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Hydrogen Atom and Relatavistic Corrections - What does this Alpha mean

  • Thread starter TFM
  • Start date
  • #1
TFM
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Homework Statement



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

Homework Equations



KE Term:

[tex] \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) [/tex]

Darwin Term:

[tex] \Delta E_3 = \frac{1}{2}mc^2 \frac{(z\alpha)^4}{n^3} [/tex]

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
 

Answers and Replies

  • #2
diazona
Homework Helper
2,175
6
That would be the fine structure constant
[tex]\alpha = \frac{e^2}{4\pi\epsilon_0 \hbar c} \approx \frac{1}{137}[/tex]
 
  • #3
TFM
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I see. Thanks. Most appreciated. :smile:
 

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