Q-value Of Nuclear Reaction

Question

Two deuterium nuclei fuse to form a helium-3 nucleus and a free neutron. Using masses deuterium 2.014102 u, helium-3 3.016029 u, and neutron 1.008665 u, what is the energy released (Q-value) in this fusion reaction?

RankGuru · Accepted Answer

The Q-value of a nuclear reaction equals the net mass lost, multiplied by $931.5$ MeV/u, and a positive value means energy is released. For the reaction $^2_1	ext{D} + {}^2_1	ext{D} ightarrow {}^3_2	ext{He} + n$, the reactant mass is $2 	imes 2.014102 = 4.028204$ u and the product mass is $3.016029 + 1.008665 = 4.024694$ u. The mass difference is $\Delta m = 4.028204 - 4.024694 = 0.003510$ u. Multiplying, $Q = 0.003510 	imes 931.5 \approx 3.27$ MeV. The value 17.6 MeV belongs to the different deuterium-tritium fusion reaction and is not relevant here. The value 4.03 MeV mistakes the total reactant mass number for an energy. The value 0.0035 MeV forgets to convert the mass defect using the 931.5 MeV/u factor. A positive Q-value classifies the reaction as exothermic, releasing energy, whereas a negative Q-value would mean energy must be supplied for the reaction to occur; fusion of light nuclei such as deuterium is precisely the energy source that powers stars. This applies the NCERT mass-energy method for reaction energetics. A plausibility check confirms the answer is positive and of the order of a few MeV, the expected scale for a light-nucleus fusion releasing energy.

Q-value Of Nuclear Reaction

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