Question

Two unstable nuclei A and B at $t=0$, have decay constants $5\lambda$ and $\lambda$ respectively. At ${t=t}_0$ they have same number of nuclei. the ratio of awed nuclei respectively at $(1/e{)}^2$ is

• A. $\frac{1}{4\lambda }$
• B. $\frac{4\lambda }{3}$
• C. $2\lambda$
• D. $\frac{1}{2\lambda }$

Answer 1

The correct option is D $\frac{1}{2\lambda }$

We know $N=No{e}^{-lambdat}$

For A, $N_A=No{e}^{-\sqrt{\lambda t}}$

For B, $N_B=No{e}^{-\lambda t}$

Given $\frac{N_A}{N_B}=\frac{1}{e^2}$

$\frac{N_A}{N_B}=\frac{1}{e^{y\lambda t}}t$

$=\frac{1}{2\lambda }$

Hence, the answer is $\frac{1}{2\lambda }.$