*(Fig.1) Hydrogen fine structure (= 2p splits into 2p3/2 and 2p1/2 ) ?*

The small splitting of spectral line is seen in Hydrogen 2p energy level ( 2p → 2p3/2, 2p1/2 ).

Quantum mechanics claims this splitting is due to spin-orbit effect where electron spin is up ( down ) in 2p3/2 ( 2p1/2 ) with respect to its orbital angular momentum.

But electrons spin exceeding light speed is unrealistic. This 2p splitting (= called fine structure ) can be explained by Bohr-Sommerfeld model **without** spin.

*(Fig.2) The enregy difference between 2p3/2 and 2p1/2 is only 0.000045 eV.*

Hydrogen 2p energy splitting is very small, the energy difference between 2p3/2 and 2p1/2 is only **0.000045** eV.

This energy difference is known to be expressed by the equation which is proportional to Z^{4}/n^{3} ( Z is nuclear charge, n is principal quantum number ).

In 2p energy level in hydrogen, nuclear charge Z is 1, principal quantum number n is 2, angular momentum l is 1.

If you insert these numbers into the spin-orbit equation ( this p.4 ), you can get the above 0.000045 eV.

*(Fig.3) This Na large energy splitting is NOT due to spin-orbit !*

The problem is sodium 3p energy splitting is too **large** to explain by spin-orbit effect.

Sodium 3p electrons has n = 3, l = 1 and its energy splitting = **0.0021** eV, which is 100 times stronger than hydrogen (= 0.000045 eV ).

By inserting these numbers into the above spin-orbit equation, we obtain central positive charge Z = **3.5** which is much larger than hydrogen nuclear charge Z = **1**.

This sodium central charge means Na+ ion (= including sodium nucleus and **all** other inner electrons ), so Z should be close to **1** like hydrogen.

So the sodium 3p energy splitting is **NOT** spin-orbit but strong Coulomb effect !

*(Fig.4) ↓ Sodium real central charge is Z = 1.4 ( not 3.5 ! ) by ionization energy *

The real central positive charge Z can be estimated from sodium ionization energy of outer electron using hydrogen energy solution.

The energy required to ionize sodium outer 3p electron is **3.14** eV, which leads to central change Z = **1.4**.

If we insert this "real" sodium central change Z = 1.4 into the above spin-orbit equation, we obtain very **small** 3p energy splitting (= only **0.000054** eV ).

It is far **smaller** than the experimental value (= *0.0021* eV ) indicating those energy splitting is **NOT** due to spin-orbit effect but due to Coulomb effect by sodium inner electrons.

In larger alkali atoms (= K, Rb, Cs .. ), these energy splitting is far **larger**, and it's more *impossible* to apply unreal spin-orbit effect to them !

2017/1/20 updated. Feel free to link to this site.