Difficulty: Intermediate | Prerequisites: Parts 1 and 2 of these notes (quantum numbers, orbital shapes, Pauli Exclusion Principle).
With quantum numbers and orbital shapes in hand, you can now describe exactly where every electron sits in any atom. The rules for filling orbitals (Aufbau principle, Hund's rule, Pauli exclusion) produce the electron configurations that underpin the structure of the periodic table. From there, trends in ionisation energy, electron affinity, and atomic radius follow logically. This is the section that ties quantum mechanics to the chemistry you will use for the rest of the course.
Electrons fill orbitals in order of increasing energy, not increasing n. Within a set of degenerate orbitals, each gets one electron before any gets two (Hund's rule), and paired electrons must have opposite spins (Pauli). This filling pattern gives rise to the periodic table's block structure (s, p, d, f blocks). Ionisation energy and electron affinity generally increase across a period and decrease down a group; atomic radius does the opposite.
Polyelectronic atom
Any atom with more than one electron. The Schrodinger equation cannot be solved exactly for these, so we use the hydrogen orbital labels (1s, 2s, 2p, etc.) as an approximation.
Electron configuration
A notation showing which orbitals are occupied and how many electrons each holds, e.g. 1s²2s²2p⁶3s¹ for sodium. In simple terms, it is the electron address list for an atom.
Aufbau principle
Orbitals are filled in order of increasing energy, which is not always the same as increasing n. The name comes from the German word for "building up."
Hund's rule
When filling a set of degenerate orbitals, place one electron in each orbital (all with parallel spin) before pairing any. Think of it as people on a bus: everyone takes their own seat before anyone doubles up.
Valence electrons
The electrons in the outermost s and p orbitals of the highest occupied principal energy level. These are the electrons involved in chemical bonding and reactions.
Valence shell
The highest occupied n-level's s and p sublevels. A full valence shell (like the noble gases) is particularly stable.
Core electrons
All electrons that are not valence electrons. They occupy inner, fully filled energy levels.
Shielding (screening)
The reduction of nuclear charge felt by an outer electron, caused by the repulsion from inner (core) electrons. In simple terms, inner electrons partially block the outer electrons from feeling the full pull of the nucleus.
Effective nuclear charge (Z_eff)
The net positive charge experienced by a valence electron after accounting for shielding by core electrons. Z_eff = Z - S, where S is the shielding constant.
Ionisation energy (IE)
The energy required to remove an electron from a gaseous atom or ion. The first IE removes the outermost (easiest) electron; successive IEs remove deeper ones.
Electron affinity (EA)
The energy change when an electron is added to a gaseous atom. A large negative EA means the atom strongly attracts an extra electron.
Atomic radius (covalent radius)
Half the distance between the nuclei of two bonded identical atoms. In simple terms, the "size" of an atom.
Alkali metals (Group 1)
Lithium, sodium, potassium, rubidium, caesium, francium. Soft, highly reactive metals with one valence electron (ns¹ configuration).
Metalloid
An element with properties intermediate between metals and non-metals (e.g. silicon, germanium). They can lose or gain electrons depending on the reaction.
In hydrogen, orbitals with the same n but different l are degenerate (same energy). In multi-electron atoms, electron-electron repulsion breaks this degeneracy.
In polyelectronic atoms, for a given n: s < p < d < f in energy. This is because s orbitals penetrate closer to the nucleus and experience less shielding.
The filling order by energy: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.
Aufbau principle: fill orbitals in order of increasing energy.
Pauli Exclusion Principle: maximum two electrons per orbital, with opposite spins.
Hund's rule: for degenerate orbitals (e.g. the three 2p orbitals), place one electron in each before pairing. All unpaired electrons have parallel spin.
Hydrogen (Z = 1): 1s¹
Helium (Z = 2): 1s² (full)
Lithium (Z = 3): 1s²2s¹
Carbon (Z = 6): 1s²2s²2p² (Hund's rule: two unpaired electrons in separate p orbitals)
Neon (Z = 10): 1s²2s²2p⁶ (full valence shell, noble gas)
Sodium (Z = 11): 1s²2s²2p⁶3s¹ = [Ne]3s¹ (noble gas shorthand)
Potassium (Z = 19): [Ar]4s¹ (4s fills before 3d)
Chromium (Z = 24): [Ar]4s¹3d⁵ (exception: half-filled d sublevel is especially stable)
Copper (Z = 29): [Ar]4s¹3d¹⁰ (exception: filled d sublevel is especially stable)
Gallium (Z = 31): [Ar]4s²3d¹⁰4p¹
Row (period) number = the highest occupied principal quantum level.
The "A" group number gives the total number of valence electrons.
s-block: Groups 1 and 2 (filling the ns orbital).
p-block: Groups 13 to 18 (filling the np orbitals).
d-block: Groups 3 to 12, the transition metals (filling the (n-1)d orbitals).
f-block: lanthanides and actinides (filling the (n-2)f orbitals).
Elements in the same group share the same valence shell structure, which is why they have similar chemical properties.
First ionisation energy: the energy needed to remove the outermost valence electron.
Increases left to right across a period, because nuclear charge (Z) increases while the valence electrons are in the same shell, so they are held more tightly.
Decreases top to bottom down a group, because the valence electron is in a higher n-level, farther from the nucleus.
Removing a core electron costs dramatically more energy than removing a valence electron (e.g. IE₁ for Na = 5.14 eV; IE₂ = 47.3 eV).
Electron affinity: the energy released when an atom gains an electron.
Halogens (Group 7) have the highest electron affinities because gaining one electron completes a noble gas configuration.
Nitrogen has nearly zero electron affinity because its 2p sublevel is exactly half-filled; adding an electron forces pairing.
O²⁻ is unstable in isolation (second EA is positive), but exists in ionic compounds because lattice energy compensates.
Decreases left to right across a period, because increasing Z pulls electrons closer to the nucleus while the shell stays the same.
Increases top to bottom down a group, because electrons fill orbitals with higher n, which are larger.
Configuration: [noble gas]ns¹. One valence electron, easily lost.
Very soft, highly reactive metals. Rarely found pure in nature.
React vigorously with water: 2X(s) + 2H₂O(l) → 2XOH(aq) + H₂(g).
Reactivity increases down the group: lower ionisation energy and larger atomic radius make it easier to lose the valence electron.
Metals (left and centre of the table): tend to lose electrons. Good conductors, malleable.
Non-metals (upper right): tend to gain electrons. Poor conductors, brittle as solids.
Metalloids (along the staircase): intermediate properties. Important in semiconductors (silicon, germanium).
Orbital filling order by energy:
1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p
Maximum electrons per sublevel:
s sublevel (l = 0): 2 electrons (1 orbital)
p sublevel (l = 1): 6 electrons (3 orbitals)
d sublevel (l = 2): 10 electrons (5 orbitals)
f sublevel (l = 3): 14 electrons (7 orbitals)
General formula: each sublevel holds 2(2l + 1) electrons. Each shell n holds a maximum of 2n² electrons total.
Electron configurations explain why copper is a good conductor (its loosely held 4s electron), why noble gases are chemically inert (full valence shells), and why silicon is a semiconductor (four valence electrons, metalloid properties). The periodic trends in ionisation energy and electron affinity predict which elements form cations, which form anions, and the types of bonds that result.
Students often think 3d fills before 4s because 3 < 4. It does not. The 4s orbital is lower in energy than 3d in neutral atoms, so it fills first. (When ionising transition metals, however, 4s electrons are removed first.)
Students often assume chromium's configuration is [Ar]4s²3d⁴. It is [Ar]4s¹3d⁵. A half-filled d sublevel offers extra stability. The same applies to copper: [Ar]4s¹3d¹⁰, not [Ar]4s²3d⁹.
Students sometimes think "valence electrons" includes d electrons for transition metals. For main-group elements, valence electrons are only those in the highest occupied s and p sublevels.
Students often think atomic radius increases across a period. It decreases, because more protons pull the electron cloud inward.
⚠️ Writing electron configurations is heavily tested. Know the filling order cold, including the Cr and Cu exceptions.
⚠️ Noble gas shorthand: be able to write [Ne]3s²3p⁵ for chlorine, [Ar]4s²3d⁷ for cobalt, etc.
⚠️ Periodic trend questions: "which has the larger first ionisation energy, Na or Cl?" (Cl, because it is further right in the same period). "Which is larger, Li or Cs?" (Cs, because it is further down the group).
⚠️ Know why halogens have high electron affinity (one electron short of a noble gas configuration) and why nitrogen has low EA (half-filled p sublevel).
⚠️ Expect a question asking you to identify the point where successive ionisation energies jump dramatically (e.g. Na: IE₁ is small, IE₂ is huge, because IE₂ breaks into a core shell).
Fill in the blank: the electron configuration of phosphorus (Z = 15) is [Ne]______.
True or false: in a polyelectronic atom, the 3s and 3p orbitals have the same energy.
Fill in the blank: ionisation energy tends to ______ across a period from left to right.
True or false: the alkali metals become less reactive as you go down the group.
Fill in the blank: atomic radius tends to ______ down a group.
Answers: 1. 3s²3p³. 2. False (3s is lower in energy than 3p in multi-electron atoms). 3. Increase. 4. False (they become more reactive). 5. Increase.
Q: Write the full electron configuration and noble gas shorthand for iron (Z = 26).
A: Full: 1s²2s²2p⁶3s²3p⁶4s²3d⁶. Shorthand: [Ar]4s²3d⁶.
Q: Why is chromium's configuration [Ar]4s¹3d⁵ rather than [Ar]4s²3d⁴?
A: A half-filled d sublevel (five electrons, one in each d orbital with parallel spins) provides extra stability due to favourable exchange energy. One electron is promoted from 4s to 3d to achieve this.
Q: Rank the following in order of increasing first ionisation energy: K, Ca, Ga, Ge, As, Se, Br, Kr.
A: K < Ca < Ga < Ge < As < Se < Br < Kr (general increase across Period 4, with minor dips at Ga and Se due to subshell effects).
Q: Which has the larger atomic radius, Na or Cl? Explain.
A: Na has the larger atomic radius. Both are in Period 3, but Cl has more protons (17 vs 11), pulling the same-shell electrons inward. Radius decreases across a period.
Q: Why does fluorine have a very high (negative) electron affinity?
A: Fluorine is 1s²2s²2p⁵. Adding one electron completes the 2p sublevel, giving it a noble gas configuration ([Ne]). The strong nuclear charge (Z = 9) in such a small atom means the extra electron is held tightly.
Electron configurations connect directly to chemical bonding (the next major topic in most courses), because the number and arrangement of valence electrons determine bond type, bond order, and molecular geometry. Periodic trends in IE and EA also predict electronegativity, which governs bond polarity. The concept of shielding and effective nuclear charge recurs in transition-metal chemistry and coordination compounds.
electron configuration, Aufbau principle, Hund's rule, Pauli Exclusion Principle, orbital filling order, noble gas shorthand, valence electrons, valence shell, core electrons, shielding, screening, effective nuclear charge, Z_eff, polyelectronic atom, s-block, p-block, d-block, f-block, transition metals, ionisation energy, first ionisation energy, successive ionisation energies, electron affinity, atomic radius, covalent radius, periodic trends, periodic table, alkali metals, Group 1, metals, non-metals, metalloids, chromium exception, copper exception, General Physics Ch 12