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Following the Aufbau principle, you’d predict that chromium (element 24) is [Ar] 4s² 3d⁴ and copper (element 29) is [Ar] 4s² 3d⁹. Both predictions are wrong. Experiments show:
- Chromium: [Ar] 4s¹ 3d⁵
- Copper: [Ar] 4s¹ 3d¹⁰
In each case, one electron has moved from 4s into 3d. These are the two most famous exceptions to the filling rules, and they show that the rules are approximations, not laws.
The usual explanation: half-filled and filled subshells
A half-filled d subshell (d⁵) and a completely filled one (d¹⁰) are unusually stable.
- In chromium, moving one electron from 4s to 3d creates six unpaired electrons, one in the 4s orbital and one in each of the five 3d orbitals, all with parallel spins. Electrons with parallel spins in different orbitals have a quantum mechanical energy advantage called exchange energy, and they also avoid the repulsion of sharing an orbital.
- In copper, moving one electron gives a complete 3d¹⁰ subshell, which is symmetrical and stable.
The key enabling factor is that 4s and 3d are very close in energy in these atoms. When two levels are nearly equal, a small extra stabilization from half-filled or filled subshells is enough to tip the balance.
The fuller picture
“Half-filled and filled subshells are stable” is a helpful rule of thumb, but it’s not the whole story — which is why it doesn’t predict every exception. The real configuration of an atom is whichever arrangement has the lowest total energy, and that depends on a subtle balance of electron–nucleus attraction, electron–electron repulsion and exchange energy. For elements in the middle of the table these contributions nearly cancel, and the lowest-energy arrangement can be surprising.
Common exceptions
Period 4
| Element | Expected | Actual |
|---|---|---|
| Chromium (24) | [Ar] 4s² 3d⁴ | [Ar] 4s¹ 3d⁵ |
| Copper (29) | [Ar] 4s² 3d⁹ | [Ar] 4s¹ 3d¹⁰ |
Period 5 — more exceptions, because 5s and 4d are even closer in energy
| Element | Actual |
|---|---|
| Niobium (41) | [Kr] 5s¹ 4d⁴ |
| Molybdenum (42) | [Kr] 5s¹ 4d⁵ |
| Ruthenium (44) | [Kr] 5s¹ 4d⁷ |
| Rhodium (45) | [Kr] 5s¹ 4d⁸ |
| Palladium (46) | [Kr] 4d¹⁰ (no 5s electrons at all) |
| Silver (47) | [Kr] 5s¹ 4d¹⁰ |
Period 6 and beyond
| Element | Actual |
|---|---|
| Platinum (78) | [Xe] 4f¹⁴ 5d⁹ 6s¹ |
| Gold (79) | [Xe] 4f¹⁴ 5d¹⁰ 6s¹ |
Among the lanthanides and actinides there are many more (for example lanthanum, cerium, gadolinium, thorium and uranium), because 4f/5d and 5f/6d levels are also very close.
Notice that molybdenum and silver behave just like chromium and copper above them, but tungsten (below molybdenum) does not — it’s [Xe] 4f¹⁴ 5d⁴ 6s², following the normal rule. Group trends don’t always carry through, which is why these configurations have to be measured, not assumed.
Why it matters for ions
Chromium and copper ions follow the same rule as every transition metal: electrons are removed from 4s before 3d.
- Cu⁺: [Ar] 3d¹⁰ (lose the single 4s electron)
- Cu²⁺: [Ar] 3d⁹
- Cr³⁺: [Ar] 3d³
Copper(I) compounds are often colourless and copper(II) compounds coloured, because 3d¹⁰ has no room for the d–d electron jumps that absorb visible light — see transition metals.
Exams vs. reality
Most introductory courses expect you to know chromium and copper as exceptions, and sometimes their period 5 counterparts. The heavier exceptions are usually beyond the syllabus. For the superheavy elements, configurations are predicted by calculation, since they can’t be measured.
Quick answers
Why is copper 4s¹ 3d¹⁰? A completely filled 3d subshell is lower in energy overall than 4s² 3d⁹, because 4s and 3d are so close in energy.
Is chromium 4s¹ 3d⁵ or 4s² 3d⁴? 4s¹ 3d⁵, measured experimentally.
How can I check any element’s configuration? The electron configuration generator shows the real (measured or best-predicted) configuration and orbital box diagram for all 118 elements, with exceptions handled. For the underlying rules, see electron configuration rules.
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