Question

Based on conservation laws, how does the mass of the neutron compare to the mass of the proton?

Answer 1

The mass of a neutron is slightly greater than the mass of a proton.

Mass of neutron, `m_n = 939.57 (MeV)/c^2`
Mass of proton, `m_p = 938.28 (MeV)/c^2`

This can be understood as follows,

A neutron `n` can undergo a decay given my -

`n -> nu + p^+ + e^-` wherein it forms a proton `p^+` and an electron `e^-`.

Also there is formation of a neutrino `nu` in order to address conservation of spin.

Electrons and Neutrinos carry mass (although much less than mass of proton) thus it seems pretty logical to from conservation arguments to see that mass of the neutron must be greater than mass of the proton since it decays itself to form a proton (plus other mass particles).