{"id":34021,"date":"2017-11-01T14:33:02","date_gmt":"2017-11-01T14:33:02","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=34021"},"modified":"2026-03-28T10:47:29","modified_gmt":"2026-03-28T15:47:29","slug":"safety-professional-radiation-calculations","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/safety-professional-radiation-calculations\/","title":{"rendered":"Radiation Calculations"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_84polEU680k\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_84polEU680k\" data-source-videoID=\"84polEU680k\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Radiation Calculations Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Radiation Calculations\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_84polEU680k:hover {cursor:pointer;} img#videoThumbnailImage_84polEU680k {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/92-radiation-calculus-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_84polEU680k\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_84polEU680k\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Radiation Calculations\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_84polEU680k\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_84polEU680k\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_84polEU680k\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction BCs_Function() {\n  var x = document.getElementById(\"BCs\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"BCs_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"BCs\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Radioactive_Decay\" class=\"smooth-scroll\">Radioactive Decay<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#HalfLife\" class=\"smooth-scroll\">Half-Life<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Source_Strength\" class=\"smooth-scroll\">Source Strength<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hey guys! Welcome to this video over measuring nuclear radiation.<\/p>\n<p>Radiation can affect people in various ways, and can even result in death. Because of this effect, we must be able to measure the amount of radiation present.<\/p>\n<p>There are a few things you need to be aware of when making radiation calculations: decay, half-life, and source strength.<\/p>\n<h2><span id=\"Radioactive_Decay\" class=\"m-toc-anchor\"><\/span>Radioactive Decay<\/h2>\n<p>\nRadioactive decay, also commonly known as radioactivity, is a set of processes that allow unstable atomic nuclei, or nuclides to emit radiation. This happens randomly, and can not be predicted. However, on a larger scale, radioactive material does behave in a way that is possible to predict.<\/p>\n<p>Radioactive decay always occurs at an exponential rate.<\/p>\n<p>The amount of radioactive material (\\(N\\)) present after time (\\(t\\)) is given by the equation:<\/p>\n<div class=\"examplesentence\">\\(N=N_0\\times e^{-\\lambda t}\\)<\/div>\n<p>\n&nbsp;<br \/>\nHere, \\(N_0\\) is the amount of material present at time \\(t=0\\), and \\(\\lambda\\) is the decay constant of the material.<\/p>\n<h2><span id=\"HalfLife\" class=\"m-toc-anchor\"><\/span>Half-Life<\/h2>\n<p>\nThe time required for half the mass of a radioactive material to decay is known as its half-life. Half-life is the most commonly used measure of a material\u2019s rate of decay, and it can be short as a fraction of a second or as long as millions of years. <\/p>\n<p>If the half-life of the material is known, lambda, the decay constant can be calculated as \\(\\lambda=\\frac{\\text{ln}(2)}{t_{\\frac{1}{2}}}\\), where \\(t_{\\frac{1}{2}}\\) is the half-life. <\/p>\n<p>For example, suppose a sample of radium-224 starts at a mass of 10 grams. Its half-life is 3.63 days. The remaining mass of radium-224 after 8 days can be calculated by:<\/p>\n<div class=\"examplesentence\">\\(\\lambda=\\frac{\\text{ln}(2)}{3.63\\text{ days}}=0.191\\text{ disintegrations per day}\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h2><span id=\"Source_Strength\" class=\"m-toc-anchor\"><\/span>Source Strength<\/h2>\n<p>\nThe source strength of a radioactive material is defined as the number of disintegrations per second, and is measured in becquerels (Bq) or curies (Ci). One becquerel is one disintegration per second; one curie is \\(3.7&#215;10^{10}\\text{ disintegrations per second}\\). Source strength is given by the equation:<\/p>\n<div class=\"examplesentence\">\\(Q= \\frac{\\lambda m N_A}{W}\\)<\/div>\n<p>\n&nbsp;<\/p>\n<ul>\n<li>\\(Q\\) is the number of disintegrations per second<\/li>\n<li>\\(\\lambda\\) is the decay constant<\/li>\n<li>\\(M\\) is the mass of the radioisotope<\/li>\n<li>\\(N_A\\) is Avogadro\u2019s number, \\(6.02&#215;10^{23}\\frac{\\text{ g}}{\\text{g-atoms}}\\)<\/li>\n<li>\\(W\\) is the atomic weight of the radioisotope<\/li>\n<\/ul>\n<p>For example, if radium-224 has decay constant of \\(2.0289&#215;10^{-6}\\) disintegrations per second and an atomic mass of 224.02, a \\(5.8&#215;10^{12}\\) becquerel source of Ra-224 can be calculated to have a mass of <\/p>\n<div class=\"examplesentence\">\\(m=\\frac{QW}{\\lambda N_A}\\)<br \/>\n\\(=\\frac{(3.8&#215;10^{12})\\times224.02}{2.2089\\times10^{-6}\\times6.02&#215;10^{23}} = 640 \u03bcg\\)<\/div>\n<p>\n&nbsp;<br \/>\nI hope that this video was helpful!<\/p>\n<\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/safety-professional\/\">Return to Safety Professional Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Safety Professional Videos<\/p>\n","protected":false},"author":1,"featured_media":91078,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-34021","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-safety-professional-videos","7":"page_category-video-pages-for-study-course-sidebar-ad","8":"page_type-video","9":"subject_matter-business-finance"},"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO Pro 4.9.9 - aioseo.com -->\n\t<meta name=\"description\" content=\"Radiation calculus has severe real-world implications and must be appropriately worked to keep people safe. 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