Most probable speed of aluminium atoms


by Bugsy23
Tags: aluminium, atoms, probable, speed
Bugsy23
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#1
Dec3-10, 02:26 PM
P: 25
1. The problem statement, all variables and given/known data

Aluminium atoms at 1173K enter a vacuum chamber. Calculate the most probable speed for the atoms.

2. Relevant equations

vmp=[tex]\sqrt{}[/tex](2kT/m)

3. The attempt at a solution

The molar mass of aluminium is 0.0270kg mol^-1, so
vmp=[tex]\sqrt{}[/tex](2*1.381*10^-23JK^-1)*1173K/0.0270kg mol^-1=1.1*10^-9ms^-1

Which is a really tiny quantity and it seems unrealistic that particles at such a high temperature would move that slowly. I've used SI units though so I can't see where I would have gone wrong. Any help would be appreciated. Thanks
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collinsmark
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#2
Dec3-10, 03:19 PM
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Quote Quote by Bugsy23 View Post
The molar mass of aluminium is 0.0270kg mol^-1, so
vmp=[tex]\sqrt{}[/tex](2*1.381*10^-23JK^-1)*1173K/0.0270kg mol^-1=1.1*10^-9ms^-1
You're using the molar mass combined with Boltzmann constant. But that doesn't make sense. You need the mass of an individual molecule (in this case an individual aluminum atom) if you want to use Boltzmann constant. (You can do this by dividing the molar mass by Avogadro constant NA to find the mass per individual molecule [in this case atom].)

Alternatively, you can stick with the molar mass and substitute Boltzmann constant k with the gas constant R, since k = R/NA.
Bugsy23
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#3
Dec3-10, 03:37 PM
P: 25
Thanks, I've got it now


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