Submitted by Barbara Reisner / James Madison University on Sun, 09/11/2011 - 12:30
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This fall, I went to plot the radial probability function of the 4s orbital and realized that I couldn't find the radial function of the 4s orbital in any of my chemistry (or physics) books. I asked a p-chemist friend for help and we realized that every book that the two of us owns only plots the orbitals to a value of principle quantum number n=3. A google search actually wasn't a lot of help.

Does anyone happen to have the functional form of the radial function for a 4s orbital? If you share, I'll post my excel spreadsheet that calculates these. (It's likely to end up In the past, I've had students plot the wavefunction and RPF of the different orbitals as a function of r. I noticed that Maggie also has n=1 to 3 in her H atom radial factors LO - https://www.ionicviper.org/class-activity/h-atom-radial-factors.)

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Adam Johnson / Harvey Mudd College

I found this (top hit on google search, Barb...)

I think they usually have the functions listed near the pretty pictures on this site, which I love.  I can't get it to open right now, though, so I might be mis-remembering.

Barbara Reisner / James Madison University
Fair enough, Adam. I came up with the orbitron too, but was unable to find the functional form. Of course, I could be missing something.
Adam Johnson / Harvey Mudd College

Hmm.  I couldn't get that link to work, but when I got in from the main page, I could navigate here, which has the equation on it.

http://winter.group.shef.ac.uk/orbitron/AOs/4s/equations.html

R4s    = (1/96) × (24 - 36ρ + 12ρ2 - ρ3) × Z3/2 × e-ρ/2

where p = 2Zr/n where n is the principal quantum number (4 for the 4s orbital)

Thats about enough math for me.  I'll take the pretty picture any day.