Problem points$).$ Diffusion.

Diffusion in a pure element has been measured at $2$ temperatures $T_1$ and $T_2,$ yielding values $D_1$ and $D_2.$

Recall that the gas constant $R$~~$8\mathrm{.}3\frac{J}{m}o\frac{l}{K}.$

$($a$)$ Derive an equation for the activation energy of this diffusion process as a function of $T_1,T_2,D_1,$

and $D_2.$

$($b$)$ The temperatures were $T_1=600K$ and $T_2=300K,$ and it was found that $D_1=D_2$exp$(10).$

Calculate the value of the activation energy, $Q.$

$($c$)$ Propose and discuss an experiment that would allow you to determine whether atomic diffusion

proceeds by vacancy diffusion in the above material.

$($d$)$ Assume now that this experiment indeed established that atomic diffusion is mediated by vacancy

jumps. How is $Q$ related to physical properties of vacancies in that material?