Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

New formula for Hydrogen Spectral Lines

  1. Aug 2, 2014 #1
    Hi

    I have a new formula (or at least I think it's new) for predicting the wavelengths/frequencies of hydrogen's spectral lines. Please take a look and tell me if it is new. I am quite confident that it works because Bohr's original formula 'falls out' if one approximates cos(x) as 1 + x^2/2 for small x. But the formula was derived by deploying some relativistic ideas without actually knowing much about relativity! Here is the energy expression for 1s to 2s transition. Translate to frequency or wavelength with the usual E=hf=hc/λ.

    [cos(α/2) - cos(α)] * m * c^2

    Where:

    α = fine structure constant
    m = mass of electron
    c = velocity of light

    More generally for level j to level k transitions:

    [cos(α/j) - cos(α/k)] * m * c^2 (j > k).

    I have checked this formula against a set of measured values I found here:

    http://hyperphysics.phy-astr.gsu.edu/hbase/tables/hydspec.html#c1

    Interesting that - like the Bohr formula - this formula seems to consistently overestimate transition energies thus leading to slightly higher than measured frequencies and conversely lower wavelengths.

    I learnt all about the 'fine structure constant' when developing this formula - it popped up again and again!
     
  2. jcsd
  3. Aug 2, 2014 #2

    Dale

    Staff: Mentor

    New formulas should be published (along with their derivation and comparison to previous experiments) in the peer-reviewed literature. Not here on PF.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: New formula for Hydrogen Spectral Lines
  1. Formula for Density (Replies: 4)

  2. Einsteins formula (Replies: 2)

  3. Jacobi formula (Replies: 1)

Loading...