Question

A radioactive sample S1 having an activity $5\mu Ci$ has twice the number of nuclei of another sample S2 which has an activity of $10\mu Ci$. The half-lives of S1 and S2 are respectively :

• A. 20 yr and 5 yr
• B. 20 yr and 10 yr
• C. 10 yr each
• D. 5 yr each

Answer 1

The correct option is A 20 yr and 5 yr

As we know,
$r=\lambda .N$

$\therefore \frac{r_1}{r_2}=\frac{{\lambda }_1}{{\lambda }_2}.\frac{N_1}{N_2}$ (and $t_{1/2}=0.693/\lambda$)

$\frac{r_1}{r_2}=\frac{(t_{1/2}{)}_2}{(t_{1/2}{)}_1}.\frac{N_1}{N_2}$

$\therefore \frac{(t_{1/2}{)}_1}{(t_{1/2}{)}_2}=.\frac{N_1}{N_2}\times \frac{r_2}{r_1}=2\times \frac{10}{5}=4=20/5$