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## Homework Statement

The figure below shows the hyperfine structure in the transition 6s ##^2S_{1/2} - 8p ^2P_{3/2}## in 115In (

*I*= 9/2). The measurement is made using a narrow-band tunable laser and a collimated atomic beam; hence the Doppler width is greatly reduced. The 6 components shown have the following frequencies 31, 112, 210, 8450, 8515 and 8596 MHz. Draw a schematic figure of the energy levels with the appropriate quantum numbers and show the allowed transitions. Determine the hyperfine constants, in MHz, for the two fine structure levels.

## Homework Equations

[/B]

$$A=\frac{2E}{F(F+1)-I(I+1)-J(J+1)}$$

## The Attempt at a Solution

Now, since I have I and J I have F and can draw an energy diagram with all the allowed transitions.##F(^2P) = (6,5,4,3)## and .# and#F(^2s) = (5,4).## So I can draw 6 allowed transitions.

I can even take it one step further and express the two A's in terms of the energy and vise versa.

But how exactly do I solve for A? However I twist and bend I just can't get anything solvable. Neither can I connect the given frequencies to the energy differences, have no idea what so ever how they relate, see or know no pattern.