|Jan26-13, 07:08 AM||#1|
Maxwell-Boltzmann speed distribution derivatives
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.
|Jan26-13, 08:07 AM||#2|
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.
|Jan26-13, 04:54 PM||#3|
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
t[SUB]2 = Time taken for disc 2 to reach correct position = θ/ω
For a particle to pass through both notches & hit detector, t[SUB]1 must equal t[SUB]2
L/u = θ/ω → Lω/u = θ → u = Lω/θ
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