The formula
- Aufbau filling order
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p- Notation for a neutral atom, phosphorus
P: 1s² 2s² 2p⁶ 3s² 3p³- Noble gas shorthand, same atom
P: [Ne] 3s² 3p³- Electrons a subshell holds
s 2, p 6, d 10, f 14 (two per orbital)
What the symbols mean
| Symbol | Meaning | Unit |
|---|---|---|
n | Principal quantum number, the shell, written as the leading digit | 1, 2, 3, ... (dimensionless) |
s, p, d, f | Subshell labels, holding 1, 3, 5 and 7 orbitals respectively | dimensionless |
superscript | Number of electrons in that subshell | count |
[Ne], [Ar], [Kr] | Noble gas core, standing in for that element's full configuration | 10, 18 and 36 electrons respectively |
Z | Atomic number, which for a neutral atom equals the total electron count | count |
When it applies
- The atom is in its ground state. An excited atom has an electron promoted out of the Aufbau order, and an ion needs its charge applied first.
- The electron count is right: Z electrons for a neutral atom, Z minus the charge for a cation, Z plus the charge for an anion.
- Hund's rule governs any partly filled subshell, so count unpaired electrons from the orbital diagram rather than from the written configuration.
- Chromium, copper and several heavier transition metals sit one electron off the straight Aufbau prediction, so check those against a table.
Worked example
Problem. Write the ground-state electron configuration of iron (Z = 26), give the noble gas shorthand, and say how many unpaired electrons it has.
- Iron is neutral, so it holds 26 electrons. Fill in Aufbau order and stop when the running total reaches 26.
- 1s² 2s² 2p⁶ 3s² 3p⁶ accounts for 2 + 2 + 6 + 2 + 6 = 18 electrons, which is the argon core.
- The 4s subshell fills before 3d, so add 4s² to reach 20, then place the last 6 electrons in 3d: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶. Total 18 + 2 + 6 = 26, as required.
- Replace the argon core with its symbol for the shorthand: [Ar] 4s² 3d⁶.
- For unpaired electrons, draw the five 3d orbitals. Hund's rule puts one electron in each of the five first, and the sixth pairs up with one of them, leaving 4 unpaired.
Answer. Fe: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶, shorthand [Ar] 4s² 3d⁶, with 4 unpaired electrons.
Common mistakes
- Filling 3d before 4s. The 4s subshell is lower in energy in the neutral atom and fills first, even though it carries the higher principal quantum number.
- Forgetting to adjust the electron count for an ion. Fe³⁺ has 23 electrons, not 26, and transition metals lose their s electrons before their d electrons.
- Reading unpaired electrons off the written configuration. 3d⁶ looks like three pairs on paper, but Hund's rule makes it four singles and one pair.
- Treating the noble gas shorthand as a different answer. [Ar] 4s² 3d⁶ and the full string describe the same atom, and most courses accept either unless one is asked for by name.
Related formulas
- Lewis structure:
1 count valence electrons, 2 connect atoms with single bonds, 3 complete octets on outer atoms, 4 put leftovers on the central atom, 5 form multiple bonds if the central atom is short - Molar mass:
M = Σ (atoms of each element × atomic mass) - Covalent bond:
ΔEN = |EN(A) - EN(B)|