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Calculating Spacing Using Ideal Gas Law

by cyberdeathreaper
Tags: ideal, spacing
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cyberdeathreaper
#1
Apr26-05, 05:36 PM
P: 46
Here's the question:

For what temperatures are the atoms in an ideal gas at pressure [itex] P [/itex] quantum mechanical?

Hint: Use the idea gas law
[tex]
PV = N k_B T
[/tex]
to deduce the interatomic spacing.

Answer:
[tex]
T < \left( \frac{1}_{k_B} \right) \left( \frac{h^2}_{3m} \right)^{\left( \frac{3}_{5} \right)} \left( P^\frac{2}_{5} \right)
[/tex]

-------------

Now, I have been given the formula for the typical de Broglie wavelength:

[tex]
\lambda = \frac{h}_{\sqrt{3 m k_B T}}
[/tex]

Further, I know I am trying to determine when
[tex]
\lambda > d
[/tex]
where d is the interatomic spacing.

However, what I don't understand is how I can calculate a value for d given the idea gas law in the question. Any ideas?
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cyberdeathreaper
#2
Apr27-05, 04:05 PM
P: 46
More generally, is there some approach that can be used to calculate the interatomic spacing using the ideal gas law outside of the quantum mechanics context?
krab
#3
Apr27-05, 04:33 PM
Sci Advisor
krab's Avatar
P: 905
Just use [itex]d=V^{1/3}[/itex]. Doesn't that make sense to you?


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