\(M_n\) and \(M_p\) are the masses of a neutron and a proton. A nucleus of mass \(M\) has \(N\) neutrons and \(Z\) protons. The correct relation is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(M \lt (NM_n + ZM_p)\)
When nucleons come together to form a nucleus, energy is given out. This energy is the binding energy \( E_b=\Delta M c^2 \). Here the mass defect \( \Delta M \) is the total mass of the separate nucleons minus the mass of the nucleus.
Option (1) \(M \lt (NM_n + ZM_p)\) — Correct. The mass defect \( \Delta M=(NM_n+ZM_p)-M \) is positive for every bound nucleus. So the nucleus is lighter than its separate nucleons.
Option (2) \(M \gt (NM_n + ZM_p)\) — Incorrect. A heavier nucleus would have more energy than its free nucleons. It would not be bound and would break up by itself.
Option (3) \(M = (NM_n + ZM_p)\) — Incorrect. Equal masses give \( \Delta M=0 \) and so zero binding energy. Such a nucleus would not be held together.
Option (4) \(M = N(M_n + M_p)\) — Incorrect. This counts \( N \) protons instead of \( Z \). It also leaves out the mass defect.
NCERT (2026-27):
Summary – “7. The nuclear mass M is always less than the total mass, Σm, of its constituents. The difference in mass of a nucleus and its constituents is called the mass defect,”
\( \Delta M=(Zm_p+(A-Z)m_n)-M \)