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

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)  (3)1/3: 1  (D)  1: 1

Tardigrade Admin · Accepted Answer

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} π R ^{3}}

∴ ρ_{A_{1}} : ρ_{A_{2}} = \frac{1}{\frac{4}{3} π R _{0}^{3} \cdot 1 ^{3}}

= \frac{4}{3} π R_{0}^{3} (3^{1/3})^{3}

Their nuclear densities will be the same.

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

$1 : 3$

$3 : 1$

$(3)^{1/3} : 1$

$1 : 1$

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

1:3

3:1

(3)1/3:1

1:1

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

$1 : 3$

$3 : 1$

$(3)^{1/3} : 1$

$1 : 1$