Statement I: Volume of the nucleus is proportional to \( A \) where \( A \) is mass number.
Statement II: Density of nucleus is independent of mass number \( A \).
In the light of the above statements, choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Both Statement I and Statement II are true
The nuclear radius grows as the cube root of the mass number:
\( \displaystyle R = R_0 A^{1/3} \)
Statement I: Volume of the nucleus is proportional to \( A \) where \( A \) is mass number. — Correct. Cubing the radius gives a volume proportional to \( A \).
\( \displaystyle V = \frac{4}{3}\pi R^3 = \frac{4}{3}\pi R_0^3 A \;\Rightarrow\; V \propto A \)
Statement II: Density of nucleus is independent of mass number \( A \). — Correct. The mass of the nucleus is about \( mA \), where \( m \) is the mass of a nucleon, and the volume is also proportional to \( A \), so \( A \) cancels and the nuclear density is the same for all nuclei.
\( \displaystyle \rho = \frac{mA}{\frac{4}{3}\pi R_0^3 A} = \frac{3m}{4\pi R_0^3} \)
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.”