The homogeneous nucleation of liquid copper takes place under an undercooling amount of $T=236$

$K$ resulting in spherical solid nuclei. Calculate : $(15$ points$)$

a$)$ the critical radius of the nucleus required; and

b$)$ the number of copper atoms in the nucleus. Assume that the lattice parameter of the solid FCC nickel

is $0\mathrm{.}365nm$ at $850C($larger than the room temperature value$).$

Given $.$ Melting point of copper, $T_m=1085C,$

Heat of fusion, $H_f=1628\frac{J}{c}{m}^2,$ solid$-$liquid interfacial energy, ${}_{SL}=1\mathrm{.}77{10}^{-5}\frac{J}{c}{m}^2$