A.) Calculate the macroscopic
A.) Calculate the macroscopic cross section for the reaction ofnatural uranium with thermal neutrons. [abundances: 234 U=0.000054; 235 U= 0.007204; 238 U= 0.992742]
B.) The net efficiency of a 1000 MW reacotr is 34.1%. Estimatethe amount of 235 U consumed in one day. [theta(y)= 98.8;theta(f)=582.6]
Answer:
A) Macroscopic cross-section (S macro)represents theeffective target area of all the nuclei present in the volume ofthe material which is expressed in cm-1 orm-1.
It is usually derived from microscopic cross-section (i.e.,absorption cross section, σa) and atomic number density(Nv).
From the given data; abundancy of 234 nuclei =χ234 =0.000054; χ235 = 0.007204; χ238=0.992742
Atomic number density of U= ρU = 18.95g/cm3
NA = 6.022137 x 1023 mole-1;MU = 238.03 g/mole; barn = 10-28m2
Nv = (ρU /MU) x NA
=
6.022×1023/mol
= 4.794 x 1023 cm-3
S macro = Nv x (χ234 x σ234 +χ235 x σ235 + χ238 xσ238)
= 4.794 x 1023 cm-3 (0.000054 x 100 +0.007204 x 678.5 + 0.992742 + 2.71)b
S macro = 36.4 x 1023 cm-3 b
= 36.4 x 1023 cm-3 x 10-28m2
= 36.4 m-1
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