Question

The radioactive material A and B have decay constant $5\lambda$ and $\lambda$ respectively.Initially both A and B have the same number of nuclei.The ratio of the number of nuclei of A and B will be $\frac{1}{e}$ ,after the time is $\frac{x}{8\lambda }$ then $x$ is

Answer 1

Let after time $t$ the ratio of nuclei be $\frac{1}{e}$.

$N_1=N_o{e}^{-5\lambda t}$

$N_2=N_o{e}^{-\lambda t}$

Now, $\frac{N_1}{N_2}=\frac{1}{e}$

$t=\frac{1}{4\lambda }$

$\Rightarrow x=2$