Magnetic moment associated with electrons orbitting around the nucleus is given in terms of Bohr magneton $\left(\mu_{B}\right)$
$\mu_{B} = \frac{eh}{2m_{e}}$
e = electronic charge, me = electronic mass.
In nuclear physics, magnetic moments associated with the spins of protons and neutrons are expressed in nuclear magnetons $\left(\mu_{N}\right)$
$\mu_{N} = \frac{eh}{2m_{p}}$
$m_{p}$ = mass of a proton.
$\Rightarrow \, \frac{\mu_{B}}{\mu_{N}} = \frac{m_{p}}{m_{e}}$