Write electronic configuration of Cu and Cr — explain the anomaly

Question

Write the electronic configurations of Chromium (Cr, Z=24) and Copper (Cu, Z=29). Explain why these configurations are anomalous.

Solution — Step by Step

The Aufbau principle says electrons fill orbitals in order of increasing energy: 1s, 2s, 2p, 3s, 3p, 4s, 3d…

For Cr (Z=24), filling normally:
$1s^2\ 2s^2\ 2p^6\ 3s^2\ 3p^6\ 4s^2\ 3d^4$

For Cu (Z=29), filling normally:
$1s^2\ 2s^2\ 2p^6\ 3s^2\ 3p^6\ 4s^2\ 3d^9$

These are the predicted configurations. But the actual configurations are different.

Chromium (Cr, Z = 24):

[\text{Ar}]\ 3d^5\ 4s^1

(NOT $[\text{Ar}]\ 3d^4\ 4s^2$ as expected)

Copper (Cu, Z = 29):

[\text{Ar}]\ 3d^{10}\ 4s^1

(NOT $[\text{Ar}]\ 3d^9\ 4s^2$ as expected)

In both cases, one electron has “moved” from the 4s orbital to the 3d orbital compared to the expected filling.

The anomaly occurs because half-filled ( $d^5$ ) and fully-filled ( $d^{10}$ ) d subshells are extra stable compared to partially filled subshells like $d^4$ or $d^9$ .

Two reasons for this extra stability:

Symmetrical distribution: A half-filled or fully-filled set of orbitals has maximum symmetry, reducing electron-electron repulsion.
Exchange energy: More exchange interactions are possible between electrons in equal-energy orbitals when they are half-filled or fully-filled. Exchange energy stabilises the configuration.

The energy gained by achieving $3d^5$ or $3d^{10}$ is greater than the energy cost of promoting one electron from 4s to 3d.

Cr — half-filled 3d: Each of the five 3d orbitals holds exactly one electron (all spins parallel, Hund’s rule). This maximises exchange energy.

3d: \uparrow \quad \uparrow \quad \uparrow \quad \uparrow \quad \uparrow \qquad 4s: \uparrow

Cu — fully-filled 3d: All five 3d orbitals are completely filled (two electrons each). The single electron in 4s is the anomaly.

3d: \uparrow\downarrow\ \ \uparrow\downarrow\ \ \uparrow\downarrow\ \ \uparrow\downarrow\ \ \uparrow\downarrow \qquad 4s: \uparrow

Cr and Cu are the most famous examples, but similar anomalies occur in other d-block elements:

Mo (Z=42): $[\text{Kr}]\ 4d^5\ 5s^1$ (like Cr)
Ag (Z=47): $[\text{Kr}]\ 4d^{10}\ 5s^1$ (like Cu)
Au (Z=79): $[\text{Xe}]\ 4f^{14}\ 5d^{10}\ 6s^1$ (like Cu)

The pattern repeats for heavier analogues.

Why This Works

The Aufbau principle is a simplified model. It predicts the correct configuration for most elements, but the actual situation involves a careful balance of multiple energy terms: orbital energies, electron-electron repulsion, and exchange energy. When achieving a symmetrical half-filled or fully-filled d subshell gives a large enough energy gain, the system deviates from the simple Aufbau prediction.

Nature always goes to the lowest energy state — the anomalous configurations of Cr and Cu are the true ground states.

Alternative Method

You can also approach this by comparing total energies: the stabilisation from exchange interactions in $d^5$ configuration exceeds the energy required to promote from 4s to 3d. This is a more quantitative explanation used at the JEE Advanced level.

Common Mistake

A very common mistake is writing the anomalous configuration as $3d^5\ 4s^0$ for Cr (thinking all electrons go to 3d). The correct answer is $3d^5\ 4s^1$ — one electron remains in 4s. Similarly for Cu: it’s $3d^{10}\ 4s^1$ , not $3d^{10}\ 4s^0$ . Also, do not try to explain the anomaly by saying “4s and 3d energies are equal” — they’re not equal; it’s the exchange energy difference that drives the anomaly.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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