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

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

NTA AbhyasNTA Abhyas 2022

Solution:

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After $4$ minutes , both $P$ and $Q$ have an equal number of nuclei.
$\therefore$ Number of nuclei of $R$
$=\left(4 N_{0} - \frac{N_{0}}{4}\right)+\left(N_{0} - \frac{N_{0}}{4}\right)$
$=\frac{1 5 N_{0}}{4}+\frac{3 N_{0}}{4}=\frac{9 N_{0}}{2}$