As the mass number A increases, which of the following quantities related to a nucleus does not change?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Density
The radius of a nucleus is \( R = R_0 A^{1/3} \), so its volume is proportional to \( A \). The mass is also proportional to \( A \), because each nucleon has nearly the same mass. The density is therefore the same for all nuclei, about \( 2.3\times10^{17}\,\mathrm{kg\,m^{-3}} \).
\( \displaystyle \rho = \frac{A\,m_{\mathrm{n}}}{\frac{4}{3}\pi R_0^{3}A} = \frac{3\,m_{\mathrm{n}}}{4\pi R_0^{3}} \)
Option (3) Density — Correct. The ratio of mass to volume is independent of \( A \): nuclear density is constant.
NCERT (2026-27):
Size of the Nucleus – “… 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. Different nuclei are like a drop of liquid of constant density.”