Iodine-131 has a short half-life of 8.14 days. Suppose the initial amount of Iodine-131 is 50 grams. How much of the initial amount of 50 grams will be radioactive after 30 days?<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n To find the amount of Iodine-131 remaining after 30 days, we use the radioactive decay formula:<\/p>\n\n\n\n A(t) = A\u2080 \u00d7 (1\/2)^(t \/ T)<\/strong><\/p>\n\n\n\n Where:<\/p>\n\n\n\n Given:<\/strong> Step 1: Plug the values into the formula<\/strong> Step 2: Calculate the exponent<\/strong> Step 3: Calculate (1\/2)^3.686<\/strong> Step 4: Multiply by the initial amount<\/strong> Correct Answer:<\/strong> Radioactive isotopes like Iodine-131 decay over time following an exponential pattern. The rate of decay is characterized by the half-life, which is the time it takes for half of a substance to decay. In this case, the half-life is 8.14 days, which means that every 8.14 days, the amount of Iodine-131 is halved.<\/p>\n\n\n\n After one half-life, 25 grams would remain. After two, 12.5 grams. However, 30 days is not a perfect multiple of the half-life, so the decay must be calculated using the exponential formula. This approach gives a more accurate result than repeated halving, especially for times that are not exact multiples of the half-life.<\/p>\n\n\n\n This exponential decay ensures that the substance never truly reaches zero but becomes negligible after several half-lives. Iodine-131’s rapid decay is useful in medical applications, especially in treatments where short-term radiation is beneficial.<\/p>\n","protected":false},"excerpt":{"rendered":" Iodine-131 has a short half-life of 8.14 days. Suppose the initial amount of Iodine-131 is 50 grams. How much of the initial amount of 50 grams will be radioactive after 30 days? The correct answer and explanation is: To find the amount of Iodine-131 remaining after 30 days, we use the radioactive decay formula: A(t) […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-37272","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37272","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=37272"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37272\/revisions"}],"predecessor-version":[{"id":37273,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37272\/revisions\/37273"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=37272"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=37272"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=37272"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
A\u2080 = 50 grams
T = 8.14 days
t = 30 days<\/p>\n\n\n\n
A(30) = 50 \u00d7 (1\/2)^(30 \/ 8.14)<\/p>\n\n\n\n
30 \u00f7 8.14 \u2248 3.686<\/p>\n\n\n\n
(1\/2)^3.686 \u2248 0.0786<\/p>\n\n\n\n
A(30) = 50 \u00d7 0.0786 \u2248 3.93 grams<\/strong><\/p>\n\n\n\n
Approximately 3.93 grams<\/strong> of the original 50 grams of Iodine-131 will remain radioactive after 30 days.<\/p>\n\n\n\n
\n\n\n\nExplanation:<\/h3>\n\n\n\n