Typically mnemonic diagrams, that show the order of filling of orbitals, are two dimensional. One of two dimensions is quantum number n=1, 2, 3... and the other is quantum number l=0,1,2,3, just as shown here:

 

I'd like to share with you new, three dimensional diagram, where the third dimension shows magnetic quantum number "ml", in addition to "n" and "l": 3D Mnemonic Diagram.

 

3D diagram illustrates well how all three quantum numbers are interconnected in a single geometric construction known in mathematics as the tetrahedral close sphere packing.

(Do not forget to scroll up and down, when visiting that web page, there are few interesting images there.)

Edited June 30, 200817 yr by Vts
spelling error

very interesting diagrams, and very informative, but a little too complex to make a useful mnemonic for students, I think.

 

In my classes I don't teach the 2-D diagram, mostly due to its inconsistencies and it having no real benefit to a student. I've often seen students who have written out the above diagram in an exam, only to use it completely wrongly to predict the wrong electronic configuration, where they could easily have gotten the right answer simply by looking at their periodic table (and even easier still by looking at an ADOMAH PT)

I agree that for the purposes of teaching students to derive electronic configurations ADOMAH PT is, probably, the easiest.

 

However, 3D Mnemonic shows clearly the relationship between the quantum numbers "n", "l" and "ml". It makes it absolutely clear why there are no elements with the ground state electrons in the areas that are typically shaded in 2D mnemonics (such as 5g, for example) and it provides mathematical justification for the Madelung rule, which, as it was recently found, follows the same order as the tetrahedral close sphere packing.

 

Therefore, I think, 3D mnemonic would be more useful for teaching quantum theory.

Edited July 2, 200817 yr by Vts
to correct link to 3D mnemonic

quantum theory has recently been removed from my syllabus, hence my dismissal of the 3D diagram as too complex