The constancy of the binding energy per nucleon in the range \( 30 \lt A \lt 170 \), where A is the mass number shows that:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Nuclear force is short ranged
The binding energy per nucleon \( E_{bn} \) is nearly constant (about 8 MeV) for mass numbers between 30 and 170. This is the saturation of the nuclear force.
A constant \( E_{bn} \) means that each nucleon interacts only with a few nearest neighbours, however large the nucleus is. Its binding energy therefore does not depend on how many nucleons are present, which shows that the nuclear force is short ranged.
Why the other options are incorrect
Option (1) Nuclear force is attractive — Incorrect. The force is attractive, but the sign alone does not explain the constancy.
Option (3) Nuclear force is very strong — Incorrect. The strength of the force sets the size of \( E_{bn} \) (about 8 MeV), not its constancy from one nucleus to another.
Option (4) Nuclear force is long ranged — Incorrect. A long-range force would make the binding energy per nucleon increase with A.
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 Binding Energy – “… The property that a given nucleon influences only nucleons close to it is also referred to as saturation property of the nuclear force.”