The Aufbau Principle

The equations of modern atomic theory are difficult to solve. Fortunately, many of the results can be obatined by following some simple rules. These rules are known as the Aufbau principle. However, we first need to discuss quantum numbers, shells, subshells and orbitals.

The principal quantum number n - the shell

Quantum numbers abound in quantum theory. These quantum numbers serve the purpose of keeping track of the various quantum possibilities that emerge. Perhaps the most important quantum number is the "principal" quantum number n. The principal quantum number n can take on the values 1, 2, 3, 4, 5, 6, ... . Associated with each n is a principle energy level known as a shell. Thus, shell 1 has n=1, shell 2 has n=2 etc. and so on associated with it.


Each shell has subshells associated with it

Depending upon its quantum number, each shell can have one or more subshells associated with it. For the n=1 shell there is only one subshell - the s subshell. For the n=2 shell there are two subshells - the s and p subshells and so on. The number of subshells within a shell is equal to n.

 principle quantum number  number of subshells  the subshell labels
 1  1  s
 2  2  s, p
 3  3  s, p, d
 4  4  s, p, d, f

The shells, subshells and orbitals can be summarized with the diagram below for a typical atom. (A mnemonic device exists to recall this order.)

Each subshell has one or more orbitals within it

Orbitals are like "rooms" within which electrons "reside". The s subshell has one s-orbital. The p subshell has three p-orbitals. The possibilities are listed in the table below:

type of
number of
 s  s  1
 p  p  3
 d  d  5
 f  f  7
 g  g  9

The Aufbau Principle

The physical and chemical properties of elements is determined by the atomic structure. The atomic structure is, in turn, determined by the electrons and which shells, subshells and orbitals they reside in. The rules af placing electrons within shells is known as the Aufbau principle. These rules are:

 1. Electrons are placed in the lowest energetically available subshell.
 2. An orbital can hold at most 2 electrons.
 3. If two or more energetically equivalent orbitals are available (e.g., p, d etc.) then electrons should be spread out before they are paired up (Hund's rule).













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C101 Class Notes
Prof. N. De Leon