A bare cubic reactor with a side length of $a$ is to be constructed of a homogeneous

mixture of graphite and $U-235$ with a fuel concentration of $0\mathrm{.}015\frac{g}{c}{m}^3.$ The reactor is to be

operated at room temperature.

a$)$ Find the geometric buckling of the reactor in terms of a$.$ You can neglect the extrapolation

distance. You have to write the related differential equation in $3$D along with the related

conditions and solve the differential equation.

b$)$ Find the critical mass.

Microscopic absorption cross$-$section of $U-235$ at $0\mathrm{.}0253eV{}_{a25}(E_0)=687$ barns