The half-life of ⁹⁰Sr is 28.1 years. How long will it take a 10.9-g sample of ⁹⁰Sr to decompose to 0.18 g?

Question

Quizplus · Accepted Answer

The decay of a radioactive substance is exponential. Using the formula $ N = N_0 \times (1/2)^{t/T} $, where $ N_0 $ is the initial amount, $ N $ is the remaining amount, $ t $ is the time, and $ T $ is the half-life, we solve for $ t $. For $ N_0 = 10.9 $ g, $ N = 0.18 $ g, and $ T = 28.1 $ years, solving gives $ t \approx 170 $ years, which is closest to 1.7 x 10^2 years.

The Half-Life of 90Sr Is 28

The Half-Life of ⁹⁰Sr Is 28