(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A gas of electrons is contrained to lie on a two-dimensional surface. I.e. they

have no movement in the z direction but may move freely in the x and y.

a) From the equipartition theorem what is the expected average kinetic energy

as a function of T?

b) For T = 293K what speed would this correspond to?

c) The equivalent of the Maxwell-Boltzman distribution for a two-dimensional

gas is

[tex]p(v) = Cve^{-\frac{mv^{2}}{kT}}[/tex]

Define C such that,

[tex]\int^{\infty}_{0} dvp(v)=N[/tex]

3. The attempt at a solution

a) As the particles are able to move in only two dimensions the equipartition theorem reduces to only have two velocity terms x and y. therefore;

[tex]E_{k}=\frac{1}{2}m(v^{2}_{x}+v^{2}_{y})[/tex]

Where E_{k}is kinetic energy

This would mean that the total kinetic energy in terms of T would be

[tex]E_{k}=kT[/tex]

Would this be correct?

Part b) will be a simple rearrangement and calculation. no real problems there

c) I have rearranged the integration to;

[tex]C\int^{\infty}_{0}ve^{-\frac{m}{kT}v^{2}} dv=N[/tex]

But have been unable to process further. I think it is supposed to be a standard integral of some sort but have no real clue how to progress

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Maxwell-Boltzmann Distribution function and equipartition theorem

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