How many days are required for a radioactive sample,with a half-life of 5.7 d and an initial activity of 1.07 × 10⁵ Bq,to decay to an activity of 100 Bq? A) 57 d B) 46 d C) 68 d D) 39 d

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Quizplus · Accepted Answer

The decay of a radioactive sample is given by 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, and $T$ is the half-life. Rearranging for $t$, we get $t = T \times \log_2(A_0/A)$. Plugging in the given values, $t = 5.7 \times \log_2(1.07 \times 10^{15} / 100)$, we find that $t$ is approximately 57 days.

How Many Days Are Required for a Radioactive Sample,with a Half-Life