Periodic Table
T-Shirts & more
from the

Merch Store

previous home next

The INTERNET Database of Periodic Tables

There are thousands of periodic tables in web space, but this is the only comprehensive database of periodic tables & periodic system formulations. If you know of an interesting periodic table that is missing, please contact the database curator: Mark R. Leach Ph.D.

Use the drop menus below to search & select from the more than 1300 Period Tables in the database: 

  Text Search:       

Year:  2013 PT id = 597

Periodic Pyramid

A Periodic Pyramid by Jennifer N. Hennigan and W. Tandy Grubbs * Department of Chemistry, Stetson University, DeLand, Florida 32723, United States

J. Chem. Educ., 2013, 90 (8), pp 1003-1008 DOI: 10.1021/ed3007567 Publication Date (Web): June 21, 2013

The chemical elements present in the modern periodic table are arranged in terms of atomic numbers and chemical periodicity. Periodicity arises from quantum mechanical limitations on how many electrons can occupy various shells and subshells of an atom. The shell model of the atom predicts that a maximum of 2, 8, 18, and 32 electrons can occupy the shells identified by the principle quantum numbers n = 1, 2, 3, and 4, respectively. The numbers 2, 8, 18, and 32 are shown in this work to be related to the triangular numbers from mathematical number theory. The relationship to the triangular numbers, in turn, suggests an alternate method for arranging elements in terms of periodicity. The resulting three-dimensional "periodic pyramid" is highly symmetric in shape. Just as is true in the modern periodic table, each layer of the periodic pyramid can be separated into shell and subshell contributions. Examining the pyramid's structure is arguably a pedagogically useful activity for college-level introductory or physical chemistry students, as it provides an opportunity to further ponder the shell model of the atom and the origins of periodicity. The connections to number theory are used to show that the outermost subshell of a given shell contains (2n - 1) orbitals.

<Periodic Pyramid>

Thanks to Eric Scerri for the tip!
See the website and Eric's Twitter Feed.

Top of Page

previous home next
What is the Periodic Table Showing? Periodicity

© Mark R. Leach Ph.D. 1999 –

Queries, Suggestions, Bugs, Errors, Typos...

If you have any:

Suggestions for links
Bug, typo or grammatical error reports about this page,

please contact Mark R. Leach, the author, using

This free, open access web book is an ongoing project and your input is appreciated.