Question

Mass numbers of two nuclei are in the ratio of $4:3$. Their nuclear densities will be in the ratio of

• A. $4:3$
• B. ${\left(\frac{3}{4}\right)}^{\frac{1}{3}}$
• C. $1:1$
• D. ${\left(\frac{4}{3}\right)}^{\frac{1}{3}}$

Answer 1

Answer: (C)

Radius of nucleus $R=R_0{A}^{\frac{1}{3}}$
Density of nucleus $=\frac{\text{ Mass of nucleus }}{\text{ volume of nucleus }}$
$\rho =\frac{m\times A}{\frac{4}{3}\pi R^3}$
Where $m$ : mass of proton or neutron
$\rho =\frac{m\times A}{\frac{4}{3}\pi R_0{}^{3}A}$
$\rho \propto A^0$
Hence density of nucleus is independent of mass number