$15\mathrm{.}8$ Consider the nucleation rate, I, on freezing. It is normally assumed that the vibration rate of the atoms in solids is about ${10}^{13}$Hertz. Assume that in the case of copper, the energy barrier, that an atom passes over in going from a liquid to the solid is about $4\mathrm{.}8{10}^{-20}J$

$($a$)$ What is the nucleation rate per mole of copper when the supercooling is $264$ degrees?

$($b$)$ Discuss the significance of the answer to part $($a$)$ of this question.