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Homework Help: Calculating Cross Section from Neutron Absorption in a Gold Foil

  1. Jan 7, 2012 #1
    1. The problem statement, all variables and given/known data

    In an experiment carried out with a beam of thermal neutrons it is found that on traversing a 2mm thick foil of 197Au, some 70% of the neutrons are removed. What is the total thermal neutron cross-section for this isotope of gold? (Density of gold: 19300 kg m-3)

    2. Relevant equations

    1. N = N0 exp(-xnσ) - x is thickness, n is number of nuclei per unit volume, σ is cross section
    2. moles = mass/A
    3. n0 = Na x moles - Na is avagadros number, n0 is number of nuclei

    3. The attempt at a solution

    I have attempted this question and appear to have used the same method as in the solution given by the professor, but i get a different answer... Am i right?

    Firstly, to find n i substitute equation 2 into 3, giving n0 = (Na x m)/A

    Then i divide this by the volume: n = n0/V = (Na x m)/(A x V) = (Na/A) x ρ (ρ = density)

    Next i rearrange eqn 1: N/N0 = (70%)/(100%) = 0.7 = exp(-xnσ)

    This gives: σ = (-ln(0.7))/(xn)

    Now im not sure if i should be using m in grams or kilograms?

    My answer:
    σ = 3.02 x 10^(-30) m^2 = 0.0302 barns (using m in grams)
    σ = 3.02 x 10^(-27) m^2 = 30.2 barns (using m in kg)

    Neither of these answers matches the answer given, 102 barns....
    Even though my method is identical to the professors method (although he gives no intermediate results, so i dont know if/where i have gone wrong...)

    Any help is much appreciated.
    Last edited: Jan 7, 2012
  2. jcsd
  3. Jan 8, 2012 #2
    I don't seem to be able to edit my OP anymore, but i've realised i havent fully defined all the variables (units in brackets):

    . N is the number of particles remaining after the foil
    . N0 is the starting number of particles
    . x is thickness (m)
    . n is number of nuclei per unit volume (m^-3)
    . σ is cross section (m^2)
    . m is the mass (grams or kg?)
    . A is the mass number
    . Na is avagadros number
    . n0 is number of nuclei
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