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If M(A, Z), Mₚ and Mₙ represent, respectively, the mass of the nucleus ^(A)_(Z)X, the proton mass and the neutron mass, all expressed in atomic mass units (1 u = 931.5 MeV/c²), and BE denotes the binding energy in MeV, which relation is correct?

1. M(A, Z) = ZMₚ + (A - Z)Mₙ - BE/c²
2. M(A, Z) = ZMₚ + (A - Z)Mₙ + BE
3. M(A, Z) = ZMₚ + (A - Z)Mₙ - BE
4. M(A, Z) = ZMₚ + (A - Z)Mₙ + BE/c²

Correct answer: M(A, Z) = ZMₚ + (A - Z)Mₙ - BE/c²

Solution

Binding energy is released when nucleons bind, so the nuclear mass is less than the sum of constituent masses by BE/c^2: M(A,Z) = ZMp + (A-Z)Mn - BE/c^2.

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