A summary of the nuclear reactions that power our sun is 4p → ⁴He + 2e^-,with masses of 938.272 MeV/c² for a proton,3727.38 MeV/c² for the helium nucleus,and 0.511 MeV/c² for each electron.How much energy is released by each of these reactions?

Question

Quizplus · Accepted Answer

The energy released in the reaction can be calculated using the mass-energy equivalence principle, $E = mc^2$, where $E$ is the energy released, $m$ is the change in mass, and $c$ is the speed of light. The mass of the reactants (4 protons) is $4 \times 938.272 \, \text{MeV/c}^2 = 3753.088 \, \text{MeV/c}^2$. The mass of the products (1 helium nucleus + 2 electrons) is $3727.38 \, \text{MeV/c}^2 + 2 \times 0.511 \, \text{MeV/c}^2 = 3728.402 \, \text{MeV/c}^2$. The difference in mass ($\Delta m$) is $3753.088 \, \text{MeV/c}^2 - 3728.402 \, \text{MeV/c}^2 = 24.686 \, \text{MeV/c}^2$, which is the energy released by the reaction, approximately 24.69 MeV.

A Summary of the Nuclear Reactions That Power Our Sun