Two radioactive nuclei P and Q, in a given sample decay into a stable… | NEET 2011 (AIPMT, Mains)

Q103NEET 2011 · AIPMT · MAINSMedium

Law of Radioactive Decay

Two radioactive nuclei P and Q, in a given sample decay into a stable nucleus R. At time t = 0. number of P species are 4 N0 and that of Q are N0. Half -life of P (for conversion to R) is 1 minute where as that of Q is 2 minutes. Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be

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Answer: (c)

$N_P = 4N_0 \, 2^{-t/1}$ , $N_Q = N_0 \, 2^{-t/2}$ ( $t$ in minutes).
Equal when $4 \cdot 2^{-t} = 2^{-t/2} \Rightarrow 2^{t/2} = 4 \Rightarrow t = 4$ min.
Then $N_P = 4N_0/16 = N_0/4$ and $N_Q = N_0/4$ .
$N_R = 5N_0 - \frac{N_0}{2} = \frac{9N_0}{2}$ , so the answer is (c).

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