Zeeman Effect: Homework Questions on n=2 & 3 Energy Levels in 2T Magnetic Field

[lee_sarah76]

Homework Statement

Consider the splitting of the n=2 and n=3 energy levels for a hydrogen atom placed in a 2T
magnetic field. Consider only the normal Zeeman effect (ignore spin). (a) What is the separation
in energy between adjacent ml levels for the same l? (b) How many different wavelengths will
there be for 3d to 2p transitions, if ml can change only by ±1 or 0? (c) What is the wavelength for
each of those transitions?

Homework Equations

ΔE = μ*Δm_l*B <--- μ is the Bohr magneton in this case.
λ = \frac{h*c}{ΔE}

The Attempt at a Solution

Part a I was able to do easily, by plugging Δm_l = 1, and 9.274*10^-24 J/T for μ.

Part b, I had a little confusion, but I believe I did correctly, given that there are 5 possible states for m_l when n = 3 and l = 2, and 3 possible states for m_l when n = 2 and l = 1, so there are 9 possible wavelengths that could occur?

Is this correct, or do I also have to account for each of the Zeeman effects on energy and count those as different wavelengths as well?

Finally, for part c, I understand that the equation is simply λ = \frac{h*c}{ΔE}, but my confusion again lies in the part if I use the slightly altered energy states (For example, for the n = 3, l = 2, m_l = 1 state, there could be a ΔE of plus or minus 1.8548 * 10^-23 J.) or if I simply use the normal, non-affected values for E, then calculate ΔE and then λ?

Thanks, and I'd be happy to clarify if what I asked didn't make sense..

 

[TSny]

There are 9 possible transitions. But you will need to go further and see if each transition gives a different wavelength.

With the magnetic field turned on, what is the expression for the energy E_n,l,ml of a level with quantum numbers n, l and m_l? From that expression you can find ΔE for each of your 9 transitions.