Engineering Calculating the percent composition of weight of an alloy

AI Thread Summary
To calculate the percent composition of an alloy, the user has gathered the densities and atom densities of iron and carbon, along with their macroscopic scatter and absorption cross sections. They express confusion about how to proceed with determining the gram atomic weight of the alloy and the necessary ratios for weight percent calculation. The user seeks clarification on the terms "a," "s," and "b" related to the cross sections. They are looking for guidance on how to obtain the number density for their calculations. The discussion highlights the challenges faced by those unfamiliar with metal properties and calculations.
shreddinglicks
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Homework Statement
There is an alloy:
ρ=7.64 g/〖cm〗^3
Σ_a=.205 〖cm〗^(-1)
Σ_s=.956〖cm〗^(-1)

It has properties of two elements:
iron
M = 55.84 g/mol
σ_a=2.56 b
σ_s=11.2 b

carbon
M = 12 g/mol
σ_a=.0035 b
σ_s=5.55 b

Find the percent composition by weight of iron and carbon in the alloy.
Relevant Equations
Σ=σN eq 1
N=(ρN_a)/M eq 2
I found the density of carbon and iron:
ρ_fe=7.87 g/〖cm〗^3
ρ_c=2.26 g/〖cm〗^3

Using equation 2:
atom density of iron and carbon

N_fe = 8.48e22 cm^-3
N_c = 1.13e23 cm^-3

Using equation 1:
macroscopic scatter and absorption cross sections of iron and carbon

Σ_a,fe = .217 cm^-1
Σ_s,fe = .949 cm^-1

Σ_a,c = 3.95e-4 cm^-1
Σ_s,c = .627 cm^-1

I'm lost. I think I need to get the gram atomic weight of the alloy and do a ratio:

M_i/M_alloy

to get the weight percent. I need the number density to do that and I don't see a clear way of getting it. Or maybe my approach is completely wrong.
 
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σ_a=2.56 b
σ_s=11.2 b

I am a layman on metal. Could you tell me what a, s, and b are ?
 
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