# Griffiths Quantum Mechanics Problem 1.18: Characteristic Size of System

yucheng
Homework Statement:
The characteristic size (length) of ideal gas where quantum effects are non-negligible is the intermolecular distance, ##d##
Relevant Equations:
##pV = Nk_BT##
intermolecular distance means distance between particles. So, I imagine a sphere.

$$\frac{4}{3} \pi d^3 = \frac{V}{N}$$

However, Griffitfhs pictures a box instead, where

$$d^3 = \frac{V}{N}$$

And the difference between both models is a factor of ##(4\pi/3)^{2/5} \approx 1.8##, which is fairly large...

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If you fill a box with oranges, does it fill the space completely? Griffiths is correct

yucheng
yucheng
If you fill a box with oranges, does it fill the space completely? Griffiths is correct
I think I understand... So I guess I should have searched for a reliable shape to fill the whole space!