The free energy change of a system upon nucleation of a spherical solid particle of radius r from a liquid may be expressed as:

$$G$=(4/3)*(\backslash$pi r$^3)*$G$^$solid$+(4\backslash$pi r$^2)*\backslash$gamma

where $$G$^$solid is the free energy per unit volume of the solid phase relative to the liquid phase, and $\backslash$gamma is the interfacial energy between the solid and liquid phases $($and is always positive$).$ Assume that we are in a temperature regime for which $$G$^$solid$<0$

a$.$ Find what is called the critical radius rc$,$ at which d$($G$)/$dr$=0$

b$.$ Explain why the critical radius is a good name for this quantity, in terms of the stability, instability, or metastability of particles with r $>$rc and particles with r