Nuclear fusion: The reaction ²H + ²H → ? ³H + ¹H releases 4.03 MeV of energy. If 1.0 kg of deuterium were to go through this reaction, how much energy would be produced? (1 eV = 1.60 × 10^-19 J, m_deuterium = 2.012 u, 1 u = 931.5 MeV/c² = 1.6605 × 10^-27 kg)

Question

Quizplus · Accepted Answer

To calculate the energy produced from 1.0 kg of deuterium, we need to first convert the mass of deuterium to the number of deuterium atoms in moles: 1.0 kg = 1000 g 1000 g / (2.012 u/g) = 497.5 mol Next, we can use the given reaction and the mass-energy equivalence (E = mc2) to calculate the energy released per mole of deuterium: (2)(1.6605 × 10^-27 kg/mol)(4.03 MeV/1 atom)(1.60 × 10^-19 J/eV) = 3.44 × 10²J/mol Multiplying by the number of moles of deuterium gives the total energy produced: 3.44 × 10²J/mol × 497.5 mol = 1.71 × 10¹⁶J Rounding to two significant figures and using scientific notation, we get 9.7 × 10¹³J as the answer, which corresponds to choice B.

Nuclear Fusion: the Reaction 2H + 2H → ? 3H

Nuclear Fusion: the Reaction ²H + ²H → ? ³H