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Find most likely values of L, S, J for barium

  1. Nov 2, 2016 #1
    The spectrum of barium contains the following series of energy levels (given relative to ground):
    1.521, 1.567, 1.676 (all in eV)
    What are the most likely values of L, S, J?

    2. Relevant equations

    3. The attempt at a solution
    I tried using the Lande interval rule, giving the lowest state the value j, then the 1.567 level j+1 and j+2 for 1.676. If the change between 1.521 and 1.567 is ##\Delta E = 0.046## and the change between 1.567 and 1.676 is ##\Delta E_2 = 0.109##, then ##\Delta E_2 \approx \frac{12}{5} \Delta E##. So by the interval rule
    ##\Delta E = 2B(j+1)## (1)
    ##\frac{12}{5}\Delta E = 2B(j+2)## (2)
    Dividing (1) by (2) to get rid of the constant,
    ##\frac{5}{12} = \frac{j+1}{j+2}## which would give me ##j = -\frac{2}{7}##. Which is wrong. But that's the only method I can think of! Have I made a mistake or should I be using a different approach?

    I'm also very confused by the phrase 'most likely' values; should the method I'm meant to use give multiple possibilities? Thanks for any help!
  2. jcsd
  3. Nov 7, 2016 #2
  4. Nov 8, 2016 #3


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    Do you know other relevant rules beside Lande? Even then, it is a rule, not an exact law. What values for j are possible in Barium (e.g. integer, half integer ...)? What is the nearest possible value to the one you calculated?
  5. Nov 8, 2016 #4
    Hi, thanks for your reply! Fairly sure I've solved it, assumed the levels were part of a triplet as the question says a series of energy levels, which would mean the j values are j, j+1, j+2 with j associated with the lowest energy levels. Then S = 1 for a triplet and J = L + S gives you the L value.

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