Electronic Configuration

Aufbau principle. In the ground state, orbitals fill in order of increasing energy, lowest first. The energy ordering of subshells is fixed by the $(n+l)$ rule: the subshell with the lower value of $n+l$ fills first; if two subshells tie on $n+l$, the one with the lower $n$ fills first. Applying this rule subshell by subshell produces the standard filling sequence:

where: each symbol is a subshell labelled by principal quantum number $n$ and orbital type ($s,p,d,f$ for $l = 0,1,2,3$); the ordering is by increasing $n+l$, with ties broken by lower $n$. The famous case is $4s$ ($n+l=4+0=4$) filling before $3d$ ($n+l=3+2=5$), even though $3d$ has the smaller principal quantum number.

Pauli exclusion principle. No two electrons in an atom can share all four quantum numbers. Since $n, l, m_l$ specify one orbital, this caps every orbital at two electrons, and those two must have opposite spins, $+\tfrac12$ and $-\tfrac12$.

Hund's rule. Electrons occupying degenerate orbitals (same subshell, same energy) go in singly, with parallel spin, one to each orbital, before any orbital in that subshell gets a second electron. This minimises electron-electron repulsion and maximises the number of unpaired, parallel spins in the ground state. For example, nitrogen ($Z=7$, configuration $1s^2\,2s^2\,2p^3$) places one electron in each of the three degenerate $2p$ orbitals ($2p_x, 2p_y, 2p_z$) rather than pairing two in one orbital and leaving another empty — giving nitrogen three unpaired, parallel-spin electrons, consistent with its observed paramagnetism and its tendency to form three covalent bonds.

Writing configurations. Configurations are written as filled subshells with electron-count superscripts, e.g. oxygen ($Z=8$): $1s^2\,2s^2\,2p^4$.

Stability of half-filled and fully-filled subshells. Configurations with an exactly half-filled ($p^3$, $d^5$, $f^7$) or fully-filled ($p^6$, $d^{10}$, $f^{14}$) subshell are extra stable, thanks to greater symmetry and larger exchange energy — the quantum stabilisation gained when same-spin electrons occupy degenerate orbitals. This is why chromium and copper deviate from the naive Aufbau prediction.

Question. Write the ground-state electronic configuration of chromium ($Z=24$), state why it deviates from the strict Aufbau prediction, and predict copper's ($Z=29$) configuration by the same reasoning.

Step 1. Fill strictly by the Aufbau order up to 24 electrons: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^4$, written with the argon core as $[Ar]\,3d^4\,4s^2$. This is the naive prediction from mechanically following the filling sequence.

Step 2. Compare it against the observed ground state. Chromium's actual configuration is $[Ar]\,3d^5\,4s^1$: one electron has shifted from $4s$ into $3d$.

Step 3. Explain the shift using subshell stability. A half-filled $3d^5$ (one electron in each of the five $3d$ orbitals, all parallel spin) combined with $4s^1$ is more stable overall than $3d^4\,4s^2$, because the extra symmetry and exchange energy of a half-filled $d$ subshell outweigh the cost of leaving $4s$ singly occupied.

Step 4. Apply the identical reasoning to copper. Strict Aufbau up to 29 electrons gives $[Ar]\,3d^9\,4s^2$; shifting one $4s$ electron into $3d$ gives a fully-filled $3d^{10}$ plus $4s^1$, which is more stable than $3d^9\,4s^2$ for the same symmetry-and-exchange-energy reason. Chromium: $[Ar]\,3d^5\,4s^1$; copper: $[Ar]\,3d^{10}\,4s^1$ — both trade a filled $4s^2$ for the extra stability of a half-filled or fully-filled $3d$ subshell.

Competitive stretch

Neighbouring elements test whether you apply this reasoning selectively and correctly. Manganese ($Z=25$, one more electron than chromium) follows strict Aufbau without any anomaly: $[Ar]\,3d^5\,4s^2$. Here $3d^5\,4s^2$ is already the stable arrangement — the half-filled $3d^5$ is achieved without needing to strip an electron from $4s$, so there is no shift and no exception to explain. Zinc ($Z=30$) is similarly regular: $[Ar]\,3d^{10}\,4s^2$, a fully-filled $3d^{10}$ reached by ordinary Aufbau filling, again with no anomaly. The lesson is that the chromium/copper shift happens only when the naive Aufbau configuration is one electron short of a half-filled or fully-filled $d$ subshell — not whenever a $d^5$ or $d^{10}$ appears.

• Filling $3d$ before $4s$ because $3 < 4$ — the $(n+l)$ rule gives $4s$ ($n+l=4$) before $3d$ ($n+l=5$).
• Pairing electrons in one orbital of a subshell before every orbital in it has at least one electron — this violates Hund's rule.
• Thinking Pauli's principle limits a whole subshell to 2 electrons, rather than limiting each individual orbital to 2 electrons with opposite spin.
• Memorising chromium and copper as isolated exceptions instead of understanding the half-filled/fully-filled stability argument, which is what CBSE actually tests.

Ask the tutor: Want to practice writing full and abbreviated configurations for a few tricky elements like chromium, copper, or the ones right after them?