Question

An alloy is composed of elements A (78%) and B (12%) by weight. The density of the alloy is 1.95 g/cm³. The properties of these elements are shown below:

Element	Gram Atomic Weight	σa (barns)	σs (barns)
A	22.1999	0.19	1.38
B	25.0055	0.21	2.44

Determine:

The atom densities for the two elements.

The atomic density for element A:

              b. The absorption and scattering macroscopic cross sections for thermal neutrons.

              c. The mean free paths for absorption and scattering.

Answer 1

1. The atom density is the number of atoms of a given type per unit volume of the material.

To calculate the atom density of a substance use :- N * N_A / M

Where : M    =   gram atomic weight

N =   atom density (atoms/cm )³ =   density (g/cm )³

^{N_A =   Avogadro's number (6.022 x 1023 atoms/mole)}

The atomic density for element A = 1.521 * 6.022 x 10²³ / 22.1999

= 0.4125 x 10²³ (g/cm )³

b. Use this atom density to calculate the macroscopic cross section.

The macroscopic cross section is the probability of a given reaction occurring per unit travel of the neutron. Ʃ is related to the microscopic cross section by the relationship shown below.

Ʃ = Nσ