From the binding energy curve, which of the following is true?

The correct answer is Option (1) → The greater the binding energy, the less is the total mass of a bound system.

The binding energy \( E_b \) of a nucleus is the energy equivalent of its mass defect. The mass defect is the amount by which the nucleus is lighter than its separate nucleons.

    \( E_b=\Delta M\,c^{2} \)

    \( \displaystyle M=[Zm_p+(A-Z)m_n]-\frac{E_b}{c^{2}} \)

Option (1) The greater the binding energy, the less is the total mass of a bound system. — Correct. A greater \( E_b \) means a larger mass defect, so the bound system is lighter than the same nucleons would be if they were free.

Option (2) The greater the binding energy, the more is the total mass of a bound system. — Incorrect. Binding lowers the mass. The nucleus is always lighter than its constituents, and more so when the binding energy is greater.

Option (3) Binding energy has no correlation with the mass of the bound system. — Incorrect. By Einstein’s relation \( E_b=\Delta M\,c^{2} \), the mass defect of the system fixes its binding energy.

NCERT (2026-27):
Nuclear Energy – “… Now, the greater the binding energy, the less is the total mass of a bound system, such as a nucleus.”