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Allowed energies for electrons in hydrogenic atoms

  1. Apr 23, 2010 #1
    I have a question which may seem stupid, but I think I missing something here.

    I see 2 equations describing allowed energies for electrons in hydrogenic atoms, being:
    [tex]E = -\frac{hcRZ^2}{n^2}[/tex]
    [tex]E = -\frac{RZ^2}{n^2}[/tex]
    I assume that both are correct, but what makes the difference? Is it the same R for both of them? or the second R includes the h and c inside?
    How would I tell the difference?

    Please enlighten me. Thanks :)
  2. jcsd
  3. Apr 23, 2010 #2


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    Science Advisor

    They are trying to express the same relation, and you are correct that in the second version, the h and c have been "absorbed" into the R. In the first case the dimension of R is 1/length, and R comes from the Rydberg formula for the wavelength of a photon coupling two H-atom energy levels. In the second case, the dimension of R is energy, and the R stands for the Rydberg unit of energy, which is defined as the ground state energy of the H-atom in the approximation of infinite nuclear mass. The atomic unit of energy, the hartree, is exactly two Rydbergs.
  4. Apr 23, 2010 #3
    Ok, thank you.
    It's just that some textbooks use either one, and none explain the difference.

    Now I understand!
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