The binding energy per nucleon is nearly constant for nuclei with \( 30\lt A\lt 170 \). This is mainly because
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → the nuclear force is short-ranged, so a nucleon interacts only with the neighbours within its range
Option (1) the nucleus is a dense mass of nucleons — Incorrect. Nuclear matter is very dense. But density alone says nothing about how strongly each nucleon is bound. The constant value comes from the short range of the force between nucleons.
Option (2) the nuclear force is short-ranged, so a nucleon interacts only with the neighbours within its range — Correct. A nucleon inside a large nucleus is bound only by the few neighbours within the range of the nuclear force. Adding more nucleons does not change the binding energy of a nucleon inside, so the binding energy per nucleon stays nearly constant.
Option (3) the binding energy of the nucleons is very large — Incorrect. A large binding energy does not make it the same for every nucleus. Light nuclei (A < 30) have a much smaller binding energy per nucleon.
Option (4) the nuclear force is zero up to a certain distance and then increases — Incorrect. The nuclear force is repulsive for separations below about 0.8 fm and attractive beyond it. It falls rapidly to zero at distances of a few femtometres.
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. 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.”