Some Bohr-like diagrams

So as I was working (or at least reading up on) a home assignment having to do with elementary particles (quarks, bosons and all that) I got to thinking about the quantum property of spin. There really is nothing like it, having been unknown to man and science for all of history until like a century ago and yet it plays some part in basically every phenomenon. The most common consequence of course, known at least indirectly by every school student being that the number of electrons allowed to be contained in an electron shell is even as each corresponding as each other quantum state allows for two the coexistence of a spin-up-electron along with a spin-down-electron.

This led me back to atomic theory and how you learn to conceptualize different atomic electron configurations. The two ways I was taught back in high school being two draw Bohr diagrams and simply list the number of electrons in each shell like $2,6,18,8$ for krypton (Kr) for example which becomes extremely cluttered if you draw out the electrons so that they are equally spaced (see right). The other way being to list the electron configuration in the standard notation $1s^22s^63s^2p^63d^{10}4s^24p^6$ which you of course can shorten to $[Ar]3d^{10}4s^24p^6$ if you know the configuration for Argon (Ar). The latter of course being superior as it describes the subshell configurations.

Still… Bohr diagrams are appealing in their simplicity and I recall that I had terrible difficulty understanding what the deal or point with subshells was. Sometimes subshells are visualized by splitting a circle representing a shell into a collection of closely packed circles but this is really the worst possible thing to do as it makes it look as if subshells are physical subshells. I spent a couple of hours thinking about how one should draw an appropriate electron configuration diagram which would satisfy three general principles:

1. The electrons should be easy to count. It is well known that the human brain can subitize, that is count numbers of grouped objects numbering 1 to 7 so groups so effort should be taken to visually group electrons.
2. The state of an individual electron should be possible and simple to read out
3. It should be simple to convert the diagram into the text-representation
4. The partitioning of an electron shell into subshells should not lead one to think they have different energies

What I came up with was to draw a conventional Bohr-diagram and divide each circle into equally sized lines and then divide those line segments into the angular magnetic numbers and finally group electrons in pairs signifying the relevance of spin. The result for drawing out Krypton, which we discussed earlier, can be seen as following:

I rather enjoy this representation. It suffers from the fact that it still yields no indication of what the subshells are, that is how they are related to angular momentum but I don’t see a way to work that into a two dimensional diagram. The real advantage as I see it are that the numberologies of how many electron fit in a shell and so on are obvious and it is easy to count the electrons in groups of 2, 6 and 10. The major thing I don’t like about it is that I have hidden the fourth electron shell f which while it does not play any part for matter which only has 4 electron shells it is still relevant for a lot if interesting a frequently occurring matter. If one would divide into 4 parts instead of 3 adding the f-layer

Now another nicety I find in representing the atom schematically this way is that it is easier to illustrate that atoms high up enough in the periodic system don’t always fill up a lower subshell before electrons are added to a higher shell as is the case with Chromium (Cr).

The same basic information is available in writing out the configuration by $[Ar] 3d^5 4s^1$ but is perhaps less convincing.I might try out some refinements on this scheme in the future or figure out a major flaw but I found it nice to work on today.