How do I make a sine waveform continuous graph of the energy levels of sodium atom against the radial distance from the nucleus?

1 Answer
Oct 20, 2017

Well...

  • you'd need a lot of math you probably don't know yet, to get the most probable distance of an electron away from the nucleus for each atomic orbital, and you would need each atomic orbital energy...

  • Neither of these is data that is available anywhere to this day except for hydrogen atom. In particular, no one can obtain exact wave functions for sodium atom, and thus, no one can obtain the most probable distance of all of the electrons from the nucleus quantitatively.

So, I can only do this qualitatively for the most part. I can do a rough computational work-up to get approximate atomic orbital energies.

DISCLAIMER: These are based on just basic Hartree-Fock energies, and are not the true energies! Furthermore, energies must be discrete, so I cannot make a "sine waveform continuous graph".

Plotted from Rough MolPro Calculation of HF-SCF energies, QUALITATIVE!!!

Hopefully this is what you are looking for. Here, the energy starts at #-"498 kJ/mol"# for the #3s# orbital.

The following was the relevant part of the MolPro output. Again, this is very qualitative!