Electron impact ionization cross section

[gothloli]

Homework Statement

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.

Homework Equations

Q = ionization cross section
I = K(V,B)xNxQxdxI_e
Where I = (0.17 x 10^-11, K(V,B) =1, d = 0.1 cm, and I_e = 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.

The Attempt at a Solution

To[/B] 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.

 

[Quantum Defect]

Homework Statement

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.

Homework Equations

Q = ionization cross section
I = K(V,B)xNxQxdxI_e
Where I = (0.17 x 10^-11, K(V,B) =1, d = 0.1 cm, and I_e = 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.

The Attempt at a Solution

To[/B] 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.

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

 

[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?

 

[Quantum Defect]

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

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

 

[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+

 

[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.

 

[Quantum Defect]

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.

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