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.

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  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)

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