Normal Zeeman effect of hydrogen atoms

[kraigandrews]

Homework Statement

When specially prepared Hydrogen atoms with their electrons in the 6d state are placed into a strong uniform magnetic field, the degenerate energy levels split into several levels. This is the so called normal Zeeman effect.

A) Ignoring the electron spin what is the largest possible energy difference, if the magnetic field is 2.28 Tesla?

After a certain period the electrons return to the 1s ground state in the Hydrogen atoms.

B) What will be the energy difference between the lowest and the highest observed "ground" state still in the same magnetic field?

Homework Equations

Delta_E=m_l*$\mu$_b*B, where $\mu$_b=5.7884 eV/T

The Attempt at a Solution

for a)
since it is in 6d i think m_l=5 then it should just be a plug and chug to get: 6.599E-4 eV but this isn't right. So I am not sure where i went wrong.

for b) I am not sure what to do.

 

[BruceW]

If it is 6d, this means that its principle quantum number is 6 and its orbital angular momentum quantum number is 2 (since it goes s=0, p=1, d=2).
So we are given the orbital angular momentum quantum number, so what are the possible values for the magnetic quantum number? And what is the greatest possible difference in ml? (Its not 5).
For b, for the 1s state, think what do we know about the possible values of ml?