Show all work so I can better understand how to master this topic. I included constants in case you need them.
Problem 5
An experimental cylindrical reactor of one meter (1-m) diameter and 1-m height is outputting 500-kW of thermal power. The reactor is composed of graphite with U-235 randomly impregnated throughout to a density of N23s = Nc/1000, with a graphite (carbon) number density of Nc-12=8.31022/cm3.
(a) What is the average neutron flux for this reactor?
Rieak = Rg L2 B2
(c) What is the neutron leakage rate and non-leakage probability?
Potentially useful numbers:
σU-235=98.8 b U235=582.6 b C=0.0035b The transport mean-free-path for carbon is Ar=2.72 cm
Conversion that may come in handy:
1 eV = 1.602 x 10-19 J 1 amu = 931.49 MeV N = 6.022 x 1023 atoms/mol 1 tonne = 1000 kg 1 Ci = 3.7101 Bq 1 Gy = 100 rad 1 Sv = 100 rem Recoverable energy from 1 fission process: 190 MeV NRC occupational exposure limit: 5 rem/y.
Potentially useful atomic masses
Isotope Atomic mass (u) Proton 1.007276466879 Neutron 1.00866491585 H-1 1.00782503223 H-2 2.01410177812 He-4 4.00260325413 O-16 15.99491461957 U-235 235.043930131 U-238 238.050788423
Radiation Quality Factors
Type of Radiation QF X-rays, gamma rays beta particles 1
alpha particles 20 thermal neutrons (1 keV) 2 fast neutrons (1 MeV)