Question

The Sun generates energy because of nuclear reactions that occur in its core. A sequence of reactions that do this is called the PP I chain (pronounced “p p one chain”). In the PP I chain, four protons fuse into a helium-4 nucleus and two positrons, since charge is conserved. Also emitted are two neutrinos, since angular momentum is conserved. The neutrinos have no charge and negligible mass. Assume all motion in the PP I chain is non-relativistic, except for the neutrinos. How many MeV of energy does one PP I chain generate? Include the energy generated by the positrons annihilating with electrons that must already be in the Sun, since the Sun is electrically neutral.

Answer 1

Write the reaction:

4 ¹H⁺ → ⁴He²⁺ + 2e⁺ + 2v_e

This reaction releases more than 20 MeV of energy:

$$E=\Delta mc^2,\\ \Delta m=4m_p-m_\text{He},\\ \Delta m=4\cdot1.67262158\cdot10^{-27}-6.6464731\cdot10^{-27}=\\ =4.401322\cdot10^{-29}\text{ kg}.\\ E=\frac{4.401322\cdot10^{-29}\cdot(3\cdot10^8)}{1.602\cdot10^{-19}}=24.7\text{ MeV}.$$