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## Homework Statement

The [itex]\alpha[/itex] lines of Paschen in the hydrogen spectrum are due to transitions [itex]n=4 \to n=3[/itex]. Identify the allowed [itex]4p \to 3d[/itex] transitions and determine the change in wavelength for each transition if there's an external B field of 2T.

## Homework Equations

[itex]\Delta E=m_l \mu _B B[/itex].

[itex]E=\frac{hc}{\lambda}[/itex].

## The Attempt at a Solution

I graphed all transitions possible (it's an enormous mess).

Now say I want to calculate the difference of wavelength of with and without the magnetic field for the transition 4p, m=0 and 3d, m=1 (it's allowed). I have that [itex]m_l=1[/itex].

So applying the first formula I gave, this gives [itex]\Delta E \approx 1.85 \times 10^{-23}J=1.16\times 10^{-4}eV[/itex].

Applying the second formula this gives me [itex]\Delta \lambda \approx 0.01 m[/itex].

I know this result is totally senseless. It's way too big, enormous. From memory Paschen lines are in the near infrared so about 800 nm and a bit up. Nothing like 0.01m!

I really don't know what I'm doing wrong.

I would appreciate some help.