Question

A radioactive sample decays through two different decay processes $\alpha -decay$ and $\beta -decay$. Half-life time for $\alpha -decay$ is $3h$ and half-life time for $\beta -decay$ is $6h$. What will be the ratio of number of initial radioactive nuclei to the number of radioactive nuclei present after $6h$?

Answer 1

Here after $6hr$, two half time for $\alpha$ decay and one half time for $\beta$ decay will occur.

Let initial number of nuclei $=N_0$

After two half time for $\alpha$ decay, number of nuclei $=N_0/4$ and
After one half time for $\beta$ decay, number of nuclei $=\frac{N_0/4}{2}=N_0/8$

Ratio of number of initial radioactive nuclei to the number of radioactive nuclei present after $6hr$ $=\frac{N_0}{N_0/8}=8$