Calculate the energy for vacancy formation in nickel $($Ni$),$ given that the equilibrium number of vacancies at $1123K$ is $4\mathrm{.}7{10}^{22}$ ato $m\frac{s}{m^3}.$ The atomic weight and density $($at $1123K)$ for Ni are, respectively, $58\mathrm{.}69\frac{g}{m}ol$ and $8\mathrm{.}80\frac{g}{c}{m}^3.$

a$.$ Write the relevant equation for calculating the equilibrium vacancy concentration.

b$.$ Rearrange the equation to solve for activation energy

c$.$ Write the relevant equation for calculating the total number of atomic sites in $Ni$

d$.$ Calculate the total number of atomic sites in Ni$.$ Your answer should be in units of atoms $\frac{?}{m^3},$

e$.$ Calculate the vacancy formation energy.