Question

The atoms in a gas can be treated as classical particles if their De Broglie wavelength is much smaller than the aveage separation between the particles d. consider monatomic helium gas (mHec^2 = 3727. molar mass = 4g/mol) at 1 atmosphere of pressure and room temperature.
Estimate d for this gas.

Answer 1

From the ideal gas law:

P V = N k T

you find the number density n = N/V:

n = P/(k T)

If the average distance is d, then you have V/d^3 atoms, so:

N = V/d^3 ------->

n = 1/d^3

We thus have:

d = (k T/P)^(1/3)