Electronic Configuration: MDCAT Chemistry notes
Electronic Configuration for MDCAT: Aufbau principle and n + l rule, Pauli and Hund's rules, chromium and copper exceptions, ions and unpaired electrons.
Rules for filling orbitals
Aufbau principle
Electrons fill orbitals in order of increasing energy, lowest first. 1s is the lowest-energy orbital. The order is found by the $(n+l)$ rule:
- The subshell with the lower $n+l$ value fills first.
- If two subshells have the same $n+l$, the one with lower $n$ fills first.
| Subshell | 4s | 3d | 4p | 5s | 4d | 5p | 6s | 4f | 5d | 6p |
|---|---|---|---|---|---|---|---|---|---|---|
| $n+l$ | 4 | 5 | 5 | 5 | 6 | 6 | 6 | 7 | 7 | 7 |
Filling order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p. So after 5d is complete the next electron enters 6p, and after 6d it enters 7p. Among 4s, 2p, 3s and a (non-existent) 2d, 4s has the highest energy.
Pauli exclusion principle
No two electrons in an atom have the same four quantum numbers, so each orbital holds at most two electrons of opposite spin.
Hund's rule
In degenerate orbitals (equal energy, e.g. the three 2p orbitals) electrons occupy separate orbitals singly with parallel spins before any pairing occurs. Nitrogen ($2p^3$) therefore has 3 unpaired electrons.
Configurations to know
| Element (Z) | Configuration | Unpaired electrons |
|---|---|---|
| B (5) | $1s^22s^22p^1$ | 1 |
| C (6) | $1s^22s^22p^2$ | 2 |
| N (7) | $1s^22s^22p^3$ | 3 |
| Na (11) | $[Ne]3s^1$ | 1 |
| Ar (18) | $1s^22s^22p^63s^23p^6$ | 0 |
| Ca (20) | $[Ar]4s^2$ (3p holds 6) | 0 |
| Cr (24) | $[Ar]3d^54s^1$ | 6 |
| Fe (26) | $[Ar]3d^64s^2$ | 4 |
| Ni (28) | $[Ar]3d^84s^2$ | 2 |
| Cu (29) | $[Ar]3d^{10}4s^1$ | 1 |
| Zr (40) | $[Kr]5s^24d^2$ | 2 |
Paramagnetism increases with the number of unpaired electrons: among H, Be, B and C, carbon (2 unpaired) is the most paramagnetic.
Exceptions: chromium and copper
Half-filled ($d^5$) and completely filled ($d^{10}$) subshells are extra stable. So one 4s electron moves into 3d: Cr is $[Ar]3d^54s^1$, not $3d^44s^2$; Cu is $[Ar]3d^{10}4s^1$. Na and Cr both have a single outer s electron.
Ions
Transition metals lose their 4s electrons first, then 3d. Fe is $[Ar]3d^64s^2$; $Fe^{2+}$ is $[Ar]3d^6$ (4 unpaired); $Fe^{3+}$ is $[Ar]3d^5$ (5 unpaired, extra stable). $Ca^{2+}$ loses both 4s electrons and has the argon structure 2, 8, 8.
Worked examples
- Element with four unpaired electrons in the ground state: Fe, $Z=26$ ($3d^6$: one pair and four singles).
- $[Kr]5s^24d^8$ accounts for 36 + 10 = 46 electrons, so $Z=46$ (palladium). Note that palladium's actual ground state is an exception, $[Kr]4d^{10}$; exam questions of this type simply count electrons.
Common MDCAT traps
- 4s fills before 3d, but 4s electrons are removed first on ionisation.
- Hund's rule, not Aufbau or Pauli, explains filling of degenerate orbitals.
- Cr is $3d^54s^1$ and Cu is $3d^{10}4s^1$.
- Count unpaired electrons using Hund's rule: $d^6$ has 4, $d^5$ has 5, $d^8$ has 2.
- Using $(n+l)$: when values tie, lower $n$ fills first (3d before 4p).
Quick revision
- 1s has the lowest energy.
- After 5d comes 6p; after 6d comes 7p.
- $Fe^{3+}$: 5 unpaired electrons.
- Boron has 1 unpaired electron.
- Ni: $3d^84s^2$.