Zeeman Splitting, Paschen-Back Effect

[hhhmortal]

Homework Statement

In a very strong applied field the sodium resonance lines is foudn to have components at 588.5 nm, 589 nm and 590.1 nm. What is the strength of the applied field?

The Attempt at a Solution

So I have:

3P_(1/2) --> 3S_(1/2)

AND

3P_(3/2) ---> 3S_(1/2)


Then I know, for strong magnetic fields:

E = (m_l + 2m_s ) B μ_B

I found the max change in (m_l + 2m_s ) to be about 2 and the change in E to be hc/∆λ and I know ∆λ is 0.8 nm :

If I put all this into the equation I get B to be very large, which is clearly wrong..what I am I doing wrong?


Thanks.

 

[hhhmortal]

Is anyone able to help me with this question?