The decay rate for a certain mass of a radioa | vedclass

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Question

(A) From the graph, at $t = 0 \, hr$, the initial decay rate $R_0 = 200 \, 	ext{decays/sec}$.At $t = 2 \, hr$, the decay rate $R = 100 \, 	ext{decay

Vedclass · Accepted Answer

$\frac{25}{2} \, 	ext{decays/sec}$

Vedclass · Answer

(A) From the graph, at $t = 0 \, hr$, the initial decay rate $R_0 = 200 \, 	ext{decays/sec}$.At $t = 2 \, hr$, the decay rate $R = 100 \, 	ext{decays/sec}$.Since the decay rate becomes half of its initial value in $2 \, hr$, the half-life $T_{1/2} = 2 \, hr$.The decay rate at any time $t$ is given by $R = R_0 \left( \frac{1}{2} ight)^{t/T_{1/2}}$.For $t = 8 \, hr$, $R = 200 \left( \frac{1}{2} ight)^{8/2} = 200 \left( \frac{1}{2} ight)^4 = \frac{200}{16} = \frac{25}{2} \, 	ext{decays/sec}$.

The decay rate for a certain mass of a radioactive substance measured at different times varies with time as shown in the figure. The count rate at $t = 8 \, hr$ will be:

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