## Time for air molecules to cross a room

Teaching Guidance for 14-16

Once students understand the thinking behind estimates of mean free path, *s* , they can estimate the time for air molecules to cross a room. Assume there are no convection currents.

In time *T* seconds the straightened-out path of a molecule of air is 500 *T* metres. The number of collisions it makes in that time is 500 *T* / *s* which is 5 × 10^{9} x *T* collisions. The average progress from start to finish will be *s* √ *N* which is the length of the room, say 6 m.

Hence 6 = √( 5 × 10^{9} x *T*) x 10^{-7}. And so the time for an air molecule to cross the room is 720 000 seconds, more than a week!

The same kind of story applies to neutrons diffusing from the inner regions of a nuclear reactor. Also for the particles of light (photons) cannoning their way out from the inner layers of the Sun.