Calculate the consumption rate of uranium atoms in UO2 fuel

Calculate the consumption rate of uranium atoms in UO2 fuel that is 5 percentage by weight enriched in U-235 and is exposed to a thermal neutron flux of 10 14 n/cm2s. Density of 5 percentage - enriched UO2 is 11 g/cm3.

Solution

UO₂ contains U-235 and U-238 atoms and O₂ molecules.

absorption cross sections are

U-235   ^U235 = 591 b

U-238 ^U238   = 2.42 b

O-16   = 4.0

enirchment is 5%

corss section of U = 591*0.05 +2.42*0.95 = 31.85 b

corss section of O₂  = 2*4.0 = 8b

corss section of UO₂ = 31.85 + 8 = 39.85 b

density of UO₂ = 11.0

Avgadro number N_A = 0.6023 e-24

1 b= e-24 cm

macrosocpic cross section UO₂ å = (11*0.6023e-24/238+2*16)*39.85e-24

                                                                        = 0.78 cm^-1

Neutron flux = 10¹⁴ n/cm²

neutrons aborbed = 0.78*10¹⁴ = 7.8e+13 /cm

for every neutron abosrbed one U atom is consumed.

Consider a cube of 1 cc of uranium it will have

11*0.6023e+24/238 atoms out of which 7.8 e+13 will abosrb a neutron from the flux and undergo nuclear reaction and are consumed

the consumtion rate = 7.8e+13/0.0278e24

                                        = 2.8e-9 /s