A deuterium nucleus and a tritium nucleus undergo the fusion reaction D + T → ⁴₂He + n. The measured masses are M(D) = 2.0141 u, M(T) = 3.0160 u, M(He) = 4.0026 u and M(n) = 1.0087 u. Take 1 u·c² = 931.5 MeV. If the released energy is N MeV, rounded to the nearest integer, find N.
Physics · Nuclear physics · nuclear fission and fusion ,nuclear reactor
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Question

A deuterium nucleus and a tritium nucleus undergo the fusion reaction D + T → ⁴₂He + n. The measured masses are M(D) = 2.0141 u, M(T) = 3.0160 u, M(He) = 4.0026 u and M(n) = 1.0087 u. Take 1 u·c² = 931.5 MeV. If the released energy is N MeV, rounded to the nearest integer, find N.

Physics · Nuclear physics · nuclear fission and fusion ,nuclear reactor

G1 Physics · Accepted Answer

Initial mass: M(initial) = M(D)+M(T) = 2.0141+3.0160 = 5.0301 u. Final mass: M(final) = M(He)+M(n) = 4.0026+1.0087 = 5.0113 u. Mass defect: Δm = M(initial)−M(final) = 5.0301−5.0113 = 0.0188 u. Energy released: Q = Δm·c² = 0.0188×931.5 = 17.5122 MeV. Rounded to the nearest integer, Q ≈ 18 MeV. Hence N = 18.