Question 11.35: Find the typical de Broglie wavelength associated with a He atom in helium gas at room temperature (27 2C) and 1 atm pressure, and compare it with the mean separation between two atoms under these conditions.

Hint: $$\lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}}$$
Step 1:
Find the average energy of gas at T.
The average energy of gas at T is given as:

Step 2: Find the de Broglie wavelength of the He atom.
De Broglie wavelength is given by the relation:
$\mathrm{\lambda }=\frac{\mathrm{h}}{\sqrt{2\mathrm{mE}}}$
Where, m = Mass of a He atom

Step 3: Find the mean distance between two atoms.

The mean separation between two atoms of the gas is given by the relation:

Hence, the mean separation between the atoms is much greater than the de Broglie wavelength.