# How does fusion work in the Sun if neutrons have more mass than protons?

According to my textbook, the next result of the fusion reactions in the Sun is: 4H -> He + neutrinos + gamma photons

However, if hydrogen atoms are basically a proton and helium atoms are 2 protons and 2 neutrons, how can this reaction work? Neutrons have more mass than protons so you would be getting more mass and energy than you put in.

Similarly, how can 4 hydrogen atoms have more mass than 1 helium atom (according to the periodic table)?

• The mass of a helium nucleus is the mass of the protons plus the mass of the neutrons minus the equivalent mass of the binding energy. – CuriousOne Sep 8 '15 at 22:37

The key is that the mass of a nucleus is not just the sum of the masses of its protons and neutrons. As a bound state, there is a binding energy associated with $^4\mathrm{He}$ that is not associated with the system of noninteracting $2n+2p$. There are different conventions on what sign to give this energy, but in the end $^4\mathrm{He}$ is less massive than $2n+2p$, and indeed even than $4p$, where we are freely going between mass and energy with $E = mc^2$.