If ice homogeneously nucleates at $-39\mathrm{.}5C,$ calculate the critical radius given values of $-3\mathrm{.}1{10}^8\frac{J}{m^3}$ and $25{10}^{-3}\frac{J}{m^3},$ respectively, for the latent heat of fusion and the surface energy.

$($Give answer in units of ${10}^{-9}m)$