# Zeeman effect exercise

Gold Member

## Homework Statement

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

## Homework Equations

$\Delta E=m_l \mu _B B$.
$E=\frac{hc}{\lambda}$.

## 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 $m_l=1$.
So applying the first formula I gave, this gives $\Delta E \approx 1.85 \times 10^{-23}J=1.16\times 10^{-4}eV$.
Applying the second formula this gives me $\Delta \lambda \approx 0.01 m$.
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.

Gold Member
Nevermind, the approach is right. I just made a calculator mistake with the product "hc".

Redbelly98
Staff Emeritus
Homework Helper

By the way, both eV energy units and the product hc comes up so frequently in quantum mechanics that it's a good idea to remember (or right down, wherever you have a list of physics constants) it's value:

hc = 1240. eV-nm​

The energy-wavelength conversions will go quicker that way.

Gold Member