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

The correct option is D $1:1$

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 $=\frac{A}{\frac{4}{3}\pi R^3}$
$\therefore \rho A_1:\rho A_2=\frac{1}{\frac{4}{3}\pi R_0^3\cdot 1^3}=\frac{3}{\frac{4}{3}\pi R_0^3{\left(3^{1/3}\right)}^3}$
Their nuclear densities will be the same.