The binding energy per nucleon of a nucleus is best described as

The correct answer is Option (3) → the average energy per nucleon needed to separate the nucleus into its nucleons

The binding energy \( E_b \) of a nucleus is the energy needed to separate it into its protons and neutrons. Dividing it by the mass number \( A \) gives the binding energy per nucleon, \( E_{bn}=E_b/A \).

Option (1) the energy needed to pull the least tightly bound nucleon out of the nucleus — Incorrect. One nucleon may be held more loosely or more tightly than the rest. \( E_{bn} \) is an average taken over all \( A \) nucleons.

Option (2) the total energy needed to break the nucleus up into all its separate nucleons — Incorrect. This is the binding energy \( E_b \) of the whole nucleus. It still has to be divided by \( A \).

Option (3) the average energy per nucleon needed to separate the nucleus into its nucleons — Correct. \( E_{bn} \) shares the total binding energy equally among the \( A \) nucleons.

Option (4) the energy given out per nucleon when the nucleus splits into two fragments — Incorrect. In fission the energy given out per nucleon is only the gain in \( E_{bn} \), about 0.9 MeV for a nucleus with \( A=240 \). The value of \( E_{bn} \) itself is about 7.6 MeV.

NCERT (2026-27):
Nuclear binding energy – “… We can think of binding energy per nucleon as the average energy per nucleon needed to separate a nucleus into its individual nucleons. …”