- #1

shreddinglicks

- 212

- 6

- 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.

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.