Question

The ratio of radii of nuclei ${}_{13}{\text{Al}}^{27}$ and ${}_{52}{\text{X}}^P$ is $3:5$. The number of neutrons in the nuclei of X will be

Answer 1

$r\propto A^{\frac{1}{3}}\Rightarrow \frac{r_1}{r_2}={\left(\frac{A_1}{A_2}\right)}^{1/3}\mathrm{Substituting}\mathrm{the}\mathrm{values}\frac{3}{5}={\left(\frac{27}{P}\right)}^{1/3}\Rightarrow \frac{27}{125}=\frac{27}{P}P=125$
Number of neutrons in atom
$X=P-52$
$=125-52$
$=73$