The energy released in the fusion of four protons into doubly ionized helium (also known as helium-4 or alpha particle) can be estimated using the principles of nuclear physics and the concept of mass-energy equivalence.
The fusion reaction that occurs in the Sun and other stars is known as the proton-proton chain. The first step of this chain involves the fusion of two protons to form deuterium, a nucleus consisting of one proton and one neutron:
2 protons → deuterium + positron + neutrino
The reaction continues with the fusion of another proton with deuterium to produce a helium-3 nucleus:
proton + deuterium → helium-3 + photon
Finally, two helium-3 nuclei combine to form a helium-4 nucleus (doubly ionized helium), releasing two protons in the process:
helium-3 + helium-3 → helium-4 + 2 protons
The net reaction, combining the steps above, can be represented as:
4 protons → helium-4 + 2 protons + energy
To estimate the energy released in this fusion process, we can utilize Einstein's famous equation, E = mc², which relates energy (E) to mass (m) and the speed of light (c). The energy released is equivalent to the mass defect, which is the difference in mass between the initial particles (four protons) and the final products (helium-4 and two protons).
The mass of four individual protons is greater than the mass of a helium-4 nucleus and two protons combined. The difference in mass, multiplied by the square of the speed of light, gives the energy released.
It is important to note that the actual calculation of this energy release involves complex nuclear physics equations, considering factors like nuclear binding energies, reaction rates, and temperature. The precise value can be obtained through detailed nuclear models and experimental data.