# Homework Help: Cross Section calculation

1. Nov 24, 2007

### JohnSimpson

1. The problem statement, all variables and given/known data
I've been asked to find the cross section of a hydrogen atom in thermal equalibrum at 6000K for a photon which induces a transition from the ground state to the first excited state. The density of states for n=2 is 4x the density of states for n=1

i.e. g(E2) = 4*g(E1)

The lifetime of the n=2 state is 1.6 x 10^-9 s.

2. Relevant equations

3. The attempt at a solution

The incident photon has an energy E = hf = hc/lambda

Since the system is in thermal equlibrum, it has an average energy = kT. I am not sure what exact this is the average energy of though, the atoms? the photons? Everything?

From what I understand, the cross section is some kind of area of interaction for the process that will somehow depend on the energy of the incident photon. With this in mind, I wrote down the radius of the hydrogen atom for n =1

r1 = (epsilon)h^2 / pi * e^2 * m_e

I'm still not entirely comfortable with what the density of states represents for n=1 and n=2 respectively. I know that it sort of represents a "Price" to put an electron at that level, but I might be incorrect in saything that.

It would be very helpful if someone could clear up my misconceptions and nudge me in the right direction, thank you

2. Nov 25, 2007

### JohnSimpson

Update: I've managed to write down the number of particles in the n=1 state at any time, which is given by

g(E1)f(E1) where f(E1) is the maxwell-boltzmann probability of finding a hydrogen atom with energy E1 corresponding to ground state, and similarly the number of n=2 hydrogen atoms is

4g(E1)f(E2)

3. Nov 25, 2007

### JohnSimpson

Anyone able to point me in the right direction?