What are mass defect and binding energy of a nucleus? Calculate the binding energy per nucleon of ⁴₂He. (Nuclear mass 4.00151 u, mₚ = 1.00727 u, mₙ = 1.00866 u, 1 u = 931.5 MeV)

1. 1 · Define mass defect. ΔM = Zmₚ + Nmₙ − M: how much lighter the nucleus is than its free nucleons.
2. 2 · Define binding energy. Eb = ΔM c²: the energy needed to separate the nucleus into free nucleons.
3. 3 · Find the mass defect. ΔM = 2(1.00727) + 2(1.00866) − 4.00151 = 4.03186 − 4.00151 = 0.03035 u.
4. 4 · Convert to energy. Eb = 0.03035 × 931.5 MeV ≈ 28.3 MeV.
5. 5 · Find the value per nucleon. 28.3 MeV ÷ 4 ≈ 7.07 MeV per nucleon.
6. 6 · Close in one line. So, helium-4 is tightly bound, with about 7 MeV holding each nucleon.

Scoring tip: Keep five decimal places in the masses until the subtraction, or the small mass defect will come out wrong.