- #1
John Greger
- 34
- 1
Okey so I think this question or a similar one was here recently but I can't find it so creating a new.
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.
[/B]
$$A=\frac{2E}{F(F+1)-I(I+1)-J(J+1)}$$
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.
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.