\/a>.<\/span><\/p>\r\n<h3 id='bohr'  id=\"boomdevs_4\"><span style=\"font-family: verdana, geneva, sans-serif;\">Bohr<\/span><\/h3>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"><a href=\"http:\/\/pt.wikipedia.org\/wiki\/Niels_Bohr\" target=\"_blank\" rel=\"noopener noreferrer\">Bohr<\/a> deu um passo adicional na constru\u00e7\u00e3o da mec\u00e2nica qu\u00e2ntica em 1913 ao aplicar os conceitos de Planck no modelo at\u00f4mico de Rutherford e ganhou seu pr\u00eamio <a href=\"http:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/1922\/\" target=\"_blank\" rel=\"noopener noreferrer\">Nobel de F\u00edsica de 1922<\/a>.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Energia e momento consistem em conceitos b\u00e1sicos da f\u00edsica. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A f\u00edsica cl\u00e1ssica define o <a href=\"http:\/\/en.wikipedia.org\/wiki\/Momentum\" target=\"_blank\" rel=\"noopener noreferrer\">Momento Linear<\/a> &#8211; p &#8211; <span id='easy-footnote-1-1714' 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\/#easy-footnote-bottom-1-1714\" title=\" Equa\u00e7\u00e3o 2\"><sup>1<\/sup><\/a><\/span>como massa vezes a velocidade e o <a href=\"http:\/\/http:\/\/en.wikipedia.org\/wiki\/Angular_momentum\" target=\"_blank\" rel=\"noopener noreferrer\">Momento Angular<\/a>\u00a0 &#8211; L &#8211; <span id='easy-footnote-2-1714' 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\/#easy-footnote-bottom-2-1714\" title=\" Equa\u00e7\u00e3o 3\"><sup>2<\/sup><\/a><\/span>como o momento de in\u00e9rcia vezes a velocidade angular ou o produto vetorial da posi\u00e7\u00e3o pelo momento linear.<\/span><\/p>\r\n<figure id=\"attachment_1934\" aria-describedby=\"caption-attachment-1934\" style=\"width: 141px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/momento_p.png\"><img decoding=\"async\" class=\"wp-image-1934\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/momento_p.png\" alt=\"momento_p\" width=\"141\" height=\"41\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/momento_p.png 152w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/momento_p-150x44.png 150w\" sizes=\"(max-width: 141px) 100vw, 141px\" \/><\/a><figcaption id=\"caption-attachment-1934\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Equa\u00e7\u00e3o 2. momento linear<\/span><\/figcaption><\/figure>\r\n<figure id=\"attachment_1959\" aria-describedby=\"caption-attachment-1959\" style=\"width: 252px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/Momento_angular.png\"><img decoding=\"async\" class=\"wp-image-1959\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/Momento_angular.png\" alt=\"Momento_angular\" width=\"252\" height=\"41\" \/><\/a><figcaption id=\"caption-attachment-1959\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Equa\u00e7\u00e3o 3. momento angular<\/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;\"><em>p<\/em> \u00e9 o momento linear;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>m<\/em> \u00e9 a massa da part\u00edcula;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>v<\/em> \u00e9 a velocidade da part\u00edcula;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>L<\/em> \u00e9 o momento angular;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>I<\/em> \u00e9 o momento de in\u00e9rcia;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>\u03c9<\/em> \u00e9 a velocidade angular da part\u00edcula;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">r \u00e9 o vetor posi\u00e7\u00e3o<\/span>.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por outro lado, a Equa\u00e7\u00e3o 4 relaciona a energia cin\u00e9tica com o momento.<\/span><\/p>\r\n<figure id=\"attachment_1940\" aria-describedby=\"caption-attachment-1940\" style=\"width: 404px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/energia_c_2.png\"><img decoding=\"async\" class=\"wp-image-1940\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/energia_c_2.png\" alt=\"energia_c_2\" width=\"404\" height=\"77\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/energia_c_2.png 436w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/energia_c_2-300x57.png 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><\/a><figcaption id=\"caption-attachment-1940\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Equa\u00e7\u00e3o 4. Momento x Energia Cin\u00e9tica<\/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<sub>c<\/sub> \u00e9 a energia cin\u00e9tica;<\/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;\">m \u00e9 a massa;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">v \u00e9 a velocidade.<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Como energia e momento se encontram relacionados, Bohr aplicou a equa\u00e7\u00e3o de Planck ao momento angular. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Apenas as \u00f3rbitas com momento angular igual aos valores da equa\u00e7\u00e3o de Bohr seriam est\u00e1veis. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Este conceito representou o primeiro choque da mec\u00e2nica qu\u00e2ntica; <strong>a energia e o momento angular se tornaram grandezas discretas.<\/strong><\/span><\/p>\r\n<figure id=\"attachment_1950\" aria-describedby=\"caption-attachment-1950\" style=\"width: 461px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/bohr_1.png\"><img decoding=\"async\" class=\"wp-image-1950\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/bohr_1.png\" alt=\"equa\u00e7\u00e3o de Bohr\" width=\"461\" height=\"77\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/bohr_1.png 497w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/bohr_1-300x50.png 300w\" sizes=\"(max-width: 461px) 100vw, 461px\" \/><\/a><figcaption id=\"caption-attachment-1950\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Equa\u00e7\u00e3o 5. Equa\u00e7\u00e3o de Bohr<\/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;\">L \u00e9 o momento angular;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">n \u00e9 um n\u00famero inteiro maior que zero;<\/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;\">\u03c9 \u00e9 a velocidade angular;\u00a0<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A partir da Equa\u00e7\u00e3o 3 do Cap\u00edtulo <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/atomos\/\">\u00c1tomos<\/a>, que descreve a velocidade do el\u00e9tron do modelo de Rutherford, Bohr formulou as express\u00f5es abaixo, que fornecem a velocidade e o raio do el\u00e9tron do \u00e1tomo de hidrog\u00eanio.<\/span><\/p>\r\n<figure id=\"attachment_1963\" aria-describedby=\"caption-attachment-1963\" style=\"width: 278px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/velo_eletron.png\"><img decoding=\"async\" class=\"wp-image-1963 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/velo_eletron.png\" alt=\"velocidade do el\u00e9tron\" width=\"278\" height=\"94\" \/><\/a><figcaption id=\"caption-attachment-1963\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Equa\u00e7\u00e3o 6. Velocidade do El\u00e9tron<\/span><\/figcaption><\/figure>\r\n<figure id=\"attachment_1978\" aria-describedby=\"caption-attachment-1978\" style=\"width: 256px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/raio_bohr1.png\"><img decoding=\"async\" class=\"wp-image-1978 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/raio_bohr1.png\" alt=\"Raio de Bohr\" width=\"256\" height=\"99\" \/><\/a><figcaption id=\"caption-attachment-1978\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Equa\u00e7\u00e3o 7. Raio da \u00f3rbita dos El\u00e9trons<\/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;\">v<sub>e<\/sub> \u00e9 a velocidade do El\u00e9tron;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">q<sub>e<\/sub> \u00e9 a carga do El\u00e9tron;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b5<sub>0<\/sub> \u00e9 a permissividade el\u00e9trica no v\u00e1cuo;<\/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;\">m<sub>e<\/sub> \u00e9 a massa do El\u00e9tron;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">n \u00e9 um n\u00famero inteiro maior que zero.<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p>&nbsp;<\/p>\r\n<hr \/>\r\n<h6 id='exerc\u00edcio-proposto'  id=\"boomdevs_5\"><strong><span style=\"font-family: verdana, geneva, sans-serif;\">Exerc\u00edcio Proposto<\/span><\/strong><\/h6>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Calcule a velocidade do El\u00e9tron e seu raio para n=1 e compare com os resultados obtidos com a f\u00f3rmula do Cap\u00edtulo <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/atomos\/\">\u00c1tomos<\/a>\u00a0e com o raio te\u00f3rico do hidrog\u00eanio.<\/span><\/p>\r\n<hr \/>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A energia total do el\u00e9tron consiste na soma das suas energias cin\u00e9tica e potencial. A Equa\u00e7\u00e3o 4 fornece a energia cin\u00e9tica e a Equa\u00e7\u00e3o 8 a energia potencial eletrost\u00e1tica:<\/span><\/p>\r\n<figure id=\"attachment_1969\" aria-describedby=\"caption-attachment-1969\" style=\"width: 314px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/energia_potencial.png\"><img decoding=\"async\" class=\"wp-image-1969 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/energia_potencial.png\" alt=\"Energia Potencial Eletrost\u00e1tica\" width=\"314\" height=\"92\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/energia_potencial.png 314w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/02\/energia_potencial-300x88.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><\/a><figcaption id=\"caption-attachment-1969\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Equa\u00e7\u00e3o 8. Energia Potencial Eletrost\u00e1tica<\/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;\">q \u00e9 a carga el\u00e9trica;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">r \u00e9 a dist\u00e2ncia;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03b5<sub>0<\/sub> \u00e9 a permissividade el\u00e9trica no v\u00e1cuo;<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Desta maneira, a Equa\u00e7\u00e3o 9 fornece a energia total do el\u00e9tron.\u00a0<\/span><\/p>\r\n<figure id=\"attachment_44023\" aria-describedby=\"caption-attachment-44023\" style=\"width: 645px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-44023 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/04\/energia_total_2.png\" alt=\"\" width=\"645\" height=\"116\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/04\/energia_total_2.png 645w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/04\/energia_total_2-300x54.png 300w\" sizes=\"(max-width: 645px) 100vw, 645px\" \/><figcaption id=\"caption-attachment-44023\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 9. Energia total do el\u00e9tron<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">As equa\u00e7\u00f5es 10 e 11 apresentam a for\u00e7a de atra\u00e7\u00e3o eletrost\u00e1tica do proton e el\u00e9tron do \u00e1tomo de hidrog\u00eanio do <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/atomos\/\">modelo de Rutherford<\/a> e a for\u00e7a centr\u00edpeta.<\/span><\/p>\r\n<figure id=\"attachment_9295\" aria-describedby=\"caption-attachment-9295\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"size-medium wp-image-9295\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/forca_eletrica-300x98.png\" alt=\"\" width=\"300\" height=\"98\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/forca_eletrica-300x98.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/forca_eletrica.png 303w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-9295\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 10. For\u00e7a Eletrost\u00e1tica<\/figcaption><\/figure>\r\n<figure id=\"attachment_9296\" aria-describedby=\"caption-attachment-9296\" style=\"width: 242px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-9296 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/forca_centripeta.png\" alt=\"\" width=\"242\" height=\"92\" \/><figcaption id=\"caption-attachment-9296\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 11. For\u00e7a centr\u00edpeta<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">De acordo com Wolf<span id='easy-footnote-3-1714' 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\/#easy-footnote-bottom-3-1714\" title=\" p\u00e1gina 97\"><sup>3<\/sup><\/a><\/span>, Equa\u00e7\u00e3o 12 fornece o equil\u00edbrio entre for\u00e7a de atra\u00e7\u00e3o eletrost\u00e1tica e a for\u00e7a centr\u00edpeta.<\/span><\/p>\r\n<figure id=\"attachment_9310\" aria-describedby=\"caption-attachment-9310\" style=\"width: 411px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/rutheford_3.png\"><img decoding=\"async\" class=\"wp-image-9310 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/rutheford_3.png\" alt=\"\" width=\"411\" height=\"99\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/rutheford_3.png 411w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/rutheford_3-300x72.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><\/a><figcaption id=\"caption-attachment-9310\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 12. Equil\u00edbrio no modelo Rutheford<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Substituindo a Equa\u00e7\u00e3o 12 na Equa\u00e7\u00e3o 9, obt\u00eam-se que a energia total do el\u00e9tron equivale \u00e0 metade da energia potencial, conforme mostra a Equa\u00e7\u00e3o 13.<\/span><\/p>\r\n<figure id=\"attachment_9319\" aria-describedby=\"caption-attachment-9319\" style=\"width: 567px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/energia_total_1.png\"><img decoding=\"async\" class=\"wp-image-9319 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/energia_total_1.png\" alt=\"\" width=\"567\" height=\"112\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/energia_total_1.png 567w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/energia_total_1-300x59.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/a><figcaption id=\"caption-attachment-9319\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 13. Energia Total do Hidrog\u00eanio<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Al\u00e9m disso, a energia total possui sempre valores negativos, demonstrando a estabilidade do sistema, e <\/span><span style=\"font-family: verdana, geneva, sans-serif;\">\u00a0tende a zero quando o raio e n tendem para infinito. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A energia potencial negativa decorre da escolha da refer\u00eancia zero para dist\u00e2ncia infinita porque a for\u00e7a eletrost\u00e1tica diminui com a dist\u00e2ncia.<\/span>\u00a0<\/p>\r\n<hr \/>\r\n<h6 id='reflex\u00e3o'  id=\"boomdevs_6\"><span style=\"font-family: verdana, geneva, sans-serif;\">Reflex\u00e3o<\/span><\/h6>\r\n<p style=\"padding-left: 40px;\"><span style=\"font-family: verdana, geneva, sans-serif;\">Ser\u00e1 que isto explica o n\u00famero m\u00e1ximo de linhas na Tabela Peri\u00f3dica? <\/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;\">Calcule o valor desta energia para n=8.<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Calcule a diferen\u00e7a de energia dos n\u00edveis 7 e 8.<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Compare com a energia refletida pela terra a 25 \u00baC sobre a \u00e1rea deste \u00e1tomo.<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<hr \/>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Apesar do sucesso na \u00e9poca, o modelo de Bohr ainda apresentava lacunas, que ele contornou postulando as seguintes condi\u00e7\u00f5es:<\/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;\">As express\u00f5es somente valem para \u00f3rbitas discretas com determinados n\u00edveis de energia;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Nessas \u00f3rbitas n\u00e3o existe o fen\u00f4meno de emiss\u00e3o de radia\u00e7\u00e3o eletromagn\u00e9tica;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A mudan\u00e7a de \u00f3rbita do El\u00e9tron somente seria poss\u00edvel pela absor\u00e7\u00e3o ou emiss\u00e3o de energia em m\u00faltiplos inteiros de h x f.<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A partir desses postulados Bohr determinou o raio das \u00f3rbitas dos el\u00e9trons de acordo com a Equa\u00e7\u00e3o 14.<\/span><\/p>\r\n<figure id=\"attachment_9312\" aria-describedby=\"caption-attachment-9312\" style=\"width: 353px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/raio_bohr.png\"><img decoding=\"async\" class=\"size-full wp-image-9312\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/raio_bohr.png\" alt=\"\" width=\"353\" height=\"101\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/raio_bohr.png 353w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/raio_bohr-300x86.png 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/a><figcaption id=\"caption-attachment-9312\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 14. Raio das \u00f3rbitas dos el\u00e9trons<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Observem que esta express\u00e3o equivale \u00e0 Eq. 7 e a \u00fanica diferen\u00e7a consiste na utiliza\u00e7\u00e3o de h cortado no lugar de h.<\/span><\/p>\r\n<p><strong><span style=\"font-family: verdana, geneva, sans-serif;\">Denomina-se o n\u00famero n de n\u00famero qu\u00e2ntico principal.<\/span><\/strong><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">No caso de <strong>n=1<\/strong>, a Equa\u00e7\u00e3o 15 representa o valor do raio da \u00f3rbita do El\u00e9tron do Hidrog\u00eanio e se tornou conhecida como <strong>Raio de Bohr.<\/strong><\/span><\/p>\r\n<figure id=\"attachment_22436\" aria-describedby=\"caption-attachment-22436\" style=\"width: 512px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/raio_bohr_2.png\"><img decoding=\"async\" class=\"wp-image-22436 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/raio_bohr_2.png\" alt=\"\" width=\"512\" height=\"103\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/raio_bohr_2.png 512w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/raio_bohr_2-300x60.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/a><figcaption id=\"caption-attachment-22436\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 15. Raio de Bohr<\/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;\">\u03b1<sub>0<\/sub> \u00e9 o raio de Bohr<span id='easy-footnote-4-1714' 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\/#easy-footnote-bottom-4-1714\" title=\" 5,291 772 109 (80)x10&lt;sup&gt;-11&lt;\/sup&gt;[m] aproximadamente 53pm \"><sup>4<\/sup><\/a><\/span>;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">h cortado \u00e9 a constante de Planck dividida 2\u03c0;<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">m<sub>e<\/sub> \u00e9 a massa do El\u00e9tron;<\/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;\">\u03b1 \u00e9 a constante de estrutura fina<span id='easy-footnote-5-1714' 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\/#easy-footnote-bottom-5-1714\" title=\"equa\u00e7\u00e3o 6 em &lt;a href=&quot;https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/&quot;&gt;Estrutura da Mat\u00e9ria&lt;\/a&gt;\"><sup>5<\/sup><\/a><\/span>;<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A beleza da teoria de Bohr consiste em apresentar a primeira estimativa te\u00f3rica da dist\u00e2ncia entre o n\u00facleo e o el\u00e9tron do \u00e1tomo envolvendo apenas constantes f\u00edsicas.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Mas como comprovar que este c\u00e1lculo se encontra correto?\u00a0<\/span><\/p>\r\n<h3 id='bohr-na-pr\u00e1tica'  id=\"boomdevs_7\"><span style=\"font-family: verdana, geneva, sans-serif;\">Bohr na pr\u00e1tica<\/span><\/h3>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O Cap\u00edtulo <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/atomos\/\">\u00c1tomos<\/a> apresentou a Emiss\u00e3o At\u00f4mica e os resultados experimentais de Rydberg. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A constante de Rydberg obtida originalmente de forma experimental foi de 109 677,581 0 cm<sup>-1\u00a0<\/sup><span id='easy-footnote-6-1714' 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\/#easy-footnote-bottom-6-1714\" title=\"\u00a0 WOLF, pg.94,Eq. 8.2\"><sup>6<\/sup><\/a><\/span>.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Comparando a <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/atomos\/\">Equa\u00e7\u00e3o<\/a> 6 no Cap\u00edtulo \u00c1tomos com a Equa\u00e7\u00e3o 1 deste cap\u00edtulo, obtem-se que<span id='easy-footnote-7-1714' 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\/#easy-footnote-bottom-7-1714\" title=\" WOLF, pg 94 a 98\"><sup>7<\/sup><\/a><\/span>:<\/span><\/p>\r\n<figure id=\"attachment_9342\" aria-describedby=\"caption-attachment-9342\" style=\"width: 335px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/Rht.png\"><img decoding=\"async\" class=\"size-full wp-image-9342\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/Rht.png\" alt=\"\" width=\"335\" height=\"107\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/Rht.png 335w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/Rht-300x96.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><\/a><figcaption id=\"caption-attachment-9342\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 16. Constante de Rydberg te\u00f3rica<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A diferen\u00e7a entre o valor experimental e o te\u00f3rico \u00e9 de apenas 0,05%. <\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Portanto, a teoria de Bohr passou em seu primeiro teste pr\u00e1tico.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Substituindo a Equa\u00e7\u00e3o 16 na Equa\u00e7\u00e3o 15, a energia dos n\u00edveis do \u00e1tomo de Hidrog\u00eanio em fun\u00e7\u00e3o da constante de Rydberg ocorre da seguinte maneira:<\/span><\/p>\r\n<figure id=\"attachment_22510\" aria-describedby=\"caption-attachment-22510\" style=\"width: 301px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/Energia_Rydberg.png\"><img decoding=\"async\" class=\"wp-image-22510 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/Energia_Rydberg.png\" alt=\"\" width=\"301\" height=\"89\" \/><\/a><figcaption id=\"caption-attachment-22510\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 17. Energia de Bohr em fun\u00e7\u00e3o da constante de Rudberg<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Figura 15 mostra que os El\u00e9trons absorvem ou emitem energia ao mudarem de n\u00edvel de acordo com as equa\u00e7\u00f5es de Bohr. Uma das formas poss\u00edveis desta troca de energia ocorre atrav\u00e9s da absor\u00e7\u00e3o ou emiss\u00e3o de luz<span id='easy-footnote-8-1714' 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\/#easy-footnote-bottom-8-1714\" title=\" que s\u00e3o f\u00f3tons\"><sup>8<\/sup><\/a><\/span>, utilizada em LEDs e c\u00e9lulas fotovoltaicas.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Este fen\u00f4meno qu\u00e2ntico permitiu a constru\u00e7\u00e3o de todos os semicondutores respons\u00e1veis pela eletr\u00f4nica, telecomunica\u00e7\u00f5es e eletr\u00f4nica de pot\u00eancia modernos. Al\u00e9m disso, ele gerou outros Pr\u00eamios Nobel.<\/span><\/p>\r\n<p>&nbsp;<\/p>\r\n<figure id=\"attachment_22517\" aria-describedby=\"caption-attachment-22517\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/Bohr2.png\"><img decoding=\"async\" class=\"wp-image-22517 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/Bohr2.png\" alt=\"\" width=\"800\" height=\"600\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/Bohr2.png 800w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/Bohr2-300x225.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/Bohr2-768x576.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><figcaption id=\"caption-attachment-22517\" class=\"wp-caption-text\">Figura 15. Mudan\u00e7a de \u00f3rbita dos El\u00e9trons nos \u00c1tomos<\/figcaption><\/figure>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Conforme anteriormente, energia e momento angular se encontram relacionados. Portanto, o momento tamb\u00e9m se tornou uma grandeza qu\u00e2ntica.<\/span><\/p>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Infelizmente o modelo de Bohr n\u00e3o explica o comportamento dos outros \u00e1tomos com mais Pr\u00f3tons e El\u00e9trons, e, desta maneira, conclu\u00edmos<\/span><span style=\"font-family: verdana, geneva, sans-serif;\">\u00a0o estudo da &#8220;<em>velha teoria qu\u00e2ntica<\/em>&#8221; <span id='easy-footnote-9-1714' 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\/#easy-footnote-bottom-9-1714\" title=\"conforme definido por HAAR\"><sup>9<\/sup><\/a><\/span>. Talvez velha para os f\u00edsicos, mas moderna para os engenheiros.\u00a0<\/span><\/p>\r\n<hr \/>\r\n<h6 id='material-complementar'  id=\"boomdevs_8\"><span style=\"font-family: verdana, geneva, sans-serif;\">Material complementar<\/span><\/h6>\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;]e5_V78SWGF0[\/wpdevart_youtube]<\/p>\r\n<p>&nbsp;<\/p>\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;]FlIrgE5T_g0[\/wpdevart_youtube]<\/p>\r\n<hr \/>\r\n<p class=\"wp-block-group__inner-container\"><span style=\"font-family: verdana, geneva, sans-serif;\"><span style=\"font-size: 48px; font-weight: bold; letter-spacing: -0.0415625em;\">Refer\u00eancias<\/span><br \/><\/span><\/p>\r\n<ol>\r\n<li><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, 1905.<\/span><\/li>\r\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">HAAR, T., <strong>The Old Quantum Theory<\/strong>, Pergamon, 1967.<\/span><\/li>\r\n<li><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>, 2 edi\u00e7\u00e3o<strong>,\u00a0<\/strong>Springer-Verlag, 1987.<\/span><\/li>\r\n<li>Imagem de &lt;a href=&#8221;https:\/\/pixabay.com\/pt\/users\/geralt-9301\/?utm_source=link-attribution&amp;amp;utm_medium=referral&amp;amp;utm_campaign=image&amp;amp;utm_content=7854066&#8243;&gt;Gerd Altmann&lt;\/a&gt; por &lt;a href=&#8221;https:\/\/pixabay.com\/pt\/\/?utm_source=link-attribution&amp;amp;utm_medium=referral&amp;amp;utm_campaign=image&amp;amp;utm_content=7854066&#8243;&gt;Pixabay&lt;\/a&gt;<\/li>\r\n<li>Imagem de &lt;a href=&#8221;https:\/\/pixabay.com\/pt\/users\/geralt-9301\/?utm_source=link-attribution&amp;amp;utm_medium=referral&amp;amp;utm_campaign=image&amp;amp;utm_content=3871218&#8243;&gt;Gerd Altmann&lt;\/a&gt; por &lt;a href=&#8221;https:\/\/pixabay.com\/pt\/\/?utm_source=link-attribution&amp;amp;utm_medium=referral&amp;amp;utm_campaign=image&amp;amp;utm_content=3871218&#8243;&gt;Pixabay&lt;\/a&gt;<\/li>\r\n<li>Imagem de &lt;a href=&#8221;https:\/\/pixabay.com\/pt\/users\/inggwolf-283834\/?utm_source=link-attribution&amp;amp;utm_medium=referral&amp;amp;utm_campaign=image&amp;amp;utm_content=362944&#8243;&gt;Guido Wolf&lt;\/a&gt; por &lt;a href=&#8221;https:\/\/pixabay.com\/pt\/\/?utm_source=link-attribution&amp;amp;utm_medium=referral&amp;amp;utm_campaign=image&amp;amp;utm_content=362944&#8243;&gt;Pixabay&lt;\/a&gt;<\/li>\r\n<\/ol>\r\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">\r\n\r\n\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; forced-color-adjust: 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-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; border-start-start-radius: 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: 0px; 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; 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-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; 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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; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; 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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; forced-color-adjust: 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-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; border-start-start-radius: 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: 0px; 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; forced-color-adjust: 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-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; border-start-start-radius: 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: 0px; 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; forced-color-adjust: 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-end-end-radius: initial; border-end-start-radius: initial; 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-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; forced-color-adjust: 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-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; border-start-start-radius: initial; inset: initial; box-shadow: initial; box-sizing: initial; 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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; forced-color-adjust: 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-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; border-start-start-radius: 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: 0px; 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; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; 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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: 0px; 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; forced-color-adjust: 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; 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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: 0px; 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; 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-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; 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Portanto, ela se tornou a base te\u00f3rica para o estudo dos materiais, principalmente os el\u00e9tricos e magn\u00e9ticos. 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