Rankers Physics

Uncategorized: Practice Problem & Solution

43. 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 $4 N_0$ and that of Q are $N_0$. 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: (2011 Mains)
$3N_0$
$\frac{9N_0}{2}$
$\frac{5N_0}{2}$
$2N_0$

Solution Explained:

To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:

Equating remaining nuclei: $4N_0(1/2)^{t/1} = N_0(1/2)^{t/2}$, solving gives $2^{t/2} = 4$ so $t = 4$ min. Remaining $P = 4N_0(1/16) = N_0/4$ and $Q = N_0(1/4) = N_0/4$. Formed $R = 5N_0 - (N_0/4 + N_0/4) = 4.5N_0 = \frac{9N_0}{2}$.

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