Maxwell-Boltzmann speed distribution derivatives

[devious b]

Hi everyone,

Molecules move into a vacuum chamber from an oven at constant T. The molecules then pass through a slit. They reach two rotating discs before finally reaching a detector.

Show that a molecule that passes through the first slit will reach the detector if it has speed, u = ωL/θ.

After it passes through the slit, the beam of particles is directed towards 2 discs that are a fixed distance apart (L). They both have a notch in them, the 2nd disc's notch is offset from the 1st by 1/6∏. T is constant, common angular speed is ω & L = 0.262m.

My question is, do I simply say that the most probable speed is equal to u?

√(2KT/m) = u = ωL/θ

Any clues would be appreciated.

Thanks:)

 

[sophiecentaur]

I think you are looking too deep into the question. It's not about velocity distribution but they have given you a 'scenario' for a fairly straightforward dynamics problem. They just want to find which speed will get "a" molecule through the shutter which the two spinning slits present.

 

[devious b]

You're absolutely right, I completely over-thought the problem. So,

t<sub>1 = Time particle takes between the 2 discs = d/u = L/u

t2 = Time taken for disc 2 to reach correct position = θ/ω

For a particle to pass through both notches & hit detector, t1 must equal t2

So,

L/u = θ/ω → Lω/u = θ → u = Lω/θ

Thanks</sub>