The mass equivalent of $931\, MeV$ energy is

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.

In a nuclear fission process,a nucleus $A$ divides into two nuclei $B$ and $C$. If their binding energies are ${E_a}$,${E_b}$,and ${E_c}$ respectively,which of the following relations is correct?

Binding energy of a certain nucleus is $18 \times 10^8 \ J$. How much is the difference between the total mass of all the nucleons and the nuclear mass of the given nucleus (in $\mu g$)?

We are given the following atomic masses:
$^{238}_{92}U = 238.05079 \; u$
$^{4}_{2}He = 4.00260 \; u$
$^{234}_{90}Th = 234.04363 \; u$
$^{1}_{1}H = 1.00783 \; u$
$^{237}_{91}Pa = 237.05121 \; u$
Here,the symbol $Pa$ represents the element protactinium $(Z=91)$.
$(a)$ Calculate the energy released during the alpha decay of $^{238}_{92}U$.
$(b)$ Show that $^{238}_{92}U$ cannot spontaneously emit a proton.

The mass defect for the nucleus of helium is $0.0303 \, a.m.u.$ What is the binding energy per nucleon for helium in $MeV$?