The diffusivity of nickel $($Ni$)$ atoms in a solid face$-$centered cubic $($FCC$)$ iron lattice is $1\mathrm{.}0{10}^{-13}\frac{m^2}{s}$ at $1300C$ and $1\mathrm{.}0{10}^{-16}\frac{m^2}{s}$ at $1000C.$ The average activation energy for the diffusion of $Ni$ atoms in the FCC iron lattice is most nearly

A$.280k\frac{J}{m}ol$

B$.380k\frac{J}{m}ol$

C$.580k\frac{J}{m}ol$

D$.880k\frac{J}{m}ol$