A sample of radon gas has an activity of 140.0 mCi. If the half-life of radon is 1,500.0 y, how long before the activity of the sample is 10.0 mCi?

Question

Quizplus · Accepted Answer

The activity of a radioactive sample decreases exponentially with time, according to the formula $A = A_0 \times (1/2)^{t/T}$, where $A$ is the final activity, $A_0$ is the initial activity, $t$ is the time elapsed, and $T$ is the half-life of the substance. To find the time $t$ when the activity decreases from 140.0 mCi to 10.0 mCi, we can set up the equation $10 = 140 \times (1/2)^{t/1500}$. Solving for $t$, we find that $t \approx 5710$ years, which corresponds to choice E.

A Sample of Radon Gas Has an Activity of 140