Mathematical Solution for the Lithium Ion (Li++)
Having related the most probable distance between the nucleus and electron for ionized helium in our transformed space, I can extend the technique to an electron and a doubly ionized lithium ion (Li++).
I will again use exactly the same technique as before but now I will use a charge for the nucleus of 3. Also from the literature the third ionization potential for lithium is -122.4 eV. So I will iterate electron to nucleus spacing until I get -122.4 eV ionization potential.
Table showing assumed electron to ionized lithium (Li++) nucleus spacing and calculated third ionization potentials.
For a lithium nucleus with two electrons removed (Li++) I get an electron to nucleus spacing of about 0.176 ang. This time when I went looking on the internet I could not find a reported result.
Below is a graph showing force as a function of distance calculated using the transformed space technique, Coulombs law is shown for comparison.
Graph showing the force as a function of distance for the electron to the LI++ nucleus.
Below is a graph showing energy as a function of distance calculated using the transformed space technique, Coulombs law is shown for comparison.
Graph showing the energy as a function of distance for the electron to the LI++ nucleus.
So if you are reading this and know of an experimental result for this spacing I would appreciate hearing from you.