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