# Help with a probability question

1. Mar 20, 2006

### justinbaker

solved

thanks for the help, i just solved it and did not have time to update the thread.

"Earths atmosphere is made up of a ratio of nitrogen to oxygen. The ratio is 78:21. Assumming constant temp, what is the ratio at 10km. Explain why your result is qualitatively reasonable. (Hint: this problem concerns the number density of oxygen molecules as a function of height. The denisty is related in a simple way to the probability that a given oxygen molecule will be found at a particular height.)

Last edited: Mar 20, 2006
2. Mar 20, 2006

### nrqed

Is it part of a stat mech class?
If it is, then I would guess they have in mind you using the fact that the probability of finding a particle with energy E is proportional to $e^{-E/kT}$. In this example, the energy is simply mgy (the kinetic energy will drop out..see below). Then the ratio of density at different altitude will simply be the ratio of the exponentials evaluated at those altitudes (since the temperature is taken to be constant, the kinetic energy will be the same and will drop out in the ratios). Because of the presence of m in the equation, the probability distributions with altitude will be different for the different molecules.
That's my guess...

Pat