# Calculating Spacing Using Ideal Gas Law

by cyberdeathreaper
Tags: ideal, spacing
 P: 46 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 $$PV = N k_B T$$ to deduce the interatomic spacing. Answer: $$T < \left( \frac{1}_{k_B} \right) \left( \frac{h^2}_{3m} \right)^{\left( \frac{3}_{5} \right)} \left( P^\frac{2}_{5} \right)$$ ------------- Now, I have been given the formula for the typical de Broglie wavelength: $$\lambda = \frac{h}_{\sqrt{3 m k_B T}}$$ Further, I know I am trying to determine when $$\lambda > d$$ 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?
 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?
 Sci Advisor P: 905 Just use $d=V^{1/3}$. Doesn't that make sense to you?

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