If ice homogeneously nucleates at $-20\mathrm{.}1C,$ calculate the critical radius given values of $-3\mathrm{.}1{10}^8\frac{J}{m^3}$ and $25{10}^{-3}\frac{J}{m^2},$ respectively, for the latent heat of fusion and the surface free energy.

${10}^{-9}m$