{"id":18075,"date":"2020-06-26T18:23:21","date_gmt":"2020-06-26T18:23:21","guid":{"rendered":"https:\/\/www.radiation-dosimetry.org\/o-que-e-equilibrio-radioativo-definicao\/"},"modified":"2020-07-24T05:42:17","modified_gmt":"2020-07-24T05:42:17","slug":"o-que-e-equilibrio-radioativo-definicao","status":"publish","type":"post","link":"http:\/\/www.radiation-dosimetry.org\/pt-br\/o-que-e-equilibrio-radioativo-definicao\/","title":{"rendered":"O que \u00e9 Equil\u00edbrio Radioativo &#8211; Defini\u00e7\u00e3o"},"content":{"rendered":"<div class=\"su-quote su-quote-style-default\">\n<div class=\"su-quote-inner su-u-clearfix su-u-trim\">Na f\u00edsica dos decaimentos nucleares, existe um equil\u00edbrio radioativo quando um nucl\u00eddeo radioativo est\u00e1 decaindo na mesma taxa em que est\u00e1 sendo produzido.\u00a0O equil\u00edbrio radioativo n\u00e3o \u00e9 estabelecido imediatamente, mas s\u00f3 ocorre ap\u00f3s um per\u00edodo de transi\u00e7\u00e3o.\u00a0Dosimetria de Radia\u00e7\u00e3o<\/div>\n<\/div>\n<div class=\"su-divider su-divider-style-dotted\"><\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<p>Na f\u00edsica dos\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/radiation-protection\/radioactivity-nuclear-decay\/\"><strong>decaimentos nucleares<\/strong><\/a>\u00a0,\u00a0existe\u00a0um\u00a0<strong>equil\u00edbrio radioativo<\/strong>\u00a0quando um nucl\u00eddeo radioativo est\u00e1 decaindo na mesma taxa em que est\u00e1 sendo produzido.\u00a0O n\u00facleo de desintegra\u00e7\u00e3o \u00e9 geralmente chamado de\u00a0<strong>n\u00facleo pai<\/strong>\u00a0e o n\u00facleo remanescente ap\u00f3s o evento como\u00a0<strong>n\u00facleo filha<\/strong>\u00a0.\u00a0O n\u00facleo da filha pode ser est\u00e1vel ou radioativo.\u00a0Se for radioativo, decai em um n\u00facleo filha e assim por diante.\u00a0Assim, cada n\u00facleo progenitor radioativo pode iniciar uma s\u00e9rie de decaimentos, com cada produto de decaimento tendo sua pr\u00f3pria caracter\u00edstica constante de decaimento.<\/p>\n<p>A concentra\u00e7\u00e3o dos n\u00facleos filha no equil\u00edbrio radioativo depende principalmente das propor\u00e7\u00f5es de\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radioactive-decay\/radioactive-decay-law\/half-life\/\">meia-vida<\/a>\u00a0(ou\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radioactive-decay\/radioactive-decay-law\/decay-constant\/\">constantes de decaimento<\/a>\u00a0) dos n\u00facleos pai e filha.\u00a0Como a taxa de produ\u00e7\u00e3o e a taxa de decaimento s\u00e3o iguais, o n\u00famero de \u00e1tomos presentes permanece constante ao longo do tempo.\u00a0De qualquer forma, um equil\u00edbrio radioativo n\u00e3o \u00e9 estabelecido imediatamente, mas s\u00f3 ocorre ap\u00f3s um\u00a0<strong>per\u00edodo de transi\u00e7\u00e3o<\/strong>\u00a0.\u00a0Esse per\u00edodo \u00e9 da ordem de poucas meias-vidas do n\u00facleo de maior dura\u00e7\u00e3o na cadeia de decaimento.\u00a0No caso de cadeias de decaimento radioativo, um equil\u00edbrio radioativo pode ser estabelecido entre cada membro da cadeia de decaimento.<\/p>\n<p><a href=\"http:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/radioactive-equilibrium-equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-25266 lazy-loaded\" src=\"http:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/radioactive-equilibrium-equation.png\" alt=\"equil\u00edbrio radioativo - equa\u00e7\u00e3o\" width=\"170\" height=\"97\" data-lazy-type=\"image\" data-src=\"http:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/radioactive-equilibrium-equation.png\" \/><\/a><\/p>\n<p>Como foi escrito, a proporcionalidade das meias-vidas \u00e9 um par\u00e2metro-chave, que determina o\u00a0<strong>tipo de equil\u00edbrio radioativo<\/strong>\u00a0:<\/p>\n<ul>\n<li>O equil\u00edbrio radioativo n\u00e3o \u00e9 estabelecido quando a meia-vida do n\u00facleo pai \u00e9 menor que a meia-vida do n\u00facleo filha.\u00a0Nesse caso, a taxa de produ\u00e7\u00e3o e a taxa de decaimento de determinado membro da cadeia de decaimento n\u00e3o podem ser iguais.<\/li>\n<li><strong>O equil\u00edbrio radioativo secular<\/strong>\u00a0existe quando o n\u00facleo pai tem uma meia-vida extremamente longa.\u00a0Esse tipo de equil\u00edbrio \u00e9 particularmente importante por natureza.\u00a0Ao longo dos 4,5 bilh\u00f5es de anos da hist\u00f3ria da Terra, especialmente o ur\u00e2nio 238, o ur\u00e2nio 235 e o t\u00f3rio 232 e os membros de suas cadeias de decaimento atingiram equil\u00edbrios radioativos entre o n\u00facleo pai e os v\u00e1rios descendentes.<\/li>\n<li>Existe um\u00a0<strong>equil\u00edbrio radioativo transit\u00f3rio<\/strong>\u00a0quando a meia-vida do n\u00facleo pai \u00e9 maior que a meia-vida do n\u00facleo filha.\u00a0Nesse caso, o nucl\u00eddeo pai e o nucl\u00eddeo filha decaem essencialmente na mesma taxa.<\/li>\n<\/ul>\n<h2>Equil\u00edbrio Secular<\/h2>\n<p><strong>O equil\u00edbrio radioativo secular<\/strong>\u00a0existe quando o n\u00facleo pai tem uma\u00a0<strong>meia-vida extremamente longa<\/strong>\u00a0.\u00a0<strong>O equil\u00edbrio secular<\/strong>\u00a0\u00e9 t\u00edpico para\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radioactive-decay\/radioactive-decay-chain\/radioactive-series-radioactive-cascade\/\"><strong>s\u00e9ries radioativas naturais<\/strong><\/a>\u00a0, como as\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radioactive-decay\/radioactive-decay-chain\/radioactive-series-radioactive-cascade\/thorium-series\/\">s\u00e9ries de t\u00f3rio<\/a>\u00a0\u00a0ou de\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radioactive-decay\/radioactive-decay-chain\/radioactive-series-radioactive-cascade\/uranium-series\/\">ur\u00e2nio<\/a>\u00a0.\u00a0Para a s\u00e9rie de ur\u00e2nio com ur\u00e2nio-238 (com uma meia-vida de 4,47 bilh\u00f5es de anos), onde todos os elementos da cadeia est\u00e3o em\u00a0<strong>equil\u00edbrio secular<\/strong>\u00a0, cada um dos descendentes acumulou uma quantidade de equil\u00edbrio e todos deca\u00edram \u00e0 taxa definido pelo pai original.\u00a0A \u00fanica exce\u00e7\u00e3o \u00e9 o elemento est\u00e1vel final (chumbo-206) no final da cadeia.\u00a0Seu n\u00famero de \u00e1tomos est\u00e1 aumentando constantemente.\u00a0Em qualquer caso, um\u00a0<strong>equil\u00edbrio radioativo<\/strong>n\u00e3o \u00e9 estabelecido imediatamente, mas s\u00f3 ocorre ap\u00f3s um\u00a0<strong>per\u00edodo de transi\u00e7\u00e3o<\/strong>\u00a0.\u00a0Esse per\u00edodo \u00e9 da ordem de poucas meias-vidas do n\u00facleo de vida mais longa da cadeia de decaimento (\u00a0<strong><sup>234<\/sup>\u00a0U<\/strong>\u00a0para a\u00a0<strong>s\u00e9rie de ur\u00e2nio<\/strong>\u00a0;\u00a0<sup>231<\/sup>\u00a0Pa para a s\u00e9rie de actinium).\u00a0No caso de cadeias de decaimento radioativo, um equil\u00edbrio radioativo pode ser estabelecido entre cada membro da cadeia de decaimento.<\/p>\n<p><a href=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/Secular-Equilibrium-Radioactive-Equilibrium.png\"><img loading=\"lazy\" class=\"aligncenter size-large wp-image-25270 lazy-loaded\" src=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/Secular-Equilibrium-Radioactive-Equilibrium-1024x590.png\" alt=\"Equil\u00edbrio Secular\" width=\"1024\" height=\"590\" data-lazy-type=\"image\" data-src=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/Secular-Equilibrium-Radioactive-Equilibrium-1024x590.png\" \/><\/a><\/p>\n<p>Como pode ser visto, o\u00a0<strong>equil\u00edbrio secular<\/strong>\u00a0\u00e9 particularmente importante por natureza.\u00a0Ao longo dos 4,5 bilh\u00f5es de anos da hist\u00f3ria da Terra, especialmente o ur\u00e2nio 238, o ur\u00e2nio 235 e o t\u00f3rio 232 e os membros de suas cadeias de decaimento atingiram\u00a0<strong>equil\u00edbrios radioativos<\/strong>entre o n\u00facleo pai e os v\u00e1rios descendentes.\u00a0As meias-vidas de todos os seus descendentes s\u00e3o extremamente vari\u00e1veis \u200b\u200be \u00e9 dif\u00edcil representar uma escala de tempo que varia de segundos a milh\u00f5es de anos.\u00a0Como os radiois\u00f3topos-filhas t\u00eam meias-vidas diferentes, o equil\u00edbrio secular \u00e9 alcan\u00e7ado ap\u00f3s algum tempo.\u00a0Na longa cadeia de decaimento de um elemento naturalmente radioativo, como o ur\u00e2nio-238, onde todos os elementos da cadeia est\u00e3o em equil\u00edbrio secular, cada um dos descendentes acumulou uma quantidade de equil\u00edbrio e todos decaiu na taxa definida pelo pai original.\u00a0Se e quando o equil\u00edbrio for alcan\u00e7ado, cada is\u00f3topo filha sucessivo estar\u00e1 presente em propor\u00e7\u00e3o direta \u00e0 sua meia-vida (ou \u00e0 sua constante de decaimento).<\/p>\n<p><a href=\"http:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/radioactive-equilibrium-equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-25266 lazy-loaded\" src=\"http:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/radioactive-equilibrium-equation.png\" alt=\"equil\u00edbrio radioativo - equa\u00e7\u00e3o\" width=\"170\" height=\"97\" data-lazy-type=\"image\" data-src=\"http:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/radioactive-equilibrium-equation.png\" \/><\/a><\/p>\n<p>Como sua\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/radiation-protection\/radioactivity-nuclear-decay\/\">atividade<\/a>\u00a0\u00e9 inversamente proporcional \u00e0 sua\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radioactive-decay\/radioactive-decay-law\/half-life\/\">meia-vida<\/a>\u00a0, cada nucl\u00eddeo na cadeia de decaimento finalmente contribui com tantas transforma\u00e7\u00f5es individuais quanto a cabe\u00e7a da cadeia.\u00a0<strong>A cascata radioativa<\/strong>\u00a0no equil\u00edbrio secular influencia significativamente a radioatividade (\u00a0<strong>desintegra\u00e7\u00f5es por segundo<\/strong>\u00a0) de amostras e materiais naturais.\u00a0Todos os descendentes est\u00e3o presentes, pelo menos temporariamente, em qualquer amostra natural, seja de metal, composto ou mineral.\u00a0Por exemplo,\u00a0<strong>o ur\u00e2nio puro-238<\/strong>\u00a0\u00e9\u00a0<strong>fracamente radioativo<\/strong>\u00a0(proporcional \u00e0 sua meia-vida longa), mas um\u00a0<strong>min\u00e9rio de ur\u00e2nio<\/strong>\u00a0\u00e9 cerca de\u00a0<strong>13 vezes mais radioativo<\/strong>\u00a0(aproximadamente 13 descendentes na cadeia de decaimento) do que o metal puro ur\u00e2nio-238 por causa de seus is\u00f3topos filhos (por exemplo, r\u00e1don, r\u00e1dio etc.) que ele cont\u00e9m.\u00a0Os is\u00f3topos de r\u00e1dio inst\u00e1veis \u200b\u200bn\u00e3o s\u00e3o apenas emissores significativos de radioatividade, mas, como est\u00e1gio seguinte da cadeia de decaimento, eles tamb\u00e9m geram rad\u00f4nio, um g\u00e1s radioativo pesado, inerte e de ocorr\u00eancia natural.\u00a0Al\u00e9m disso, o calor em decomposi\u00e7\u00e3o do ur\u00e2nio e seus produtos (como o r\u00e1don, o r\u00e1dio, etc.) contribuem para o aquecimento do n\u00facleo da Terra.\u00a0Juntamente com o t\u00f3rio e o pot\u00e1ssio-40 no manto da Terra, acredita-se que esses elementos sejam a principal fonte de calor que mant\u00e9m o l\u00edquido do n\u00facleo da Terra.<\/p>\n<p>O\u00a0<strong>equil\u00edbrio secular<\/strong>\u00a0pode ocasionalmente ser interrompido quando um dos n\u00facleos intermedi\u00e1rios deixa a amostra (por exemplo, o rad\u00f4nio liberado do solo) onde seus ancestrais est\u00e3o confinados.\u00a0\u00c9 importante considerar essas interrup\u00e7\u00f5es locais no uso de t\u00e9cnicas de namoro.\u00a0A interrup\u00e7\u00e3o do equil\u00edbrio secular tamb\u00e9m influencia a radioatividade do combust\u00edvel nuclear novo.\u00a0A maioria dos PWRs usa o\u00a0<strong>combust\u00edvel de ur\u00e2nio<\/strong>\u00a0, que est\u00e1 na forma de\u00a0<strong>di\u00f3xido<\/strong>\u00a0de\u00a0<strong>ur\u00e2nio<\/strong>\u00a0.\u00a0Mas esse di\u00f3xido de ur\u00e2nio deve ser quimicamente purificado e a maior parte de sua cadeia de decomposi\u00e7\u00e3o n\u00e3o est\u00e1 presente no combust\u00edvel nuclear novo.<\/p>\n<h3>Equil\u00edbrio radioativo de ur\u00e2nio-234<\/h3>\n<p><span>O is\u00f3topo de ur\u00e2nio-234 \u00e9 um membro da s\u00e9rie de ur\u00e2nio.\u00a0Esse is\u00f3topo tem meia-vida de apenas 2,46 x 10\u00a0<\/span><sup><span>5<\/span><\/sup><span>\u00a0anos e, portanto, n\u00e3o pertence a\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/glossary\/primordial-matter\/\"><span>nucl\u00eddeos primordiais<\/span><\/a><span>\u00a0(ao contr\u00e1rio de\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\"><sup><span>235<\/span><\/sup><span>\u00a0U<\/span><\/a><span>\u00a0e\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\"><sup><span>238<\/span><\/sup><span>\u00a0U<\/span><\/a><span>\u00a0).\u00a0Por outro lado, este is\u00f3topo ainda est\u00e1 presente na crosta terrestre, mas isso \u00e9 devido ao fato de\u00a0<\/span><sup><span>234<\/span><\/sup><span>\u00a0U \u00e9 um\u00a0<\/span><strong><span>produto de decaimento indireta de\u00a0<\/span><\/strong><strong><sup><span>238<\/span><\/sup><\/strong><strong><span>\u00a0U<\/span><\/strong><span>\u00a0.\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\"><sup><span>238<\/span><\/sup><span>\u00a0U<\/span><\/a><span>\u00a0decai por\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/alpha-particle\/\"><span>decaimento alfa<\/span><\/a><span>\u00a0em\u00a0<\/span><sup><span>234<\/span><\/sup><span>\u00a0U.\u00a0<\/span><sup><span>234<\/span><\/sup><span>\u00a0U decai por decaimento alfa em 230Th, exceto fra\u00e7\u00e3o muito pequena (da ordem de ppm) de n\u00facleos que decai por\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radioactive-decay\/spontaneous-fission\/\"><span>fiss\u00e3o espont\u00e2nea<\/span><\/a><span>.<\/span><\/p>\n<p><span>Em uma amostra natural de ur\u00e2nio, esses n\u00facleos est\u00e3o presentes nas propor\u00e7\u00f5es inalter\u00e1veis \u200b\u200bdo\u00a0<\/span><strong><span>equil\u00edbrio radioativo<\/span><\/strong><span>\u00a0da\u00a0filia\u00e7\u00e3o de\u00a0<\/span><sup><span>238<\/span><\/sup><span>\u00a0U na propor\u00e7\u00e3o de um \u00e1tomo de\u00a0<\/span><sup><span>234<\/span><\/sup><span>\u00a0U para cerca de 18 500 n\u00facleos de\u00a0<\/span><sup><span>238<\/span><\/sup><span>\u00a0U. Como resultado desse equil\u00edbrio, esses dois os is\u00f3topos (\u00a0<\/span><sup><span>238<\/span><\/sup><span>\u00a0U e\u00a0<\/span><sup><span>234<\/span><\/sup><span>\u00a0U) contribuem igualmente para a radioatividade do ur\u00e2nio natural.<\/span><\/p>\n<h2><span>Equil\u00edbrio Radioativo Transit\u00f3rio<\/span><\/h2>\n<p><span>O\u00a0<\/span><strong><span>equil\u00edbrio radioativo transit\u00f3rio<\/span><\/strong><span>\u00a0existe quando a meia-vida do n\u00facleo pai \u00e9 maior que a meia-vida do n\u00facleo filha, mas a concentra\u00e7\u00e3o do n\u00facleo pai diminui significativamente no tempo.\u00a0Nesse caso, o nucl\u00eddeo pai e o nucl\u00eddeo filha podem decair essencialmente na mesma taxa, mas ambas as concentra\u00e7\u00f5es de nucl\u00eddeos diminuem \u00e0 medida que a concentra\u00e7\u00e3o dos n\u00facleos pais diminui.\u00a0Ao contr\u00e1rio do equil\u00edbrio secular, a meia-vida dos n\u00facleos-filha n\u00e3o \u00e9 desprez\u00edvel em compara\u00e7\u00e3o com a meia-vida dos pais.<\/span><\/p>\n<p><a href=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/Transient-Equilibrium-Radioactive-Equilibrium.png\"><img loading=\"lazy\" class=\"aligncenter size-large wp-image-25269 lazy-loaded\" src=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/Transient-Equilibrium-Radioactive-Equilibrium-1024x606.png\" alt=\"Equil\u00edbrio transit\u00f3rio - Equil\u00edbrio radioativo\" width=\"1024\" height=\"606\" data-lazy-type=\"image\" data-src=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/Transient-Equilibrium-Radioactive-Equilibrium-1024x606.png\" \/><\/a><\/p>\n<p><span>Um exemplo desse tipo de processo de decomposi\u00e7\u00e3o de composto \u00e9 um gerador de tecn\u00e9cio-99m que produz tecn\u00e9cio-99m para procedimentos de diagn\u00f3stico de medicina nuclear a partir do molibd\u00eanio-99.\u00a0A curta meia-vida de 6 horas do Technetium-99m torna imposs\u00edvel o armazenamento e tornaria o transporte muito caro.\u00a0Portanto, para fins m\u00e9dicos, o molibd\u00eanio-99 \u00e9 usado para produzir tecn\u00e9cio-99m.\u00a0Esses dois is\u00f3topos est\u00e3o em\u00a0<\/span><strong><span>equil\u00edbrio transit\u00f3rio<\/span><\/strong><span>.\u00a0A constante de decaimento para o molibd\u00eanio-99 \u00e9 consideravelmente menor que a constante de decaimento para o tecn\u00e9cio-99m.\u00a0Embora a constante de decaimento para o molibd\u00eanio-99 seja menor, a taxa real de decaimento \u00e9 inicialmente maior que a do molibd\u00eanio-99 devido \u00e0 grande diferen\u00e7a em suas concentra\u00e7\u00f5es iniciais.\u00a0\u00c0 medida que a concentra\u00e7\u00e3o da filha aumenta, a taxa de decaimento da filha se aproxima e, eventualmente, corresponde \u00e0 taxa de decaimento do pai.\u00a0Quando isso ocorre, \u00e9 dito que eles est\u00e3o em\u00a0\u00a0<\/span><strong><span>equil\u00edbrio transit\u00f3rio<\/span><\/strong><span>\u00a0.\u00a0No caso do gerador Technetium-99m, o equil\u00edbrio transit\u00f3rio ocorre ap\u00f3s cerca de quatro meias-vidas.\u00a0Hoje, o tecn\u00e9cio-99m \u00e9 o elemento mais utilizado na medicina nuclear e \u00e9 empregado em uma ampla variedade de estudos de imagem de medicina nuclear.<\/span><\/p>\n<p><span>Al\u00e9m disso, o equil\u00edbrio transit\u00f3rio pode ocasionalmente ser interrompido quando um dos n\u00facleos intermedi\u00e1rios deixa a amostra onde seus ancestrais est\u00e3o confinados.<\/span><\/p>\n<p><strong><span>Equil\u00edbrio radioativo transit\u00f3rio com fonte &#8211; exemplo<\/span><\/strong><\/p>\n<p><span>Um exemplo especial de equil\u00edbrio radioativo s\u00e3o as concentra\u00e7\u00f5es de iodo-135 e\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/nuclear-power\/reactor-physics\/reactor-operation\/xenon-135\/\"><span>xenon-135<\/span><\/a><span>\u00a0em um\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/nuclear-power-plant\/nuclear-reactor\/\"><span>reator nuclear<\/span><\/a><span>\u00a0, mas, neste caso, a queima do xen\u00f4nio deve ser levada em considera\u00e7\u00e3o.\u00a0Observe que, nesse caso especial, a meia-vida do n\u00facleo pai \u00e9 menor que a meia-vida do n\u00facleo filha.\u00a0A produ\u00e7\u00e3o e remo\u00e7\u00e3o de xen\u00f4nio pode ser caracterizada pelas seguintes\u00a0<\/span><strong><span>equa\u00e7\u00f5es diferenciais<\/span><\/strong><span>\u00a0:<\/span><\/p>\n<p><a href=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/xenon-135-iodine-135-equations.png\"><img loading=\"lazy\" class=\"aligncenter size-large wp-image-18622 lazy-loaded\" src=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/xenon-135-iodine-135-equations-1024x470.png\" alt=\"\" width=\"1024\" height=\"470\" data-lazy-type=\"image\" data-src=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/xenon-135-iodine-135-equations-1024x470.png\" \/><\/a><\/p>\n<p><a href=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/xenon-equilibrium-iodine-equilibrium.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-18613 lazy-loaded\" src=\"http:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/calculation-effective-dose-uniform-300x117.png\" alt=\"equil\u00edbrio de xen\u00f4nio - equil\u00edbrio de iodo\" width=\"300\" height=\"237\" data-lazy-type=\"image\" data-src=\"http:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/calculation-effective-dose-uniform-300x117.png\" \/><\/a><span>Quando a\u00a0<\/span><strong><span>taxa de produ\u00e7\u00e3o<\/span><\/strong><span>\u00a0de iodo \u00e9 igual \u00e0\u00a0<\/span><strong><span>taxa de remo\u00e7\u00e3o<\/span><\/strong><span>\u00a0de iodo,\u00a0existe\u00a0<\/span><strong><span>equil\u00edbrio<\/span><\/strong><span>\u00a0.\u00a0Esse equil\u00edbrio tamb\u00e9m \u00e9 conhecido como &#8220;reservat\u00f3rio de xen\u00f4nio 135&#8221;, pois todo esse iodo deve sofrer uma deteriora\u00e7\u00e3o do xen\u00f4nio.\u00a0Em equil\u00edbrio, a concentra\u00e7\u00e3o de iodo permanece constante e \u00e9 designada\u00a0<\/span><strong><span>N\u00a0<\/span><\/strong><strong><sub><span>I<\/span><\/sub><\/strong><strong><span>\u00a0(eq)<\/span><\/strong><span>\u00a0.\u00a0A equa\u00e7\u00e3o a seguir para a concentra\u00e7\u00e3o de equil\u00edbrio de iodo pode ser determinada a partir da equa\u00e7\u00e3o anterior definindo\u00a0<\/span><strong><span>dN\u00a0<\/span><\/strong><strong><sub><span>I<\/span><\/sub><\/strong><strong><span>\u00a0\/ dt = 0<\/span><\/strong><span>\u00a0.\u00a0Como a concentra\u00e7\u00e3o de iodo de equil\u00edbrio \u00e9 proporcional \u00e0 taxa de rea\u00e7\u00e3o de fiss\u00e3o, tamb\u00e9m \u00e9 proporcional ao\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/reactor-thermal-power\/\"><strong><span>n\u00edvel de pot\u00eancia do reator<\/span><\/strong><\/a><span>\u00a0.<\/span><\/p>\n<p><span>Quando a\u00a0<\/span><strong><span>taxa de produ\u00e7\u00e3o<\/span><\/strong><span>\u00a0do xen\u00f4nio 135 \u00e9 igual \u00e0\u00a0<\/span><strong><span>taxa de remo\u00e7\u00e3o<\/span><\/strong><span>\u00a0, o\u00a0<\/span><strong><span>equil\u00edbrio<\/span><\/strong><span>\u00a0existe tamb\u00e9m para o\u00a0<\/span><strong><span>x\u00eanon<\/span><\/strong><span>\u00a0.\u00a0A concentra\u00e7\u00e3o de xen\u00f4nio permanece constante e \u00e9 designada\u00a0<\/span><strong><span>N\u00a0<\/span><\/strong><strong><sub><span>Xe<\/span><\/sub><\/strong><strong><span>\u00a0(eq)<\/span><\/strong><span>\u00a0.\u00a0A seguinte equa\u00e7\u00e3o (1) para a concentra\u00e7\u00e3o de equil\u00edbrio de xen\u00f4nio pode ser determinada a partir da equa\u00e7\u00e3o anterior, definindo\u00a0<\/span><strong><span>dN\u00a0<\/span><\/strong><strong><sub><span>Xe<\/span><\/sub><\/strong><strong><span>\u00a0\/ dt = 0<\/span><\/strong><span>\u00a0.\u00a0Para que o xen\u00f4nio 135 esteja em equil\u00edbrio, o iodo 135 tamb\u00e9m deve estar em equil\u00edbrio.\u00a0Substituindo a express\u00e3o pela concentra\u00e7\u00e3o de iodo de equil\u00edbrio 135 na equa\u00e7\u00e3o para o xen\u00f4nio de equil\u00edbrio (1), resulta o seguinte (2).<\/span><\/p>\n<p><a href=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/Xenon-Worth-different-power-levels.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-18613 lazy-loaded\" src=\"http:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/calculation-effective-dose-uniform-300x117.png\" alt=\"Xenon Worth - diferentes n\u00edveis de pot\u00eancia\" width=\"300\" height=\"259\" data-lazy-type=\"image\" data-src=\"http:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/calculation-effective-dose-uniform-300x117.png\" \/><\/a><span>A partir desta equa\u00e7\u00e3o, pode-se observar que o valor de equil\u00edbrio do\u00a0<\/span><strong><span>xen\u00f4nio 135<\/span><\/strong><span>\u00a0aumenta \u00e0 medida que a pot\u00eancia aumenta, porque o numerador \u00e9 proporcional \u00e0\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/reaction-rate\/\"><span>taxa de rea\u00e7\u00e3o de fiss\u00e3o<\/span><\/a><span>\u00a0.\u00a0Mas o fluxo t\u00e9rmico tamb\u00e9m est\u00e1 no denominador.\u00a0Portanto, como o fluxo t\u00e9rmico excede algum valor, a\u00a0<\/span><strong><span>queima de xen\u00f4nio<\/span><\/strong><span>\u00a0come\u00e7a a dominar e, a aproximadamente 10\u00a0<\/span><sup><span>15<\/span><\/sup><span>\u00a0n\u00eautrons.cm\u00a0<\/span><sup><span>-2<\/span><\/sup><span>\u00a0.s\u00a0<\/span><sup><span>-1<\/span><\/sup><span>\u00a0, a concentra\u00e7\u00e3o de xen\u00f4nio-135 se aproxima de um valor limite.\u00a0As concentra\u00e7\u00f5es de iodo de equil\u00edbrio 135 e xen\u00f4nio 135 em fun\u00e7\u00e3o do fluxo de n\u00eautrons s\u00e3o ilustradas na figura a seguir.<\/span><\/p>\n<h2><span>Equa\u00e7\u00f5es de Bateman<\/span><\/h2>\n<p><span>Na f\u00edsica, as\u00a0<\/span><strong><span>equa\u00e7\u00f5es de Bateman<\/span><\/strong><span>\u00a0s\u00e3o um conjunto de equa\u00e7\u00f5es diferenciais de primeira ordem, que descrevem a evolu\u00e7\u00e3o no tempo das concentra\u00e7\u00f5es de nucl\u00eddeos em cadeia de decaimento serial ou linear.\u00a0O modelo foi formulado por Ernest Rutherford em 1905 e a solu\u00e7\u00e3o anal\u00edtica para o caso de decaimento radioativo em uma cadeia linear foi fornecida por Harry Bateman em 1910. Este modelo tamb\u00e9m pode ser usado em c\u00f3digos de deple\u00e7\u00e3o nuclear para resolver problemas de transmuta\u00e7\u00e3o e decaimento nuclear.<\/span><\/p>\n<p><span>Por exemplo, o ORIGEN \u00e9 um sistema de c\u00f3digo de computador para calcular o ac\u00famulo, deteriora\u00e7\u00e3o e processamento de materiais radioativos.\u00a0O ORIGEN usa um m\u00e9todo exponencial de matriz para resolver um grande sistema de equa\u00e7\u00f5es diferenciais ordin\u00e1rias lineares de primeira ordem acopladas (semelhantes \u00e0s\u00a0<\/span><strong><span>equa\u00e7\u00f5es de Bateman<\/span><\/strong><span>\u00a0) com coeficientes constantes.<\/span><\/p>\n<p><span>As\u00a0<\/span><strong><span>equa\u00e7\u00f5es de Bateman<\/span><\/strong><span>\u00a0para o caso de decaimento radioativo da s\u00e9rie n &#8211; nucl\u00eddeo em cadeia linear que descreve as concentra\u00e7\u00f5es de nucl\u00eddeo s\u00e3o as seguintes:<\/span><\/p>\n<p><a href=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/Bateman-Equations-definition.png\"><img loading=\"lazy\" class=\"aligncenter size-large wp-image-25271 lazy-loaded\" src=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/Bateman-Equations-definition-1024x597.png\" alt=\"Equa\u00e7\u00f5es de Bateman\" width=\"1024\" height=\"597\" data-lazy-type=\"image\" data-src=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/Bateman-Equations-definition-1024x597.png\" \/><\/a><\/p>\n<p><strong><span>Equa\u00e7\u00f5es de Bateman para Transmuta\u00e7\u00e3o Nuclear<\/span><\/strong><\/p>\n<figure id=\"attachment_18460\" class=\"wp-caption alignright\" aria-describedby=\"caption-attachment-18460\"><a href=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/Fuel-Depletion-Isotopic-Changes.png\"><img loading=\"lazy\" class=\"size-medium wp-image-18459 lazy-loaded\" src=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/Fuel-Depletion-Isotopic-Changes-300x226.png\" alt=\"Deple\u00e7\u00e3o de combust\u00edvel - altera\u00e7\u00f5es isot\u00f3picas\" width=\"300\" height=\"226\" data-lazy-type=\"image\" data-src=\"https:\/\/www.radiation-dosimetry.org\/wp-content\/uploads\/2019\/12\/Fuel-Depletion-Isotopic-Changes-300x226.png\" \/><\/a><figcaption id=\"caption-attachment-18460\" class=\"wp-caption-text\"><span>Altera\u00e7\u00f5es isot\u00f3picas de 4% de combust\u00edvel de ur\u00e2nio-235 em fun\u00e7\u00e3o da queima de combust\u00edvel.<\/span><\/figcaption><\/figure>\n<p><span>Como foi escrito, esse modelo tamb\u00e9m pode ser usado em\u00a0<\/span><strong><span>c\u00f3digos de deple\u00e7\u00e3o nuclear<\/span><\/strong><span>\u00a0para resolver problemas\u00a0<\/span><strong><a href=\"https:\/\/www.nuclear-power.com\/nuclear-power\/reactor-physics\/reactor-operation\/fuel-burnup\/nuclear-transmutation\/\"><span>de transmuta\u00e7\u00e3o nuclear<\/span><\/a><\/strong><span>\u00a0e\u00a0<\/span><strong><span>decaimento<\/span><\/strong><span>\u00a0.\u00a0No caso de transmuta\u00e7\u00e3o, as constantes de decaimento que governam as\u00a0<\/span><strong><span>equa\u00e7\u00f5es de Bateman<\/span><\/strong><span>\u00a0para um caso de decaimento s\u00e3o substitu\u00eddas por constantes de transmuta\u00e7\u00e3o.\u00a0Pela constante de transmuta\u00e7\u00e3o \u03bb\u00a0<\/span><sub><span>i, j<\/span><\/sub><span>\u00a0, entendemos a probabilidade da produ\u00e7\u00e3o do\u00a0<\/span><em><span>i-<\/span><\/em><span>\u00a0nucl\u00eddeo por unidade de tempo a partir da\u00a0destrui\u00e7\u00e3o\u00a0do\u00a0<\/span><em><span>j-<\/span><\/em><span>\u00a0\u00e9simo resultado, como resultado da intera\u00e7\u00e3o nuclear com todo o espectro de part\u00edculas em intera\u00e7\u00e3o ou devido ao decaimento nuclear natural.<\/span><\/p>\n<p><span>Essas equa\u00e7\u00f5es s\u00e3o geralmente usadas para a evolu\u00e7\u00e3o exata das mudan\u00e7as isot\u00f3picas no combust\u00edvel nuclear durante o esgotamento do combust\u00edvel.\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/nuclear-power\/reactor-physics\/reactor-operation\/fuel-burnup\/fuel-depletion-isotopic-changes-2\/\"><span>O esgotamento de combust\u00edvel<\/span><\/a><span>\u00a0geralmente \u00e9 modelado matematicamente como um conjunto de equa\u00e7\u00f5es diferenciais conhecidas como\u00a0<\/span><strong><span>equa\u00e7\u00f5es de evolu\u00e7\u00e3o<\/span><\/strong><span>\u00a0.<\/span><\/p>\n<p><span>Refer\u00eancia especial: Jerzy Cetnar, solu\u00e7\u00e3o geral das equa\u00e7\u00f5es de Bateman para transmuta\u00e7\u00f5es nucleares.\u00a0Annals of Nuclear Energy 33 (2006).\u00a0Janeiro de 2006.<\/span><\/p>\n<\/div>\n<\/div>\n<p>&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;.<\/p>\n<p>Este artigo \u00e9 baseado na tradu\u00e7\u00e3o autom\u00e1tica do artigo original em ingl\u00eas. Para mais informa\u00e7\u00f5es, consulte o artigo em ingl\u00eas. Voc\u00ea pode nos ajudar. Se voc\u00ea deseja corrigir a tradu\u00e7\u00e3o, envie-a para: translations@nuclear-power.com ou preencha o formul\u00e1rio de tradu\u00e7\u00e3o on-line. Agradecemos sua ajuda, atualizaremos a tradu\u00e7\u00e3o o mais r\u00e1pido poss\u00edvel. Obrigado.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Na f\u00edsica dos decaimentos nucleares, existe um equil\u00edbrio radioativo quando um nucl\u00eddeo radioativo est\u00e1 decaindo na mesma taxa em que est\u00e1 sendo produzido.\u00a0O equil\u00edbrio radioativo n\u00e3o \u00e9 estabelecido imediatamente, mas s\u00f3 ocorre ap\u00f3s um per\u00edodo de transi\u00e7\u00e3o.\u00a0Dosimetria de Radia\u00e7\u00e3o Na f\u00edsica dos\u00a0decaimentos nucleares\u00a0,\u00a0existe\u00a0um\u00a0equil\u00edbrio radioativo\u00a0quando um nucl\u00eddeo radioativo est\u00e1 decaindo na mesma taxa em que est\u00e1 &#8230; <a title=\"O que \u00e9 Equil\u00edbrio Radioativo &#8211; Defini\u00e7\u00e3o\" class=\"read-more\" href=\"http:\/\/www.radiation-dosimetry.org\/pt-br\/o-que-e-equilibrio-radioativo-definicao\/\" aria-label=\"More on O que \u00e9 Equil\u00edbrio Radioativo &#8211; Defini\u00e7\u00e3o\">Ler mais<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[51],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v15.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>O que \u00e9 Equil\u00edbrio Radioativo - Defini\u00e7\u00e3o<\/title>\n<meta name=\"description\" content=\"Na f\u00edsica dos decaimentos nucleares, existe um equil\u00edbrio radioativo quando um nucl\u00eddeo radioativo est\u00e1 decaindo na mesma taxa em que est\u00e1 sendo produzido. O equil\u00edbrio radioativo n\u00e3o \u00e9 estabelecido imediatamente, mas s\u00f3 ocorre ap\u00f3s um per\u00edodo de transi\u00e7\u00e3o. Dosimetria de Radia\u00e7\u00e3o\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.radiation-dosimetry.org\/pt-br\/o-que-e-equilibrio-radioativo-definicao\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"O que \u00e9 Equil\u00edbrio Radioativo - Defini\u00e7\u00e3o\" \/>\n<meta property=\"og:description\" content=\"Na f\u00edsica dos decaimentos nucleares, existe um equil\u00edbrio radioativo quando um nucl\u00eddeo radioativo est\u00e1 decaindo na mesma taxa em que est\u00e1 sendo produzido. O equil\u00edbrio radioativo n\u00e3o \u00e9 estabelecido imediatamente, mas s\u00f3 ocorre ap\u00f3s um per\u00edodo de transi\u00e7\u00e3o. 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