Sketching Energy Diagram w/ l=2, s=1/2 - m, j & mj values

[asdf12312]

Homework Statement

Sketch the energy diagram for a system with l = 2 and s = 1/2: before spin-orbit splitting, after spin-orbit splitting, after additional application of external magnetic B (label all m values).

Homework Equations

m values from -l to l (total 2l+1 values)
j values from l-s to l+s
m_j values from -j to j (total 2j+1 values)

The Attempt at a Solution

I drew a diagram but I'm not sure if it's right. and before the spin-orbit splitting I was confused, so I just drew the m values for l (not sure though).

 

[Simon Bridge]

Check:
If the electron magnetic moment did not interact with the nuclear magnetic moment, would there be any difference between the energy level of different orientations of the spin?

An additional magnetic field produces the Zeeman effect.
That is something you can look up.

Which has the bigger effect: the spin-orbit coupling or the external magnetic field?

 

[asdf12312]

I don't think there would be any change in the energy level without B field. so I don't think I need to include the m values for l=2 without spin.. I have an example of the Zeeman effect but i don't really understand it. it shows arrows going down from the lines, do I need to draw a l=1 diagram if the energies go from D (l=2) to P state? I think the external B field would have a greater effect because it has more energy levels, the spin-orbit only has like 5 levels.

 

[Simon Bridge]

Technically the Zeeman effect is the fine splitting, in the presence of a magnetic field, of the spectral lines you get when there is no magnetic field. The arrows in your notes show the transitions that give rise to the spectra.

You only need the energy-level diagram.
You should only draw as many energy levels as you have been asked to examine.

You can find articles about zeeman effect and spin-orbit coupling online.
I gave you the names as a way of hinting you should look them up ;)

 

[asdf12312]

I made another drawing, don't have the arrows because I don't think I need it, would it be something like this? there are 5 levels now before the B field. I tried looking up zeeman effect but i was confused because it looked different from my problem.

 

[Simon Bridge]

You have decided that the spin-orbit splitting is bigger than the effect of the magnet?
You have decided that "a system with l=2" means to include l=0 and l=1 as well?
If so then you have got what you wanted.

These are decisions for you to make though, because it is your course.