Identify the correct statements.
(A) Neutrons penetrate the nucleus more readily as compared to protons.
(B) It is easier to release an orbital electron, but quite difficult to release a nucleon.
(C) Nuclear density is not the same for all nuclei.
(D) The radius of the nucleus is directly proportional to the cube root of the mass number.
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (B) and (D) only
The nuclear radius is \( R = R_0 A^{1/3} \), so the volume of a nucleus is proportional to \( A \), and nucleons are bound by the strong nuclear force, with energies in MeV.
(A) Neutrons penetrate the nucleus more readily as compared to protons. — Correct. A neutron has no charge, so it feels no Coulomb repulsion from the positive nucleus; a proton is repelled.
(B) It is easier to release an orbital electron, but quite difficult to release a nucleon. — Correct. An orbital electron is bound by a few eV (13.6 eV in hydrogen), while a nucleon is bound by about 8 MeV, roughly a million times more.
(C) Nuclear density is not the same for all nuclei. — Incorrect. Mass is proportional to \( A \) and volume is proportional to \( R^{3} \propto A \), so the nuclear density is independent of \( A \) and is about the same, \( 2.3\times10^{17}\,\mathrm{kg\,m^{-3}} \), for all nuclei.
(D) The radius of the nucleus is directly proportional to the cube root of the mass number. — Correct. This is \( R = R_0 A^{1/3} \), with \( R_0 \approx 1.2\times10^{-15}\,\mathrm{m} \).
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.”
Nuclear Force – “… In Section 13.4, we have seen that for average mass nuclei the binding energy per nucleon is approximately 8 MeV, which is much larger than the binding energy in atoms.”