Question

A.) Calculate the macroscopic cross section for the reaction of natural 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%. Estimate the amount of 235 U consumed in one day. [theta(y)= 98.8; theta(f)=582.6]

Answer 1

A) Macroscopic cross-section (S _macro)represents the effective target area of all the nuclei present in the volume of the material which is expressed in cm^-1 or m^-1.

It is usually derived from microscopic cross-section (i.e., absorption cross section, σ_a) and atomic number density (N_v).

From the given data; abundancy of 234 nuclei =χ₂₃₄ = 0.000054; χ₂₃₅ = 0.007204; χ₂₃₈=0.992742

Atomic number density of U= ρ_U = 18.95 g/cm³

N_A = 6.022137 x 10²³ mole^-1; M_U = 238.03 g/mole; barn = 10^-28 m²

N_v = (ρ_U /MU) x N_A

= 6.022 x10²³/mol

= 4.794 x 10²³ cm^-3

S _macro = Nv x (χ₂₃₄ x σ₂₃₄ + χ₂₃₅ x σ₂₃₅ + χ₂₃₈ x σ₂₃₈)

                 = 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^-28 m²

                = 36.4 m^-1