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

Options

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

Answer

B

Explanation

`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 )/((3)/(4) pi R ^(3)))`
` rho _(A _(a)): rho_(A_(2))= (1)/((4)/(3)pi R _(0) ^(3) . 1 ^(3)): (3)/((4)/(3)pi R _(0) ^(3) (3 ^(1//3))^(3))`
Their nuclear densities will be the same