# Homework Help: Electron impact ionization cross section

1. Mar 23, 2015

### gothloli

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. Mar 23, 2015

### Quantum Defect

What are your pressure units? Useful Rule of Thumb: Number density = 3.0 x 10^16/(cc-Torr)

3. Mar 23, 2015

### gothloli

The pressure is in Pa, in torr it is 1.07 x 10-5, how do you get that value for the number density?

4. Mar 23, 2015

### Quantum Defect

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

5. Mar 23, 2015

### gothloli

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+

6. Mar 23, 2015

### gothloli

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.

7. Mar 23, 2015

### Quantum Defect

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