Calculating Spacing Using Ideal Gas Law

[cyberdeathreaper]

Here's the question:

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

Hint: Use the idea gas law
<br /> PV = N k_B T<br />
to deduce the interatomic spacing.

Answer:
<br /> T &lt; \left( \frac{1}_{k_B} \right) \left( \frac{h^2}_{3m} \right)^{\left( \frac{3}_{5} \right)} \left( P^\frac{2}_{5} \right)<br />

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

<br /> \lambda = \frac{h}_{\sqrt{3 m k_B T}}<br />

Further, I know I am trying to determine when
<br /> \lambda &gt; d<br />
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?

 

[cyberdeathreaper]

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]

Just use d=V^{1/3}. Doesn't that make sense to you?