One group neutron diffusion calculation

[savana]

i need a help in solving ,using 1 group approxmation , estimate the critical size of cube consisting of 75% zirconium-91 and 25% plutonium--239 by volume , when the cube is surrounded by a vacumm.

zr-91
microscopic cross section (capture)=0.00335
microscopic cross section (scattering )=5.89
density=6.4 g/cm3
Mass=90.9056 g/mol

pu-239
v=2.98 n/fission
microscopic cross section (fission)=1.81
microscopic cross section (capture)=0.05
microscopic cross section (scattering )=7.42
density=19 g/cm3
Mass=239.0522 g/mol

 

[QuantumPion]

Use the geometric and material buckling equations. When the cube is critical, Bm = Bg by definition.