Show interparticle spacing is much greater than wavelength

AI Thread Summary
The discussion revolves around the validity of the assumption that ##\hbar^2 k^2 = p^2## in the context of statistical physics. The participant derived the relationship indicating that the interparticle spacing, ##a^3 = \frac{V}{N}##, is significantly greater than the exponential term involving momentum and the de Broglie wavelength, ##\lambda_{deB}^3##. There is a focus on whether this assumption is correct and if the derived result fulfills the requirements of the original question. The implications of this relationship suggest a deeper understanding of particle behavior at different temperatures. Overall, the inquiry seeks confirmation of the mathematical approach and its relevance to the physical scenario presented.
zeeshahmad
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I have a past paper question from statistical physics:
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By assuming that ##\hbar^2 k^2=p^2##, I arrived at the result:
The interparticle spacing, ##a^3 =\frac{V}{N}## is
$$ a^3 >> e^{-\frac{p^2}{2mk_B T}} \lambda_{deB}^3$$

Is my assumption correct? and does the result complete the purpose of the question?
 
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