PROBLEM $3.$

The Lady$-$Godiva sphere is made of uranium that is $90\%$ enriched in U$-235.$ The density of this fuel is $18\mathrm{.}75\frac{g}{c}{m}^3.$

a$)$ Calculate neutron reproduction factor for this uranium composition.

b$)$ Determine infinite neutron multiplication factor of the assembly.

c$)$ What is the diffusion length of fast neutrons in this fuel?

d$)$ Determine neutron nonleakage factor and effective multiplication factor of the assembly that has a mass of $45kg.$

e$)$ What should be the radius of the assembly to make it critical?