Consider the nuclear reaction ${}^{14}_{7}$ N + ${}^{4}_{2}$ He → ${}^{17}_{8}$ O + ${}^{1}_{1}$ H.The known atomic masses are ${}^{14}_{7}$ N: 14.003074 u ${}^{4}_{2}$ He: 4.002603 u ${}^{1}_{1}$ H: 1.007825 u ${}^{17}_{8}$ O: 16.999131 u What is the Q-value (or reaction energy)of this reaction? (1 u = 931.5 MeV/c²)

Question

Quizplus · Accepted Answer

The Q-value of a nuclear reaction is calculated by finding the difference in mass between the reactants and products and then converting this mass difference into energy using Einstein's equation $E = mc^2$, where $c$ is the speed of light. The mass of the reactants is $14.003074 \, \text{u} + 4.002603 \, \text{u} = 18.005677 \, \text{u}$, and the mass of the products is $16.999131 \, \text{u} + 1.007825 \, \text{u} = 18.006956 \, \text{u}$. The mass difference is $18.005677 \, \text{u} - 18.006956 \, \text{u} = -0.001279 \, \text{u}$, which is negative, indicating that the reaction is exothermic and energy is released. Converting this mass difference to energy, $0.001279 \, \text{u} \times 931.5 \, \text{MeV/u} = 1.191 \, \text{MeV}$. Since the mass difference is negative, the energy released is also negative, indicating an exothermic reaction. Therefore, the correct answer is -1.191 MeV.

Consider the Nuclear Reaction 714{}^{14}_{7}714​ N 24{}^{4}_{2}24​ He → 817{}^{17}_{8}817​ O 11{}^{1}_{1}11​

Consider the Nuclear Reaction ${}^{14}_{7}$ N ${}^{4}_{2}$ He → ${}^{17}_{8}$ O ${}^{1}_{1}$