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Mₙ denotes the mass of a proton and Mₐ that of a neutron. A given nucleus, of binding energy B, contains Z protons and N neutrons. The mass M(N, Z) of the nucleus is given by (c is the velocity of light):

1. M(N, Z) = NMₐ + ZMₙ + B/c²
2. M(N, Z) = NMₐ + ZMₙ − B/c²
3. M(N, Z) = NMₐ + ZMₙ + ZMₐ − B/c²
4. M(N, Z) = NMₐ + ZMₙ + ZMₐ − B/c²

Correct answer: M(N, Z) = NMₐ + ZMₙ − B/c²

Solution

The mass of a nucleus is less than the sum of the masses of its constituent protons and neutrons due to the binding energy, which is released when the nucleus is formed. This energy corresponds to a mass defect, given by B/c², and is subtracted from the total mass of the nucleons.

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