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

Options

A. `1:3`
B. `3:1`
C. `(3)^(1//3):1`
D. `1:1`

Answer

D

Explanation

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 `=(A)/((4)/(3)piR^(3))`
`:.P_(A_(1)):P_(A_2)=(1)/((4)/(3)piR_(0)^(3).1^(3))=(3)/((4)/(3)piR_(0)^(3)(3^(1//3))^(3))`
Their nuclear densities will be the same.