The units of magnetic moment are

In the study of subatomic particles, a magneton—a unit of magnetic moment—is utilised. It is created by multiplying a magnet's pole strength by the distance between its poles. The Bohr magneton, which bears the name of Danish physicist Niels Bohr from the 20th century, measures approximately $9.274\times {10}^{-21}$ erg per gauss per particle. 

The nuclear magneton is equal to 1/1,836 Bohr magneton when computed using the proton's mass rather than the electron's, as was done for the Bohr magneton.

Hence, the correct option ( C).