Read the following passage and answer the questions.
A nucleus is written as \({}^{A}_{Z}\mathrm{X}\), where X is the chemical symbol of the element. Here Z is the atomic number and A is the mass number. The nucleus contains Z protons and (A − Z) neutrons. Protons and neutrons are together called nucleons. For example, the aluminium nucleus \({}^{27}_{13}\mathrm{Al}\) has 13 protons and 14 neutrons. Experiments show that a nucleus of mass number A has a radius \(R=R_0A^{1/3}\), where \(R_0=1.2\ \mathrm{fm}\) and 1 fm = \(10^{-15}\ \mathrm{m}\). The protons in a nucleus are positively charged, so they repel each other. Still, the nucleus does not fly apart. The nucleons are held together by a force of a different kind, called the nuclear force. A rough graph of the potential energy of a pair of nucleons against their separation r has a minimum at a separation \(r_0\) of about 0.8 fm.
Consider the following statements:
(A) For nuclei of average mass, the binding energy per nucleon is much larger than the binding energy of electrons in atoms.
(B) Like Coulomb’s law, the nuclear force varies inversely as the square of the separation.
(C) In a large nucleus, a nucleon is influenced only by the nucleons that lie within the short range of the nuclear force.
(D) The nuclear force is weaker than the Coulomb force between two protons.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) and (C) only
The nuclear force holds the nucleons together very strongly, but only over very short distances.
(A) For nuclei of average mass, the binding energy per nucleon is much larger than the binding energy of electrons in atoms. — True. The binding energy per nucleon of such nuclei is about 8 MeV. An electron in an atom is bound by only a few eV, for example 13.6 eV in hydrogen.
(B) Like Coulomb’s law, the nuclear force varies inversely as the square of the separation. — False. Coulomb’s law and Newton’s law of gravitation have a simple inverse-square form. The nuclear force has no simple mathematical form.
(C) In a large nucleus, a nucleon is influenced only by the nucleons that lie within the short range of the nuclear force. — True. Nucleons farther away than the range of the force have no effect on it. This is the saturation property of the nuclear force.
(D) The nuclear force is weaker than the Coulomb force between two protons. — False. The protons repel each other, yet the nucleus stays bound. This is possible only because the nuclear force is much stronger than the Coulomb force.
NCERT (2026-27):
Nuclear Force – “… for average mass nuclei the binding energy per nucleon is approximately 8 MeV, which is much larger than the binding energy in atoms. …”
Nuclear Force – “Unlike Coulomb’s law or the Newton’s law of gravitation there is no simple mathematical form of the nuclear force.”
Nuclear binding energy – “… Consider a particular nucleon inside a sufficiently large nucleus. It will be under the influence of only some of its neighbours, which come within the range of the nuclear force. …”
Nuclear Force – “… This happens only because the nuclear force is much stronger than the coulomb force. …”