The mean free path of a helium atom in helium gas at standard temperature and pressure is 0.2 um. what is the radius of the helium atom in nanometers?

Explanation:

The mean free path   of an atom is given by the following formula:

   (1)

Where:

is the Universal gas constant

is the absolute standard temperature

is the diameter of the helium atom

is the Avogadro's number

absolute standard pressure

Knowing this, let's find from (1), in order to find the radius of the helium atom:

   (2)

   (3)

   (4)

If the radius is half the diameter:

 (5)

Then:

 (6)

 (7)

However, we were asked to find this radius in nanometers. Knowing :

 (8)

Finally:

This is the radius of the helium atom in nanometers.