Consider solidification of manganese. The melting temperature of $Mn$ is $1250C,$ the solid$-$liquid interfacial energy is $0\mathrm{.}216J{m}^{-2}$ and the latent heat of fusion can be approximated with Richard's rule. Nucleation at the container wall is observed to occur at $1210C.$ The vibrational frequency of atoms is $\frac{{10}^{11}}{s},$ the molar volume of solid $Mn$ is $7\mathrm{.}4c{m}^3$ and the volume change during solidification is $5\%.$ Calculate the ratio of the activation energy for heterogeneous nucleation to that for homogeneous nucleation. Determine the radius and volume of the critical nucleus.