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Electron impact ionization cross section

  1. Mar 23, 2015 #1
    1. The problem statement, all variables and given/known data
    I want to find the ionization cross section in a mass spectrometer for the gas Argon.
    The value obtained should be in the 2x10-16 cm2 range.

    2. Relevant equations
    Q = ionization cross section
    I = K(V,B)xNxQxdxIe
    Where I = (0.17 x 10-11, K(V,B) =1, d = 0.1 cm, and Ie = 5 x 10-5 Amperes, the trouble is finding N. N is the gas density, but I'm not sure what units it's in.

    3. The attempt at a solution
    To
    find N, you could use the ideal gas law, PV = nRT, The pressure is known as 1.44x10-3
    To find N I said that N = P(Avogadro's constant)/ RT
    where R = 8.314x106, for it to be in cm3, and T is room temperature in kelvins.
    The value I get from this is 9.5x10-19, which is too small. Is there something I'm missing here, I need to get in the 10-16 range.
     
  2. jcsd
  3. Mar 23, 2015 #2

    Quantum Defect

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    What are your pressure units? Useful Rule of Thumb: Number density = 3.0 x 10^16/(cc-Torr)
     
  4. Mar 23, 2015 #3
    The pressure is in Pa, in torr it is 1.07 x 10-5, how do you get that value for the number density?
     
  5. Mar 23, 2015 #4

    Quantum Defect

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    n = PV/RT


    P = 1/760 atm
    V = 1cm^3 = 10^-3 l
    R = 0.0821 l-atm/K-mol
    T = 298 K (25 C)

    n = 5.38 x 10^-8 mole/cc-Torr => 3.24 x 10^16 /cc-Torr (I misremembered the 3.0, it should be 3.2)

    So, with your P, you should have 3.47 x 10^11/cc
     
  6. Mar 23, 2015 #5
    I calculated, and I get that value for the number density as well. N = P/kT, if you use Boltzmann constant. But with this value, the cross section is 5.71 x 10-18, which is more like the cross section for Ar2+, and not Ar+
     
  7. Mar 23, 2015 #6
    To get the right value, I had to use the partial pressure of the gas, not the whole pressure in the system. So changing the pressure works.
     
  8. Mar 23, 2015 #7

    Quantum Defect

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    Good. The number density needs to be the number density of the thing you are measuring.
     
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