$($LSN$4)$ A notional spherical weapon assembly composed of pure U$-235$ has a mass of $8\mathrm{.}30kg$ and a density of $48\mathrm{.}5\frac{g}{c}{m}^3.$ Assume the non$-$leakage probability is $0\mathrm{.}515.$

a$.$ Calculate the multiplication factor and the "reactor period" of the assembly.

b$.$ Repeat this calculation for U$-233$ and TH$-232$ using the same initial conditions$/$assumptions$.$

c$.$ Based ONLY on these data points $($multiplication factor and reactor period$),$ argue which assembly $($material$)$ will develop the most yield, the second most yield, and the third most yield $45$ microseconds after initiation.