Radioactive decay exhibits a first-order rate law, rate = -∆N/∆t = kN, where N denotes the number of radio-active nuclei present at time t. The half-life of strontium-90, a dangerous nuclear fission product, is 29 years. (a) What fraction of the strontium-90 remains after three half-lives?

Video transcript

Hey everyone, we're told that radioactive decay is a first order reaction. Burke ilium 2 50. A radioactive metallic element used in the synthesis of heavier elements has a half life of 3.2 17 hours, determine the fraction of burke ilium to 50 that remains after four half lives. So a key term here is that we have a first order reaction. So to determine the fraction remaining after an N amount of half lives, we have to use the following formula, which is one half to the N power. So we were asked to determine the fraction that remains after four half lives. So this means our N equals four, so the fraction remaining is going to be equal to have to the end power, which is for in this case Calculating this out, we get 116 which is going to be our final answer. Now, I hope this made sense. And let us know if you have any questions.