Identify the correct statements among the following.
(A) When an electron and a positron come together, they annihilate each other giving energy in the form of X-rays.
(B) The density of matter in all nuclei is almost the same.
(C) The radius of a nucleus is proportional to A1/3, where A is the mass number of the nucleus.
(D) The nuclear force does not depend on the charge of protons.
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B), (C) and (D) only
The statements test pair annihilation, the size and density of nuclei and the charge independence of nuclear force.
(A) When an electron and a positron come together, they annihilate each other giving energy in the form of X-rays. — Incorrect. Annihilation produces gamma-ray photons, each of about 0.511 MeV, not X-rays.
(B) The density of matter in all nuclei is almost the same. — Correct. Since \( R \propto A^{1/3} \), the volume is proportional to A, so the density (about 2.3 × 1017 kg m−3) does not depend on A.
(C) The radius of a nucleus is proportional to A1/3, where A is the mass number of the nucleus. — Correct. \( R = R_0 A^{1/3} \), with \( R_0 \approx 1.2 \) fm.
(D) The nuclear force does not depend on the charge of protons. — Correct. The nuclear force is nearly the same between two neutrons, two protons, or a proton and a neutron.
Shortcut: (A) is wrong, and Options (1), (2) and (3) all contain (A), so Option (4) must be the answer once (A) is judged.
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 – “… (iii) The nuclear force between neutron-neutron, proton-neutron and proton-proton is approximately the same. The nuclear force does not depend on the electric charge.”
Points to Ponder – “… (It is found that when an electron and a positron come together, they annihilate each other giving energy in the form of gamma-ray photons.)”