Q-value Of Nuclear Reaction
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?
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Solution
3.27 MeV
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 12D+12D→23He+n, the reactant mass is 2×2.014102=4.028204 u and the product mass is 3.016029+1.008665=4.024694 u. The mass difference is Δm=4.028204−4.024694=0.003510 u. Multiplying, Q=0.003510×931.5≈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.
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About This Question
- Subject
- physics
- Chapter
- atoms and nuclei
- Topic
- q-value of nuclear reaction
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
3.27 MeV
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 12D+12D→23He+n, the reactant mass is 2×2.014102=4.028204 u and the product mass is 3.016029+1.008665=4.024694 u. The mass difference is Δm=4.028204−4.024694=0.003510 u. Multiplying, Q=0.003510×931.5≈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.
This hard difficulty physics question is from the chapter atoms and nuclei, covering the topic of q-value of nuclear reaction. It appeared in the 2025 exam.
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