Read the following passage and answer the questions.
The oxygen nucleus \({}^{16}_{8}\mathrm{O}\) contains 8 protons and 8 neutrons. A student adds up the masses of 8 free protons and 8 free neutrons. She then compares this total with the mass of the oxygen nucleus. The mass of the oxygen atom is measured very precisely with a mass spectrometer, and the mass of the nucleus is found from it. The nucleus turns out to be lighter than its separate nucleons put together. This difference in mass is called the mass defect. The nucleons stay together in the nucleus because of the nuclear force. The student also looks at a graph of the binding energy per nucleon against the mass number A for a large number of nuclei. The curve is smooth and changes slowly. At nuclides such as \({}^{4}\mathrm{He}\) and \({}^{16}\mathrm{O}\), it shows small peaks.
Match List-I with List-II.
| List-I | List-II |
|---|---|
| (A) The nuclear force is short-ranged. | (I) It does not depend on the electric charge of the nucleons. |
| (B) The nuclear force is much stronger than the Coulomb force. | (II) The binding energy per nucleon is nearly constant for \(30\lt A\lt 170\). |
| (C) The nuclear force is about the same for n-n, n-p and p-p pairs. | (III) Unlike Coulomb’s law, it cannot be written as a simple formula. |
| (D) The nuclear force has no simple mathematical form. | (IV) Protons stay bound in the nucleus in spite of their repulsion. |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
(A) The nuclear force is short-ranged. — This matches (II). A nucleon inside a large nucleus feels only the neighbours within the range of the force. Adding more nucleons does not change its binding, so the binding energy per nucleon stays nearly constant for \( 30\lt A\lt 170 \).
(B) The nuclear force is much stronger than the Coulomb force. — This matches (IV). The protons repel each other, and only a much stronger attraction can keep them in the tiny nuclear volume.
(C) The nuclear force is about the same for n-n, n-p and p-p pairs. — This matches (I). A neutron has no charge, yet it feels the same nuclear force as a proton. So the force does not depend on charge.
(D) The nuclear force has no simple mathematical form. — This matches (III). Coulomb’s law and Newton’s law of gravitation are simple formulas; no such formula exists for the nuclear force.
NCERT (2026-27):
Nuclear binding energy – “(ii) The constancy of the binding energy in the range 30 < A < 170 is a consequence of the fact that the nuclear force is short-ranged. …”
Nuclear Force – “… The nuclear binding force has to dominate over the Coulomb repulsive force between protons inside the nucleus. This happens only because the nuclear force is much stronger than the coulomb force. …”
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.”
Nuclear Force – “Unlike Coulomb’s law or the Newton’s law of gravitation there is no simple mathematical form of the nuclear force.”