From the gross structure of the atom to the fine and hyperfine structure

The electron in the outer shell of the sodium atom can absorb energy and transition to a higher energetic level. However, it has two different choices as it can jump not to one but to two different energetic levels; and in the presence of a magnetic field it has even more energetic jump choices!


These phenomena are explained by the spin orbit interaction and the Zeeman effect.


At school we first learned about the gross structure of the atom with the electrons found in orbits around the nucleus and then we were taught about the orbitals corresponding to different energetic levels. For instance in the case of sodium which has 11 electrons we first learned to fill the 1st orbit or shell with 2 electrons, then the next with 8 and then have one single electron at the outer shell. Later, we were taught about the subshells s,p,d and how to write the electron configuration of the sodium atom as 1s2,2s2,2p6,3s1.

 

How do we explain the spectral lines of sodium mentioned at the section "Spectroscopy"(http://www.information-book.com/physics/spectroscopy)? The electron at the outer subshell, the 3s subshell, absorbs energy and transitions to the next energetic level. That would be a p subshell. We would expect to obtain a spectral line corresponding to this energetic transition from the s shell to the p shell (absorption or emission). However, it is demonstrated that we obtain not only one but two spectral lines! That means that are two different possible energetic jumps, two energetic transitions that can be made by the electron in the outer shell. This is explained by the theory of the spin-orbit interaction which gives rise to the fine structure of the atom.

 

What happens upon the effect of a magnetic field? 
In that case there are even more possible energetic jumps that can be made by the electron! More energetic level options are produced because of the interaction between the atom and the external magnetic field. This is explained by the Zeeman interaction which gives rise to the hyperfine structure of the atom. Please refer to Figure 1 and the relevant sections.

 

 

 

 

Spin-orbit interaction - Effect of internal magnetic field on the atom

 

References:

1. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydfin.html (scroll down for "Spin-Orbit" Interaction). Follow link "effective magnetic field" and thereafter cited link "magnetic field in the electron frame". 

2. Ref. https://bit.ly/2GYlWtK from physics.stackexchange.com

 

The energy levels of the atomic electrons are affected by the alignment of the orbital magnetic dipole moment μorb and the spin magnetic dipole moment μs. Consider the frame of reference of the electron - for instance by imagining being on the electron! In that case, you see the nucleus rotating around you (around the electron). The movement of the nucleus which is equivalent to that of a charged particle in a closed loop is equivalent to a current I running in the loop as shown in the figure at the link magnetic field in the electron frame. It is demonstrated at the figure that this current I generates a magnetic field B. We are referring to the latter as an effective magnetic field in the (rest) frame of reference of the electron which is dependent on the orbital angular momentum L. This effective magnetic field in the electron frame due to the orbital motion interacts with the spin magnetic moment of the electron (the magnetic energy of the electron spin) and affects the energy levels of the atomic electrons. We also refer to an internal magnetic field caused by the orbital motion of the electron and this is the reason that this effect is known as an "internal Zeeman effect" (more explanations at the relevant section).

 

In the case of sodium (1s22s22p63s1), due to the spin-orbit interaction, as mentioned at the link http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/sodzee.html, "the 3p level is split into states with total angular momentum j=3/2 and j=1/2 by the magnetic energy of the electron spin in the presence of the internal magnetic field caused by the orbital motion".

 

Please refer to the figure of the above link for an image showing a ΔE of 0.0021 eV between the two 3p levels and also to Figure 1 below..

 

An interesting discussion on "What Causes Electron Energies to Depend Upon the Orbital Quantum Number" is found at the link

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/orbdep.html#c1 (note: the relative position of the orbitals and their overlap determine their shielding from the effect of the nucleus). 

 

 

 

Figure 1: From the gross structure of the atom to the fine and hyperfine structure. The spin-orbit interaction is linked to the fine structure and the Zeeman interaction to the hyperfine structure.