An alloy is composed of elements A (78%) and B (12%) by weight. The density of t
ID: 1051679 • Letter: A
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
a (barns)
s (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.
Element
Gram Atomic Weight
a (barns)
s (barns)
A
22.1999
0.19
1.38
B
25.0055
0.21
2.44
Explanation / Answer
To calculate the atom density of a substance use :- N * NA / M
Where : M = gram atomic weight
N = atom density (atoms/cm )3 = density (g/cm )3
NA = 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. is related to the microscopic cross section by the relationship shown below.
= N
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