RMS/Mean Free Path
Properties of Matter

Time for air molecules to cross a room

Teaching Guidance for 14-16 PRACTICAL PHYISCS

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 × 109  x T collisions. The average progress from start to finish will be sN which is the length of the room, say 6 m.

Hence 6 = √( 5 × 109  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.

RMS/Mean Free Path
can be analysed using the quantity RMS Speed
is used in analyses relating to Brownian Motion
Limit Less Campaign

Support our manifesto for change

The IOP wants to support young people to fulfil their potential by doing physics. Please sign the manifesto today so that we can show our politicians there is widespread support for improving equity and inclusion across the education sector.

Sign today