# Homework Help: Splitting of Balmer Spectrum

1. Mar 4, 2006

### Reshma

I need to show the splitting of the $H_{\alpha}$ line of the Balmer series of a Hydrogen atom using the spin hypothesis.

Here is my work on this.
$H_{\alpha}$ is obtained from the transition of the electron from the third orbit to the second i.e. from n=3 to n=2.
Seletion rule for Hydrogen atom is: $\Delta l = \pm 1$ & $\Delta m_l = \pm 1 , 0$.
This implies transition from 3s to 2s is forbidden but transition from 3p to 2s is allowed. How do I explain the splitting of the spectral line?

2. Mar 4, 2006

### dextercioby

You need to do perturbation theory to the H atom using the spin-orbit coupling hamiltonian which should be assumed to be a time independent perturbation. One more thing: is the energy level involved in a H_alpha degenerate or not ?

Daniel.

3. Mar 5, 2006

### Reshma

I haven't studied perturbation theory. I cannot say whether the energy level of Halpha is degenerate. They can involve transition from 3 2P1/2 or 3 2P3/2.

However, since the Hydrogen atom consists of only 1 electron, so s = +1/2 or -1/2. Is it possible to show the splitting using spin hypothesis?

Last edited: Mar 5, 2006