A New Periodic Table Helps Teach the Electronic Structure of Atoms
We show how students of chemistry can easily write down the entire periodic table with a simple mnemonic. And using the diagonal orbital filling rule they can quickly construct the complete electronic structure of most atoms in their ground state.
My periodic table was invented in the late 1960's to teach my sister Susanna, who subsequently aced her chemistry class. I have taught it to many others since, including my nephew Marc Doyle, who earned his Ph.D. in chemical engineering from UC Berkeley.
When I taught it to Mike Jittlov in the mid-1990's, he made a beautiful drawing which was added to Mark Leach's Internet Database of Periodic Tables in 1997.
Inspired by Sesame Street in the 1960's teaching children alphabetic order by pronouncing the alphabet (ab-cu-def-ghi-jekul-mun-op-qur-stuv-wix-yz), we suggest that the atomic symbols can also be pronounced in their chemical order, giving us an atomic aide memoire. We can pronounce the following syllables. (Bold letters are the atomic symbols, grouped symbols are to be pronounced as one syllable, light italic letters are suggestions to remember the full names.)
It's best to learn the pronunciation by hearing it, so please click on our under one-minute audio file, while following along the symbols in the periodic table above.
The Aufbauprinzip or Building-Up Principle
This principle says that in the ground (unexcited) state of an atom, its lowest energy electron shells (atomic orbitals) fill up before any higher levels are occupied. The "principal quantum number" n describes a "shell," and the "azimuthal quantum number" l describes subshells. The subshells are named s, p, d, and f for historical reasons.
In an s subshell only two electrons are allowed by the Pauli Exclusion Principle (one "spin-up," the other "spin down"). In a p subshell, three values of the magnetic quantum number m (+1, 0, -1) multiplied by two spins allows up to six p electrons. In the d shell, 5 magnetic substates and in the f subshell 7 substates give us up to 10 d electrons and up to 14 f electrons.
You can now determine the electron configuration for any ground state atom. Let's do potassium (K), the first element in the shell n = 4. It has only one 4s electron, and we can read off the inner shell electrons by following down the diagonal rule - 1s2 2s2 2p6 3s2 3p6 4s.
In the late 1920's Charles Janet first produced a diagram with a key to the electron structure. It was not arranged to show the diagonals of Madelung's rule. Janet was first to speculate that no element past atomic number 120 would be found. Here is an updated version.
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In the late 1920's 
