Hydrogen Fine StructureWhen the familiar red spectral line of the hydrogen spectrum is examined at very high resolution, it is found to be a closelyspaced doublet. This splitting is called fine structure and was one of the first experimental evidences for electron spin.
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Index Schrodinger equation concepts Hydrogen concepts Atomic structure concepts Reference Rohlf Sec 8.6  

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SpinOrbit InteractionThe energy levels of atomic electrons are affected by the interaction between the electron spin magnetic moment and the orbital angular momentum of the electron. It can be visualized as a magnetic field caused by the electron's orbital motion interacting with the spin magnetic moment. This effective magnetic field can be expressed in terms of the electron orbital angular momentum. The interaction energy is that of a magnetic dipole in a magnetic field and takes the form When atomic spectral lines are split by the application of an external magnetic field, it is called the Zeeman effect. The spinorbit interaction is also a magnetic interaction, but with the magnetic field generated by the orbital motion of an electron within the atom itself. It has been described as an "internal Zeeman effect". The standard example is the hydrogen fine structure.

Index Schrodinger equation concepts Atomic structure concepts  

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Effective Magnetic Field of OrbitThe classical magnetic field in the electron frame of reference arising from the orbital motion is Using classical physics and assuming a circular orbit, the angular momentum is L = mrv, so this field can be expressed in terms of the orbital angular momentum L: This is making use of the Bohr model where L=nh/2π . For a hydrogen electron in a 2p state at a radius of 4x the Bohr radius, this translates to a magnetic field of about 0.03 Tesla. The magnetic field exerted on the orbiting electron as a result of the orbit produces an energy by the spinorbit interaction. This energy contribution depends upon the relative orientation of its orbital and spin angular momentum. The magnetic field at the electron is in the direction of the orbital angular momentum. The energy contribution can be expressed as With the two orientations of spin, the energy separation ΔE can be expressed as where α is the fine structure constant: Considering the example of the fine structure of the n=2 hydrogen level shown above, that substitution with the approximation that the radius = a_{0}n^{2} yields the value 
Index Schrodinger equation concepts Blatt Modern Physics Sec 9.3  

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Magnetic Field in Electron Frame

Index Schrodinger equation concepts  

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