# Show interparticle spacing is much greater than wavelength

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1. May 6, 2016

I have a past paper question from statistical physics:

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?

2. May 6, 2016