Velocity distribution of atoms

[Niles]

Hi

Say I have a container (e.g. an oven) with some atoms in it. It the container, there is an opening, from which the atoms go into a rectangular container and then continue to the rest of the experiment. The beginning of my setup is shown in the attached sketch.

My problem is that I wish to find the transverse and longitudinal velocity distribution of the atoms leaving the oven. I am pretty sure that the longitudinal velocity is given by a Maxwell distribution, which in turn deoends on the oven temperature.

However, how is the transverse velocity distribution given for such a system?


Niles.

 

[Curl]

Oh ok, what you need to do is find the statistical mean of the speeds of atoms crossing the plane into your rectangle. Just remember that all directions are equally probable.

 

[Niles]

Hi

Thanks for replying. I am not quite sure I understand what to do: First I assume that the atomic source can be modeled as a point source on the axis of the rectangle. That seems reasonable.

Can I get a hint to what I should do from here?Niles.

 

[Psi^2]

My first step would be: for first reservoir (sphere) use Maxwell – Boltzmann distribution for velocity in spherical system, and then you say that only these particles who have certain condition (angle theta, angle phi) will go into a rectangular container.

I don’t know, it could help.

 

[cjl]

The transverse one is actually the easy one (assuming transverse means parallel to the contact plane). That will simply be a normal thermal distribution (in one dimension) based on the oven's temperature. The longitudinal (perpendicular to the contact plane) is the difficult one, as it has to take into account that even though the distribution of velocities inside the oven is thermal, the distribution exiting the oven is affected by the fact that the probability of a given molecule crossing the plane is not independent of its velocity.

Unfortunately, I don't have a lot of time at the moment, but this is a problem I have solved before, and I'll try to get back to this later today.

 

[Niles]

Thanks for all the help so far to all of you.

The transverse one is actually the easy one (assuming transverse means parallel to the contact plane). That will simply be a normal thermal distribution (in one dimension) based on the oven's temperature. The longitudinal (perpendicular to the contact plane) is the difficult one, as it has to take into account that even though the distribution of velocities inside the oven is thermal, the distribution exiting the oven is affected by the fact that the probability of a given molecule crossing the plane is not independent of its velocity.

Unfortunately, I don't have a lot of time at the moment, but this is a problem I have solved before, and I'll try to get back to this later today.

I'd be very happy to hear more about your approach. To me this problem does not seem that trivial.

Best wishes,
Niles.

 

[Niles]

The transverse one is actually the easy one (assuming transverse means parallel to the contact plane). That will simply be a normal thermal distribution (in one dimension) based on the oven's temperature. The longitudinal (perpendicular to the contact plane) is the difficult one, as it has to take into account that even though the distribution of velocities inside the oven is thermal, the distribution exiting the oven is affected by the fact that the probability of a given molecule crossing the plane is not independent of its velocity.

Unfortunately, I don't have a lot of time at the moment, but this is a problem I have solved before, and I'll try to get back to this later today.

Hi cjl

Did you get a chance to look at your notes?


Niles.