The radius of a nucleus is given empirically by

PHYSICS · Subjective · CBSE · Physics · Nuclei · Nuclei

Problem

R = R_0 A^{1/3}

, where

R_0 = 1.2\,\text{fm}

. (i) Starting from this relation, derive an expression for the average nuclear density

\rho

in terms of

A

R_0

and the average nucleon mass

m_N

. (ii) Show explicitly that

\rho

is nearly independent of the mass number

A

. (iii) Explain, with reference to the saturation property of the nuclear force, why this result for constant density is physically reasonable.