Read the following statements about the volume and density of the nucleus:
A. Volume of a nucleus is directly proportional to its mass number.
B. Volume of a nucleus is independent of its mass number.
C. Density of a nucleus is directly proportional to its mass number.
D. Density of a nucleus is independent of its mass number.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A and D only
The nuclear radius is \( R = R_0A^{1/3} \), so the nuclear volume is proportional to the mass number. The mass is also proportional to \( A \), so the density is the same for all nuclei.
\( \displaystyle V = \frac{4}{3}\pi R^{3} = \frac{4}{3}\pi R_0^{3}A \propto A \)
\( \displaystyle \rho = \frac{Am}{\frac{4}{3}\pi R_0^{3}A} = \frac{3m}{4\pi R_0^{3}} \)
Here \( m \) is the mass of a nucleon; \( \rho \) contains no \( A \) (it is about \( 2.3\times10^{17}\,\mathrm{kg\,m^{-3}} \)).
(A) Volume of a nucleus is directly proportional to its mass number. — Correct. \( V \propto R^{3} \propto A \).
(B) Volume of a nucleus is independent of its mass number. — Incorrect. The volume grows in proportion to \( A \).
(C) Density of a nucleus is directly proportional to its mass number. — Incorrect. The factor \( A \) cancels between mass and volume.
(D) Density of a nucleus is independent of its mass number. — Correct. Nuclear matter has nearly constant density for all nuclei.
NCERT (2026-27):
Size of the Nucleus – “… It has been found that a nucleus of mass number \( A \) has a radius
\( \displaystyle R = R_0 A^{1/3} \qquad (13.5) \)
where \( R_0 = 1.2\times10^{-15}\,\mathrm{m} \) (\( = 1.2\,\mathrm{fm} \); \( 1\,\mathrm{fm} = 10^{-15}\,\mathrm{m} \)). This means the volume of the nucleus, which is proportional to \( R^{3} \) is proportional to \( A \). Thus the density of nucleus is a constant, independent of \( A \), for all nuclei.”