A typical dose of a radioactive sample is 27.0 mCi. How long does it take for the activity to reduce to 0.100 mCi? The half-life of the sample is 211,000 y.

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Quizplus · Accepted Answer

To find the time it takes for a radioactive sample to decay from 27.0 mCi to 0.100 mCi with a half-life of 211,000 years, we use the formula for radioactive decay: $N = N_0 \times (1/2)^{t/T}$, where $N$ is the final amount, $N_0$ is the initial amount, $t$ is the time, and $T$ is the half-life. Rearranging for $t$, we get $t = T \times \log_2(N_0/N)$. Plugging in the values, $t = 211,000 \times \log_2(27.0/0.100)$, which gives a result in the order of magnitude of $10^{16}$ years, matching choice E.

A Typical Dose of a Radioactive Sample Is 27