The density D of nuclear matter varies with the nucleon number A as

The correct answer is Option (4) → \( D\propto A^{0} \)

The radius of a nucleus of mass number A is \( R=R_0A^{1/3} \). So its volume grows in proportion to A. Its mass also grows in proportion to A, as it has about A nucleons of nearly equal mass.

    \( \begin{aligned} V &\propto R^{3} \\ &\propto A \end{aligned} \)

    \( M\propto A \)

The density is then:

    \( \begin{aligned} D &= \frac{M}{V} \\ &\propto \frac{A}{A} \\ &= A^{0} \end{aligned} \)

Therefore, the density of nuclear matter is the same for all nuclei. It does not depend on A.

NCERT (2026-27):
Size of the Nucleus – “It has been found that a nucleus of mass number A has a radius

    \( R=R_0A^{1/3} \qquad (13.5) \)

where R₀ = 1.2 × 10^–15 m (=1.2 fm; 1 fm = 10^–15 m). This means the volume of the nucleus, which is proportional to R³ is proportional to A. Thus the density of nucleus is a constant, independent of A, for all nuclei.”