# Introduction to the Aufbau Principle in Chemistry

Stable atoms have as many electrons as protons in the nucleus. The electrons gather around the nucleus in quantum orbitals following four basic rules called the Aufbau principle.

• No two electrons in the atom will share the same four quantum numbers nlm, and s.
• Electrons will first occupy orbitals of the lowest energy level.
• Electrons will fill an orbital with the same spin number until the orbital is filled before it will begin to fill with the opposite spin number.
• Electrons will fill orbitals by the sum of the quantum numbers n and l. Orbitals with equal values of (n+l) will fill with the lower n values first.

The second and fourth rules are basically the same. The graphic shows the relative energy levels of the different orbitals. An example of rule four would be the 2p and 3s orbitals. A 2p orbital is n=2 and l=2 and a 3s orbital is n=3 and l=1; (n+l)=4 in both cases, but the 2p orbital has the lower energy or lower n value and will get filled before the 3s shell.

## Using the Aufbau Principle

Probably the worst way to use the Aufbau principle to figure the fill order of an atom's orbitals is to try and memorize the order by brute force:

• 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p 8s

Fortunately, there is a much simpler method to get this order:

1. Write a column of s orbitals from 1 to 8.
2. Write a second column for the p orbitals starting at n=2. (1p is not an orbital combination allowed by quantum mechanics.)
3. Write a column for the d orbitals starting at n=3.
4. Write a final column for 4f and 5f. There are no elements that will need a 6f or 7f shell to fill.
5. Read the chart by running the diagonals starting from 1s.

The graphic shows this table and the arrows show the path to follow. Now that you know the order of orbitals to fill, you need only memorize the size of each orbital.

• S orbitals have one possible value of m to hold two electrons.
• P orbitals have three possible value of m to hold six electrons.
• D orbitals have five possible value of m to hold 10 electrons.
• F orbitals have seven possible value of m to hold 14 electrons.

This is all you need to determine the electron configuration of a stable atom of an element.

For example, take the element nitrogen, which has seven protons and therefore seven electrons. The first orbital to fill is the 1s orbital. An s orbital holds two electrons, so five electrons are left. The next orbital is the 2s orbital and holds the next two. The final three electrons will go to the 2p orbital, which can hold up to six electrons.

## Silicon Electron Configuration Example Problem

This is a worked example problem showing the steps necessary to determine the electron configuration of an element using the principles learned in the previous sections

#### Problem

Determine the electron configuration of silicon.

#### Solution

Silicon is element No. 14. It has 14 protons and 14 electrons. The lowest energy level of an atom is filled first. The arrows in the graphic show the s quantum numbers, spin up and spin down.

• Step A shows the first two electrons filling the 1s orbital and leaving 12 electrons.
• Step B shows the next two electrons filling the 2s orbital leaving 10 electrons. (The 2p orbital is the next available energy level and can hold six electrons.)
• Step C shows these six electrons and leaves four electrons.
• Step D fills the next lowest energy level, 3s with two electrons.
• Step E shows the remaining two electrons starting to fill the 3p orbital.

One of the rules of the Aufbau principle is that the orbitals are filled by one type of spin before the opposite spin starts to appear. In this case, the two spin-up electrons are placed in the first two empty slots, but the actual order is arbitrary. It could have been the second and third slot or the first and third.

The electron configuration of silicon is:

1s22s2p63s23p2

## Notation and Exceptions to the Aufbau Principal

The notation seen on period tables for electron configurations uses the form:

nOe
• n is the energy level
• O is the orbital type (s, p, d, or f)
• e is the number of electrons in that orbital shell.

For example, oxygen has eight protons and eight electrons. The Aufbau principle says the first two electrons would fill the 1s orbital. The next two would fill the 2s orbital leaving the remaining four electrons to take spots in the 2p orbital. This would be written as:

1s22s2p4

The noble gases are the elements that fill their largest orbital completely with no leftover electrons. Neon fills the 2p orbital with its last six electrons and would be written as:

1s22s2p6

The next element, sodium would be the same with one additional electron in the 3s orbital. Rather than writing:

1s22s2p43s1

and taking up a long row of repeating text, a shorthand notation is used:

[Ne]3s1

Each period will use the notation of the previous period's noble gas. The Aufbau principle works for nearly every element tested. There are two exceptions to this principle, chromium, and copper.

Chromium is element No. 24, and according to the Aufbau principle, the electron configuration should be [Ar]3d4s2. Actual experimental data shows the value to be [Ar]3d5s1. Copper is element No. 29 and should be [Ar]3d92s2, but it has been to be determined to be [Ar]3d104s1.

The graphic shows the trends of the periodic table and the highest energy orbital of that element. It is a great way to check your calculations. Another method of checking is to use a periodic table, which includes this information.