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Calculating Spacing Using Ideal Gas Law 
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#1
Apr2605, 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? 


#2
Apr2705, 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?



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