Spin Orbial Coupling - Peak splitting in Photoemmission Spectroscopy (XPS)

When we try to analyse the XPS data, we can see that some of the peaks show sharp Single peak like in case of Na 1s as shown here , and in some cases the peak is split into two parts e.g. As in case of Cl 2p. This peak splitting is observed due to spin orbital coupling.
As the name suggest, it is the coupling or interaction between spin and orbital motion of electron. So lets first understand what is spin of electron. Spin is rotation of electron around its own axis. And this rotation produces a magnetic field as shown here with a blue line. Now as electron is also revolving arond the nucleus, this angular motion also produces a magnitc field.

We can try to see this orbital motion in an alternate point of view. Where you can say that the nucleus if moving around the electron, its the same thing but a different perspective. So this motion of charged particle or nucleus creates another magnetic field, this magnetic field is shown with red line.
Now there will be interaction between these two magnetic fields, either they will be in same direction called with the field orientation or in opposite direction called against the field.
That means now the energy of electron is split in two parts one with the field, lower BE and one against the field higher BE.
And thus the peaks for such electron in XPS gets splitted in doublet.
So, lets try to understand how the coupling of spin and orbital motion takes place. So lets start from the spin. Spin is rotation of electron around its own axis. And spin quantum number has both a magnitude which is 1/2 and direction which can be + or -.
So the spin quantum number of an electron can have two possible values only I e +1/2 or -1/2.
On the other hand due to orbital motion of electron, orbital quantum number arises which is known as Azimuthal quantum number. And its value depends on the shape of orbital or total number of angular nodes in the orbital.
e.G As s orbital is not spherical and don’t have any nodes. The value of azimuthal quantum number (l) is 0.
For p orbitals all px, py and pz orbitals are similar and have one node, therefore azimuthal quantum number is 1
Similarly for d orbitals having two nodes one for dxy, dyz & dxz orbitals and one for dx2y2 and dz2 orbitals . Thus, azimuthal quantum number is 2
And finally for f orbitals it is 3for 3 nodes in orbitals.

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