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What is the nuclear spin of this atom?

  1. Jun 7, 2015 #1
    1. The problem statement, all variables and given/known data

    A singly ionized atom exhibits hyperfine structure in a ##^3P_1 \rightarrow ^3S_1## transition. Assuming ##I## is greater than ##J## and given that the ##^3S_1## levels are split by ##66~GHz## and ##54~GHz##, find the nuclear spin ##I##.

    2. Relevant equations

    [tex]E_{HFS} = \frac{A}{2} \left[ F(F+1) - I(I+1) - J(J+1) \right] [/tex]

    3. The attempt at a solution

    Since ##J=1##, the ##^3S_1## level is split by the higher level ##F=I+1## and lower level ##F = I##.
    2005_B3_Q1.png

    [tex] \frac{(I+1)(I+2) - I(I+1) - J(J+1)}{I(I+1) - I(I+1) - J(J+1)} = \frac{66}{54}[/tex]
    [tex] \frac{2I}{2} = 1.22[/tex]

    I get ##I = 1.22##, which is strange as shouldn't nuclear spin be either in multiples of ##\frac{1}{2}##?
     
  2. jcsd
  3. Jun 7, 2015 #2
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