Why is there a central line in Zeeman effect?

[Ruptor]

Why is there a central line when a magnet is used to split the electrons? I would have thought that since electrons have two characteristic states that one type would go one way and the other type the other way so the middle should be blank.

 

[Khashishi]

In the case of the normal Zeeman effect, we don't need to consider electron spin. Then you only need to care about the z component of angular momentum quantum number m. The allowable transitions in LS coupling have delta m = {-1, 0, or 1}. This gives you three lines.The presence of the magnetic field causes the energy of an "m" state to be shifted by \mu_B B m. This energy shift happens to both the upper levels and lower levels of the transition, so only the change in m matters.

 

[Ruptor]

Thanks for answering but I don't understand why the middle line is present. I have read about the Zeeman effect here
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/zeeman.html
but none of this explains what the middle line represents so can someone explain it in simple English for me.
Does the middle line say that some of the electrons are not affected by the magnetic field and so just go straight? If so why aren't they affected?

 

[cosmic dust]

It depends on the model you are using. There will be an odd number of lines if you do not take account for the spin of the electron, because the different angular momentum states of the electron will be odd (2L+1, where L is integer). In this case, the middle line is for m=0, i.e. for the state whose energy is not affected by the magnetic field. If you take account for the spin, then there will be an even number of lines because there is an even number of angular moment states (2J+1 , where J is half-integer) . Here, there is not a central line because there is not a state with J_m=0.

 

[Ruptor]

The electron has a magnetic moment therefore has to be affected by the applied magnetic field so how can there be a middle line?

 

[cosmic dust]

Have you performed an experiment and you found three lines?
Or it was somewhere else that you saw these lines? If yes, these was experimental or theoretical data? If theoretical, then did you check what model the author used? Did he/she take account for the spin of electron?

 

[Khashishi]

The "normal" Zeeman effect considers the case where the electrons are paired off with opposite spins. In this case, the interaction of the spins with the magnetic field all cancel out, and we only need to consider the interaction of the electron orbit to the magnetic field. The orbiting charge creates a magnetic moment which interacts with the external field. The strength of the magnetic moment in the direction of the field is proportional to the m quantum number. The constant of proportionality is called the Bohr magneton.

A photon carries 1 unit of angular momentum, so it can change the z component of the angular momentum of the electron configuration by -1, 0, or 1, depending on how the photon's spin is oriented, because angular momentum is conserved. If the photon's spin is oriented parallel to the magnetic field direction, then delta m is -1 or 1, depending on the direction of circular polarization. If the photon's spin is oriented perpendicular to the magnetic field direction, then delta m is 0. There is no in between.

 

[Ruptor]

Thanks Khashishi the penny has finally dropped. Once you mentioned photons I realized I was thinking about the lines in terms of electrons and not light.