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Atomic physics: sodium D-line transition missing 2 pi

  1. Jun 9, 2007 #1
    1. The problem statement, all variables and given/known data

    Find the wavelength of the sodium transition [tex]3p^{1},^{2}P -> 3s^{1},^{2}S[/tex]

    2. Relevant equations

    [tex]E_{n,l} = -\frac{hcR}{(n - d(n,l))^{2}}[/tex]

    d(3,s) = 1.374
    d(3,p) = 0.884

    [tex]\lambda = \frac{\hbar c}{\Delta E}[/tex]

    3. The attempt at a solution

    Plugging the numbers in ain't even close. However, I've found another equation that works:

    [tex]\frac{1}{\lambda} = -R[\frac{1}{(n_{i} - d_{i}(n,l))^{2}} - \frac{1}{(n_{f} - d_{f}(n,l))^{2}}][/tex]

    but since E is proportional to [tex]\hbar[/tex] and the RHS on the top equation just to h... where did the [tex]2\pi[/tex] go..?
    Last edited: Jun 9, 2007
  2. jcsd
  3. Jun 9, 2007 #2
    'Sokay. Just realised [tex]\lambda = \frac{hc}{\Delta E}[/tex] not [tex]\frac{\hbar c}{\Delta E}[/tex]. Knew it would be something stupid.
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