# Hydrogen Atom and Relatavistic Corrections - What does this Alpha mean

1. May 10, 2009

### TFM

1. The problem statement, all variables and given/known data

Okay, I need to work out the Relativistic corrections for an atom, using the First KE Term and the Darwin Term:

Calculate the energy shift of the protonium groundstate due to the relativistic correction to the kinetic energy and the Darwin term and compare it to Hydrogen

2. Relevant equations

KE Term:

$$\Delta E_1 = \frac{1}{2}mc^2 \frac{(z\alpha)^4}{n^4}\left( \frac{n}{l + \frac{1}{2}} - \frac{3}{4}\right)$$

Darwin Term:

$$\Delta E_3 = \frac{1}{2}mc^2 \frac{(z\alpha)^4}{n^3}$$

3. The attempt at a solution

I know I just need to insert the values into these equations to get out the answer. However I am niot quite sure what the alpha represents?

TFM

2. May 10, 2009

### diazona

That would be the fine structure constant
$$\alpha = \frac{e^2}{4\pi\epsilon_0 \hbar c} \approx \frac{1}{137}$$

3. May 10, 2009

### TFM

I see. Thanks. Most appreciated.