Einstein's mass-energy relation emerging out of his famous theory of relativity relates mass $(m)$ to energy $(E)$ as $E = mc^2$,where $c$ is the speed of light in vacuum. At the nuclear level,the magnitudes of energy are very small. The energy at the nuclear level is usually measured in $MeV$,where $1\,MeV = 1.6 \times 10^{-13}\,J$; the masses are measured in unified atomic mass unit $(u)$,where $1\,u = 1.6605 \times 10^{-27}\,kg$.
$(a)$ Show that the energy equivalent of $1\,u$ is approximately $931.5\,MeV$.
$(b)$ $A$ student writes the relation as $1\,u = 931.5\,MeV$. The teacher points out that the relation is dimensionally incorrect. Write the correct relation.