The Aufbau Principle - Electronic Structure and the Aufbau Principle

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The Aufbau Principle - Introduction to the Aufbau Principle

Graph showing energy of electron orbitals by quantum energy number.
Todd Helmenstine

Stable atoms have as many electrons as they do 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 n, l, m, 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 of 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.

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The Aufbau Principle - Using the Aufbau Principle

Electron Energy Level Configuration Diagram
Electron Energy Level Configuration Diagram. Todd Helmenstine

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.

First, write a column of 's' orbitals from 1 to 8.

Second, write a second column for the 'p' orbitals starting at n=2. (1p is not an orbital combination allowed by quantum mechanics)

Third, write a column for the 'd' orbitals starting at n=3.

Fourth, write a final column for 4f and 5f. There are no elements that will need a 6f or 7f shell to fill.

Finally, read the chart by running the diagonals starting from 1s.

The graphic shows this table and the arrows follow the path to follow.

Now that the order of orbitals are known to fill, all that remains is memorizing how large each orbital is.

  • s orbitals have 1 possible value of m to hold 2 electrons
  • p orbitals have 3 possible value of m to hold 6 electrons
  • d orbitals have 5 possible value of m to hold 10 electrons
  • f orbitals have 7 possible value of m to hold 14 electrons

This is all that is needed to determine the electron configuration of a stable atom of an element.

For an example, take the element nitrogen. Nitrogen 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.

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The Aufbau Principle - Silicon Electron Configuration Example

Aufbau Example Problem - Silicon Electron Configuration
Silicon Electron Configuration. Todd Helmenstine

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

Question:

Determine the electron configuration of silicon.

Solution:

Silicon is element 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 us with 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. Remember 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.

Answer

The electron configuration of silicon is 1s22s2p63s23p2.

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The Aufbau Principle - Notation and Exceptions to the Rule

Orbital Trends of the Periodic Table
Orbital Trends of the Periodic Table. Todd Helmenstine

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

nOe

where

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 8 protons and 8 electrons. The aufbau principle has 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 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 29 and should be [Ar]3d92s2, but it has been to be determined to be [Ar]3d104s1.

The graphic shows the trends of 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 that has this information on it already.