One group neutron diffusion calculation

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The discussion focuses on calculating the critical size of a cube made of 75% zirconium-91 and 25% plutonium-239 using one-group neutron diffusion approximation. Key parameters provided include the microscopic cross sections for capture, scattering, and fission, along with the densities and molecular weights of both materials. The geometric and material buckling equations are essential for determining the critical condition, where the material buckling (Bm) equals the geometric buckling (Bg). The surrounding vacuum is noted as a significant factor in the diffusion calculation. This analysis aims to establish the critical dimensions necessary for sustaining a nuclear reaction within the specified composition.
savana
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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
 
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Use the geometric and material buckling equations. When the cube is critical, Bm = Bg by definition.
 

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