Which of the following statements are correct?
(A) A nucleus of mass number \( A \) has a radius \( R \) given by the expression \( R = R_0 A^{1/3} \)
(B) Volume of nucleus is proportional to mass number \( A \)
(C) The density of nucleus increases with the radius of nucleus.
(D) Density of nuclear matter does not depend on its mass number \( A \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (B) and (D) only
The nuclear radius is found from scattering experiments to follow \( R = R_0A^{1/3} \). The volume and the density follow from it.
\( \displaystyle V = \frac{4}{3}\pi R^{3} = \frac{4}{3}\pi R_0^{3}\,A \;\Rightarrow\; V \propto A \)
\( \displaystyle \rho = \frac{\text{mass}}{\text{volume}} \approx \frac{A\,m_{\mathrm{n}}}{\frac{4}{3}\pi R_0^{3}\,A} = \frac{3\,m_{\mathrm{n}}}{4\pi R_0^{3}} \)
(A) A nucleus of mass number \( A \) has a radius \( R \) given by the expression \( R = R_0 A^{1/3} \) — Correct. This is the standard nuclear radius relation.
(B) Volume of nucleus is proportional to mass number \( A \) — Correct. \( V \propto R^{3} \propto A \), as shown above.
(C) The density of nucleus increases with the radius of nucleus. — Incorrect. \( A \) cancels in the density, so it is the same for all nuclei whatever their radius.
(D) Density of nuclear matter does not depend on its mass number \( A \) — Correct. The density is a constant, about \( 2.3\times10^{17}\,\mathrm{kg\,m^{-3}} \).
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 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.”