Physics - Modern Physics Question with Solution | TestHub

Radius of nucleus $R=R_0{ A}^{\frac{1}{3}}$

Density of nucleus $\left(\rho \right)=\frac{ \mathrm{Mass} \mathrm{of} \mathrm{nucleus} }{ \mathrm{volume} \mathrm{of} \mathrm{nucleus} }$

$\rho =\frac{\mathrm{m}\times \mathrm{A}}{\frac{4}{3}\pi {\mathrm{R}}^3}$  Where $m$: mass of proton or neutron and $A$: mass number.

$\Rightarrow \rho =\frac{m\times A}{\frac{4}{3}\pi R_0{}^3 \mathrm{A}}$

$\Rightarrow \rho \propto {\mathrm{A}}^0$

Hence, density of nucleus is independent of mass number.

Therefore, the ratio is $1:1$.