Help!!!! atomic physics??

Question

Can someone help me please... Ive just come across a past paper question whilst studying and havent a clue how to answer it...
Calculate the wavelength of the longest wavelength fine structure component of the Balmer-alpha line in hydrogen according to the Schrodinger/Dirac theory and spin orbit interaction...?

Answer 1

I can give you this to help you get started: Balmer lines are transitions of the hydrogen atom from high quantum numbers of n to the n=2 state. Normally, you'd just use the Rydberg equation to find the energy which, if I remember right, is 13.6 electron volts multiplied by (1/2^2 - 1/n_initial^2) to get the energy. This problem has the addition of fine structure, so you either have to use the Dirac hamiltonian and add a term for the energy of the electron interacting with the magnetic field (if I'm seeing this problem correctly), then get the eigenvalue by plugging the appropriate hydrogen wave functions, or you can shortcut to the fine structure equation.

Answer 2

You need to know the energy of the shortest Balmer-alpha line jump.

The wavelength is then calculated using E = hf
and c = f x lambda.

Answer 3

The answer is 42.

Answer 4

first u read the theory perfectly
then u try to do these problems.

Answer 5

That's easy, just give me a few hundred years...............

Answer 6

HUH???

Answer 7

.....

Shite, my brain just exploded