Question

A sample contains number of stable nuclei equal to ${/N}_s$ and number of unstable nuclei equal to ${/N}_u$.After a time T the activity of the sample decreased to one third of the initial activity, while the total number of nuclei (excluding decayed nuclei) became half .The ratio$N_s{/N}_u$ initially is:

Answer 1

Initially total number of nuclei $N_s+N_u$

after some the activity decreased to $1/3$

So that time the unstable nuclei remains only $N_u/3$

and thus new total is $N_s+\frac{N_u}{3}$

As given in the question the new counting is $half$ of the old one so $N_s+\frac{N_u}{3}=\frac{1}{2}(N_u+N_s)$

solving above relation we get $\frac{N_s}{N_u}=\frac{1}{3}$