The Aufbau Principle: Filling Orbitals from the Bottom Up

How do you know which orbital an electron goes into? For most atoms, the answer is a simple rule: fill the lowest-energy orbitals first. This is the Aufbau principle, from the German word Aufbau, meaning “building up”. Imagine building an atom by adding electrons one at a time: each new electron occupies the lowest-energy orbital available. Together with the Pauli exclusion principle and Hund’s rule, it lets you write the electron configuration of almost any element.

The principle

In the ground state of an atom, electrons occupy the lowest-energy orbitals available, filling them before moving to higher ones.

The “ground state” is the lowest-energy arrangement. Atoms can be excited into higher-energy arrangements by absorbing energy, but the ground state is what configurations normally describe.

Three rules work together:

1. Aufbau: fill from the lowest energy upward.
2. Pauli exclusion principle: at most two electrons per orbital, with opposite spins.
3. Hund’s rule: in a set of equal-energy orbitals, electrons go in singly with parallel spins before pairing.

The filling order

The order in which subshells fill for most elements is:

1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p

Capacities: s = 2, p = 6, d = 10, f = 14 electrons. See shells vs subshells vs orbitals.

Remembering the order

The diagonal rule

Write the subshells in rows by shell:

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

Then draw diagonal arrows from top right to bottom left, starting at 1s, and read along each arrow in turn: 1s; 2s; 2p, 3s; 3p, 4s; 3d, 4p, 5s; 4d, 5p, 6s; and so on.

The n + l rule (Madelung rule)

Each subshell has an n value (shell number) and an l value (s = 0, p = 1, d = 2, f = 3).

• Subshells fill in order of increasing n + l.
• If two subshells have the same n + l, the one with lower n fills first.

Subshell	n	l	n + l
3p	3	1	4
4s	4	0	4
3d	3	2	5
4p	4	1	5

So 3p (n + l = 4, n = 3) comes before 4s (4, n = 4), and 4s (4) before 3d (5). 3d and 4p both have n + l = 5; 3d has the lower n, so it fills first.

Use the periodic table

The easiest method is to read the periodic table left to right, top to bottom. Each block corresponds to a subshell: s-block (2 columns), p-block (6), d-block (10), f-block (14). Moving through period 4, you pass through 4s, then 3d, then 4p. See s, p, d and f blocks.

Worked examples

Oxygen (8 electrons) 1s² 2s² 2p⁴

Chlorine (17 electrons) 1s² 2s² 2p⁶ 3s² 3p⁵

Potassium (19 electrons) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ (not 3d¹)

Iron (26 electrons) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶ (Often written in shell order as …3d⁶ 4s².)

Bromine (35 electrons) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁵

Noble gas shorthand: iron is [Ar] 3d⁶ 4s², where [Ar] stands for the argon core 1s² 2s² 2p⁶ 3s² 3p⁶. See noble gas shorthand.

You can check any configuration with the electron configuration tool.

Why does 4s fill before 3d?

In a hydrogen atom, with only one electron, energy depends only on n, so 3d would be lower than 4s. In atoms with many electrons, two effects change the picture:

• Penetration: an s orbital has some electron density very close to the nucleus, inside the inner shells. A 4s electron therefore “penetrates” the inner electrons and feels more of the nuclear charge than you’d expect.
• Shielding: 3d electrons are more effectively shielded from the nucleus by inner electrons.

For potassium and calcium, these effects make 4s slightly lower in energy than 3d, so 4s fills first.

The twist: 4s electrons are lost first

Once the 3d orbitals start filling (from scandium onward), the balance shifts: 3d becomes lower in energy than 4s. That’s why, when transition metals form ions, they lose their 4s electrons first.

• Fe: [Ar] 3d⁶ 4s²
• Fe²⁺: [Ar] 3d⁶ (the two 4s electrons are lost)
• Fe³⁺: [Ar] 3d⁵

It seems contradictory (“last in, first out” doesn’t hold), but it reflects the fact that orbital energies change as electrons are added. See electron configurations of ions.

Exceptions

The Aufbau order predicts ground states correctly for most elements, but not all. The best-known exceptions are in the first transition series:

Element	Predicted	Actual
Chromium (24)	[Ar] 3d⁴ 4s²	[Ar] 3d⁵ 4s¹
Copper (29)	[Ar] 3d⁹ 4s²	[Ar] 3d¹⁰ 4s¹

In these atoms, 3d and 4s are very close in energy. A half-filled (d⁵) or completely filled (d¹⁰) d subshell has extra stability, partly from reduced electron repulsion and favourable exchange energy, so moving one electron from 4s to 3d lowers the total energy.

Similar exceptions occur for heavier elements such as molybdenum, silver and gold, and several lanthanides and actinides. See electron configuration exceptions.

Limitations

The Aufbau principle is a guide based on approximate orbital energies, not a law of nature. Orbital energies depend on the whole atom, and for heavy elements relativistic effects also play a part. Real ground-state configurations are determined by experiment (spectroscopy) and detailed calculations. Still, for the vast majority of elements, the simple filling order gets the right answer.

Why chemists still use it

If the Aufbau order has exceptions, why teach it? Because it’s right for the great majority of elements, it’s easy to apply, and it connects directly to the layout of the periodic table. It also gives the correct outer configuration for every main-group element, which is what matters for predicting bonding and reactivity. The exceptions are few, well known and explainable, and learning them is easier once the general rule is secure.

A good habit is to write the predicted configuration first, then ask: “Is this one of the known exceptions?” For the first four periods, the only ones you’re likely to meet are chromium and copper. For elements such as molybdenum, silver and gold, check a reliable data source, such as the element pages on this site.

Practice questions

1. Write the full configuration for sulfur (Z = 16).
2. Write the configuration for calcium (Z = 20).
3. Write the configuration for zinc (Z = 30) in noble gas shorthand.
4. Why does the 19th electron of potassium go into 4s rather than 3d?

Answers: (1) 1s² 2s² 2p⁶ 3s² 3p⁴; (2) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s²; (3) [Ar] 3d¹⁰ 4s²; (4) in potassium, the 4s orbital is lower in energy than 3d because 4s electrons penetrate closer to the nucleus.

Key takeaways

• The Aufbau principle: fill orbitals in order of increasing energy.
• The usual order is 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p.
• Use the diagonal rule, the n + l rule or the periodic table’s blocks to remember it.
• 4s fills before 3d, but transition metal ions lose 4s electrons first.
• Chromium and copper are the classic exceptions, favouring half-filled and filled d subshells.