# Year 12: Cambridge Physics Problem (Movement of Bromine gas in air)

1. Jun 29, 2012

### johnconnor

Bromine gas at atmospheric pressure and room temperature has a density of 6.4 kg/m3. An approximate r.m.s. speed of bromine molecules is 216.5 m/s.

Experiments show that bromine molecules take about 500s to diffuse 0.1m in air. This low speed compared with the r.m.s. speed can be attributed to the random collisions of bromine and air molecules. A bromine molecule travels an average distance λ between successive collisions and makes n collisions in travelling a distance x, where x = λ sqrt(n).

(The next 3 parts of the question deal with the value of λ, diameter of bromine molecule d, and volume occupied by a bromine molecule.)

Question:
It is known that the air molecules would move with an rms speed of approximately 500m/s, that air molecules are smaller than bromine molecules and that each bromine molecule consists of two bromine atoms. Discuss whether these facts have any significant effects on your estimates of λ and d.

Attempt:

I'm guessing that since the sizes (and therefore masses) of the bromine and air molecules are dissimilar, collision would result in a reduced post-impact speed for bromine (since air molecules are smaller and they carry more speed than bromine through conservation of momentum). Therefore the mean free path will be smaller, since the air molecules move about quicker after each collision. That means d will decrease too.