Question

Two nuclei have their mass numbers in the ratio of $1:3$ . The ratio of their nuclear densities would be

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

Answer 1

Answer: (D)

$1 : 1$

Answer 2

Density of nuclear matter is independent of mass number, so the required ratio is 1: 1.

Alternative
$A_{1}: A_{2}=1: 3$

Their radii will be in the ratio
$R_{0} A_{1}^{1 / 3}: R_{0} A_{2}^{1 / 3}$
$=1: 3^{1 / 3}$

Density $=\frac{A}{\frac{4}{3} \pi R^{3}}$
$\therefore \rho_{A_{1}}: \rho_{A_{2}}=\frac{1}{\frac{4}{3} \pi R_{0}^{3} \cdot 1^{3}}$
$=\frac{4}{3} \pi R_{0}^{3}\left(3^{1 / 3}\right)^{3}$

Their nuclear densities will be the same.