PROBLEM 5. Uranium-233 is uniformly dispersed in Li2BeF molten salt. The ratio o
ID: 3308028 • Letter: P
Question
PROBLEM 5. Uranium-233 is uniformly dispersed in Li2BeF molten salt. The ratio of Be to U-233 atoms is NeNu23 500 and the density of this mixture is 2.15 g / cm3. Microscopic cross sections for fluorine are .= 4.0 barns and 9.6 x 10-3 barns. Lithium in the mixture is 100% enriched in Li-7 a) What are the atomic densities of beryllium, fluorine, and U-233 atoms? b) Determine macroscopic absorption cross section of U-233 atoms oEstimatethe muacrocc as etion f florin atomns d) Calculate the rate of U-233 fission reactions in cm3 s neutrons / s-cm2. if the thermal flux is 2.5 x 1013Explanation / Answer
mass number of Be -7
Li - 6
, F - 19 U -233
for every 1 U-233 atoms there are 500 Be atoms , 1000 Li atoms and 2000 F atoms in the mixture.
Moelcular weight of the mixture = 233+1000*6+500*7+2000*19 = 47233
1 mole of any substance contains Na = 6.02E+23 molecules
Density of the mixture = 2.5 gm/cc
for every 3501,The mixture contains
1 U-233 atom
1000 Li
500 Be
2000 F
Atomic density of U-233 in the mixture = 2.5*0.602E+23/47233 *(1/3501) = 9.101E+14
Be = 4.551 E+17/cc
Li = 9.101 E+17/cc
F = 1.820 E+18 /cc
b) absorption cross section of U-233 = 506 b
Macroscopic absorption cross section of U-233 = 506E-24 *9.101 E+14 = 4.605 E-7 /cm
c) microscopic scattering cross section for F = 4.0E-24 *1.82E+18 = 7.28E-6 /cm
d) U-233 fission cross section = 464 b
macroscopic fission cross section = 464E-24 * 9.101E+14 = 4.223E-7 /cm
Thermal neutron flux = 2.5E+13 nuetron /s-cm2
number of nuetrons causing fission = 2.5E+13 (1- exp( -4.223E-7) )
= 1.056E+7 /s , fission reaction rate.
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