Kinetic Theory: How many molecules enter pinhole in vacuum?

[Lagraaaange]

Homework Statement

Pressure in vacuum is 10^-3 Torr. External Pressure is 1atm and 300K. Pinhole of 10^-10cm^2 made in vacuum. Assuming all molecules striking hole pass through, how many molecules leak into vacuum in 1hour?
Answer: 10^17 molecules

Homework Equations

Flux = <v>*N/4V
Rate = Flux times A

The Attempt at a Solution

I can make an DE: dN/dt = <v>N/4V*A and solve this but I have no info on N0, initial molecules. I also don't have volume. So I don't see how to obtain a numerical result.

 

[PietKuip]

Ask yourself what pressure is.

 

[mfb]

You only need N/V, molecules per volume, which you can get with the given information.
Alternatively, take an arbitrary volume, it will cancel out in the calculations anyway.

 

[Lagraaaange]

I don't see how I can get this with the information

You only need N/V, molecules per volume, which you can get with the given information.
Alternatively, take an arbitrary volume, it will cancel out in the calculations anyway.

P/kT = N/V = 2.45molecules/m^3 = ρ
Also <KE> = 3/2KT = 6.21E-21J = m/2 *<v^2>.
Now particles within vΔt make it to hole; also those within AvΔtρ make it.
Now I'm stuck. I can't get v since I don't have m. Also I'm unsure whether to invoke a Maxwell Distribution to get all velocities.

 

[TSny]

Looks like they are only asking for an order-of-magnitude answer. So, you can use any reasonable value for the mass of a molecule.