# Mass difference due to electrical potential energy

The masses of protons and neutrons are different. Suppose a proton is a sphere with a uniformly positive charge distribution. Can the mass difference between protons and neutrons be due to the electrical potential energy of the protons? Justify your answer with a simple calculation.

I do not really know the relationship between potential energy and mass difference. Isn't the difference in mass of protons and neutrons due to their quarks? (the neutron is made of two down quarks and an up quark and the proton of two up quarks and a down quark.)

• Sep 29, 2020 at 10:38

The reason for mass difference is because a proton contains 2 down quarks and 1 up quark and a neutron contains 2 up quarks and 1 down quarks(you were right about that).And since an charge of up quark is $$+\frac{2}{3}$$ and the charge of a down quark is $$-\frac{1}{3}$$ they are totally different particles so they'll have different masses (even though they fall under the same sub group). If you look up on the standard model you'd see that the mass of a down quark is almost double of that of an up quark. So yeah the mass difference is because of the deference in mass of quarks. Besides in real life a proton shouldn't have a constant mass... quark and antiquark pairs pop in and out of existence inside a proton so that mass of a proton should be constantly changing(conservation of mass doesn't apply since at the quantum level mass and energy conservation is not obeyed. Instead they obey the law of conservation of mass-energy(the mass equivalent of energy + mass))