When specially prepared Hydrogen atoms with their electrons in the 6f state are

Question

When specially prepared Hydrogen atoms with their electrons in the 6f 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.

Ignoring the electron spin what is the largest possible energy difference, if the magnetic field is 1.77 Tesla?

If we don't neglect the intrinsic spin of the electrons, then how many energy levels can we observe in the ground state?

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

Explanation / Answer

Electron Spin

Two types of experimental evidence which arose in the 1920s suggested an additional property of the electron. One was the closely spaced splitting of the hydrogen spectral lines, called fine structure. The other was the Stern-Gerlach experiment which showed in 1922 that a beam of silver atoms directed through an inhomogeneous magnetic field would be forced into two beams. Both of these experimental situations were consistent with the possession of an intrinsic angular momentum and a magnetic moment by individual electrons. Classically this could occur if the electron were a spinning ball of charge, and this property was called electron spin.

Quantization of angular momentum had already arisen for orbital angular momentum, and if this electron spin behaved the same way, an angular momentum quantum number s = 1/2 was required to give just two states. This intrinsic electron property gives:

Electron Spin

Spin "up" and "down" allows two electrons for each set of spatial quantum numbers.

An electron spin s = 1/2 is an intrinsic property of electrons. Electrons have intrinsic angular momentum characterized by quantum number 1/2. In the pattern of other quantized angular momenta, this gives total angular momentum

The resulting fine structure which is observed corresponds to two possibilities for the z-component of the angular momentum.

This causes an energy splitting because of the magnetic moment of the electron

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