Question

Mass numbers of two nuclei are in the ratio of 4:3. Their nuclear densities will be in the ratio of

(A) 4:3

(B) \(\left(\frac 34\right)^\frac 13\)

(C) 1 : 1

(D) \(\left(\frac 43\right)^\frac 13\)

Answer 1

Correct option is (C) 1 : 1

Radius of nucleus R = R₀A^1/3

 Density of nucleus = \(\frac{\text{Mass of nucleus}}{\text{volume of nucleus}}\)

\(\rho = \frac{m \times A}{\frac 43\pi R^3}\) where m: mass of proton or neutron

\(\rho = \frac {m \times A}{\frac 43\pi {R_0}^3 A}\)

\(\rho \propto A ^0\)

Hence density of nucleus is independent of mass number.