The relationship between the density (ρ) of the nuclear matter of an atom with atomic mass number (A) is as follows:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → ρ is independent of A
Experiments show that the nuclear radius grows as the cube root of the mass number, \( R = R_0A^{1/3} \), so the nuclear volume is proportional to A. The mass is also proportional to A.
\( \displaystyle V = \frac{4}{3}\pi R^{3} = \frac{4}{3}\pi R_0^{3} A \)
\( \displaystyle \rho = \frac{\text{mass}}{V} = \frac{Am}{\frac{4}{3}\pi R_0^{3}A} = \frac{3m}{4\pi R_0^{3}} \)
A cancels, so the density of nuclear matter is the same (about \( 2.3\times10^{17}\,\mathrm{kg\,m^{-3}} \)) for all nuclei, independent of A.
NCERT (2026-27):
Size of the Nucleus – “… It has been found that a nucleus of mass number A has a radius
\( \displaystyle R = R_0 A^{1/3} \qquad (13.5) \)”
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.”