One group neutron diffusion calculation

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SUMMARY

This discussion focuses on calculating the critical size of a cube composed of 75% zirconium-91 and 25% plutonium-239 using one-group neutron diffusion approximation. The relevant parameters include the microscopic cross sections for capture, scattering, and fission for both isotopes, as well as their respective densities and molar masses. The geometric and material buckling equations are essential for determining the critical dimensions, where the condition Bm = Bg must be satisfied for criticality.

PREREQUISITES
  • Understanding of one-group neutron diffusion theory
  • Familiarity with geometric and material buckling equations
  • Knowledge of microscopic cross sections for nuclear materials
  • Basic principles of nuclear reactor physics
NEXT STEPS
  • Study the derivation and application of geometric and material buckling equations
  • Research the neutron diffusion equation in nuclear reactor design
  • Explore the properties and applications of zirconium-91 and plutonium-239 in nuclear systems
  • Learn about criticality safety assessments in nuclear engineering
USEFUL FOR

Nuclear engineers, reactor physicists, and students studying nuclear reactor design and safety will benefit from this discussion.

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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