Difficulty: Advanced (this is the most exam-heavy section of the chapter)
Prerequisites: Parts 1 and 2 of these notes. You need to be comfortable with the four quantum numbers (n, ℓ, mℓ, ms) and orbital shapes (s, p, d, f) before proceeding.
This is where the theory from the earlier sections turns into practical, testable skills. You will learn how to write the electron configuration for any element, predict magnetism, and explain five major periodic trends using a small set of arguments (effective nuclear charge, distance, shielding, and electron-electron repulsions). Your instructor flagged this as the most important material in the chapter, and the AP exam agrees: periodic trend explanations appear on nearly every free-response section.
Electrons fill orbitals from lowest to highest energy following the Aufbau principle, Hund's rule, and the Pauli exclusion principle. Periodic trends in atomic radius, ionisation energy, electron affinity, electronegativity, and ionic radius are explained by effective nuclear charge (Z_eff), distance from the nucleus, shielding by core electrons, and electron-electron repulsions. The AP exam tests not just the trends but your ability to explain them using these arguments.
Electron configuration (spectroscopic notation)
The notation showing how electrons are distributed among an atom's orbitals. Written by listing subshells in order of principal quantum number with superscripts indicating the number of electrons in each (e.g. 1s² 2s² 2p⁶ 3s² 3p⁴ for sulfur).
Orbital notation (orbital diagram)
A visual representation using boxes or lines for orbitals and arrows (up/down) for electrons. Shows both electron filling order and spin.
Aufbau principle (diagonal rule)
Electrons fill orbitals starting from the lowest energy and working up. The filling order follows the diagonal rule: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.
In simple terms, each electron takes the lowest-energy seat available.
Hund's rule
The most stable arrangement of electrons in a subshell has the maximum number of unpaired electrons, all with parallel spins. Electrons fill each orbital in a subshell singly before any orbital gets a second electron.
Think of it as "everyone gets their own room before anyone shares."
Pauli exclusion principle
No two electrons in the same atom can have the same set of four quantum numbers. This means each orbital can hold a maximum of two electrons, and those two must have opposite spins (+1/2 and −1/2).
Diamagnetic
A substance in which all electrons are paired. Diamagnetic materials are slightly repelled by a magnetic field.
In simple terms, if every electron has a partner with opposite spin, the magnetic effects cancel out.
Paramagnetic
A substance with one or more unpaired electrons. Paramagnetic materials are attracted to a magnetic field but lose their magnetism when the field is removed.
Ferromagnetic
A substance that retains magnetism after exposure to an external magnetic field. Clusters of atoms (domains) have their unpaired electron spins aligned. Drop a ferromagnet and the domains misalign, destroying the magnetism.
Effective nuclear charge (Z_eff)
The net positive charge experienced by a valence electron after accounting for shielding by inner electrons. Roughly equal to the group number for main-group elements. Higher Z_eff means a stronger pull on valence electrons.
Shielding (screening)
The reduction in nuclear attraction experienced by valence electrons due to the repulsion from inner (core) electrons. Shielding increases as you move down a group (more inner shells). Shielding within the same energy level is incomplete and generally not used to explain trends across a period.
Penetration
The extent to which an electron's probability distribution extends close to the nucleus. s orbitals penetrate most, then p, then d, then f. Greater penetration means lower energy and a tighter hold by the nucleus.
Atomic radius
Half the distance between the nuclei of two bonded identical atoms. Decreases across a period (increasing Z_eff pulls the electron cloud in) and increases down a group (additional principal energy levels).
Ionisation energy (IE)
The energy required to remove an electron from a gaseous atom. Increases across a period (higher Z_eff) and decreases down a group (greater distance and shielding). Successive ionisation energies always increase; a huge jump signals removal from a new subshell or core level.
Electron affinity (EA)
The energy change when a gaseous atom gains an electron. A more negative value means more energy is released (the atom "wants" the electron more). Generally becomes more negative across a period and less negative down a group.
Electronegativity (En)
The ability of an atom in a molecule to attract shared electrons towards itself. Measured on Pauling's scale. Fluorine is the most electronegative element (4.0), francium the least (0.7). Only meaningful when atoms are bonded.
Isoelectronic
Species that contain the same number of electrons. Among isoelectronic ions, the one with more protons will be smaller because the nucleus attracts the same number of electrons more strongly.
Ionic radius
The effective radius of an ion. Cations are smaller than their parent atoms (fewer electrons, same nuclear charge). Anions are larger (more electrons, same nuclear charge, increased electron-electron repulsion).
Each electron behaves as a tiny magnet with two possible orientations: ms = +1/2 or ms = −1/2.
Diamagnetic: all electrons paired, slightly repelled by a magnetic field (e.g. He, Ne).
Paramagnetic: one or more unpaired electrons, attracted to a magnetic field (e.g. H, O, Fe).
Ferromagnetic: domains of aligned unpaired spins retain magnetism after the external field is removed (e.g. Fe, Co, Ni). Drop a ferromagnet and the domains scramble.
Aufbau principle: Electrons occupy the lowest-energy orbital available. Use the diagonal rule to determine filling order: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d, and so on.
Pauli exclusion principle: No two electrons can share the same four quantum numbers. Maximum 2 electrons per orbital, with opposite spins.
Hund's rule: Within a subshell, electrons fill each orbital singly (all with the same spin direction) before any orbital gets a second electron. This minimises electron-electron repulsions.
Use the diagonal rule to fill in order, then regroup by principal quantum number for the final written configuration.
Example: Sulfur (Z = 16): filling order gives 1s² 2s² 2p⁶ 3s² 3p⁴.
The orbital notation for S shows the 3p subshell with three orbitals: the first orbital has two electrons (paired), the second and third each have one electron (unpaired, parallel spins).
For cations, remove electrons from the highest principal energy level (outermost n) first, even if that is not the last subshell filled.
Transition metals with +2 or higher charge lose their ns electrons before nd electrons.
Example: Fe is [Ar] 4s² 3d⁶. Fe²⁺ is [Ar] 3d⁶ (the two 4s electrons leave first). Fe³⁺ is [Ar] 3d⁵.
The "dsf overlap" (where 4s fills before 3d in neutral atoms) does not apply to ions; once electrons are removed, the shell energy ranges separate more widely.
Chromium: expected [Ar] 4s² 3d⁴, actual [Ar] 4s¹ 3d⁵.
Copper: expected [Ar] 4s² 3d⁹, actual [Ar] 4s¹ 3d¹⁰.
The reason: moving one electron from 4s to 3d minimises electron-electron repulsions and lowers the total energy. Do not write that a half-filled or fully filled subshell has "special stability." That is not the correct explanation.
The AP exam requires explanations, not just knowledge of the trends. Four arguments cover nearly every case:
Effective nuclear charge (Z_eff): Roughly equals the group number. Higher Z_eff means a stronger pull on electrons. Use this across a period.
Distance: Attractive forces weaken with distance. Electrons farther from the nucleus are held more loosely. Use this down a group.
Shielding: Core electrons block the nucleus's pull on valence electrons. Use this only when comparing elements in different periods (up/down the table). Shielding within a period is incomplete.
Electron-electron repulsions: Pairing electrons in the same orbital increases repulsion, making one of them easier to remove. Use this to explain anomalies (e.g. O vs N ionisation energy).
Decreases across a period: increasing Z_eff pulls the electron cloud inward, shrinking the atom until electron-electron repulsions halt the contraction.
Increases down a group: each new period adds a principal energy level, greatly increasing the atom's size. The nucleus is also farther from the valence electrons and more shielded.
Increases across a period: higher Z_eff holds valence electrons more tightly.
Decreases down a group: greater distance from the nucleus and increased shielding by full inner shells make the outermost electron easier to remove.
Exception (IIA to IIIA, e.g. Be to B): IE drops because the electron removed from B is in a 2p orbital, which penetrates less than 2s and is therefore less tightly held.
Exception (VA to VIA, e.g. N to O): IE drops because oxygen's p⁴ electron is the first to pair in an orbital. The increased electron-electron repulsion from pairing makes that electron easier to remove, despite the higher Z_eff.
Successive IEs always increase. A dramatic jump indicates you have begun removing electrons from a deeper subshell or a core energy level.
Generally becomes more negative (more energy released) across a period: increasing Z_eff attracts the incoming electron more strongly.
Generally becomes less negative (less energy released) down a group: the incoming electron is farther from the nucleus and more shielded.
Exception: nitrogen has a less favourable EA than carbon because adding an electron to N (p³) would require pairing, introducing repulsion that overcomes the increase in Z_eff. Carbon (p²) adds an electron without pairing.
Fluorine's EA is less negative than chlorine's because the 2p orbitals are very small, creating unusually strong electron-electron repulsion.
Increases across a period: higher Z_eff and smaller radius mean the nucleus is closer to the bonding electrons.
Decreases down a group: larger radius and greater shielding weaken the pull on bonding electrons.
Fluorine is the most electronegative element. Francium is the least.
Electronegativity is only used when atoms are bonded in molecules.
Cations are smaller than their parent atoms: fewer electrons, same nuclear charge, so the nucleus pulls the remaining electrons in more tightly.
Anions are larger than their parent atoms: more electrons than protons, increased electron-electron repulsion, so the electron cloud expands.
Isoelectronic series: among ions with the same number of electrons, the one with more protons is smaller (stronger nuclear pull). Example: O²⁻ > F⁻ > Na⁺ > Mg²⁺ > Al³⁺ (decreasing radius as proton count increases).
Electron configurations determine an element's chemical behaviour. The periodic table itself is structured around the filling of s, p, d, and f orbitals, which is why elements in the same group share similar properties.
Ionisation energies explain why alkali metals are so reactive (low IE, easily lose their single valence electron) and why noble gases are inert (very high IE, full valence shell).
Electronegativity differences between bonded atoms determine whether a bond is nonpolar covalent, polar covalent, or ionic, which in turn controls molecular polarity, solubility, and intermolecular forces.
Students often explain the Cr and Cu electron configuration anomalies by claiming that "half-filled and fully filled subshells have special stability." This is incorrect. The correct explanation is that the configuration minimises electron-electron repulsions and lowers the total energy.
Students frequently remove electrons from the 3d subshell first when writing transition metal cation configurations. The ns electrons are removed first, even though ns fills before (n−1)d in neutral atoms.
Students sometimes use shielding to explain trends across a period. Shielding within the same principal energy level is incomplete and largely ineffective; Z_eff is the correct argument for across-the-period trends.
Students often assume that ionisation energy always increases smoothly across a period. There are two well-known dips: from IIA to IIIA (s² to p¹, removing a less-penetrating p electron) and from VA to VIA (p³ to p⁴, removing a newly paired electron experiencing repulsion).
⚠️ Electron configurations for any element, including transition metals and their ions, are tested in multiple-choice and free-response. Practise until these are automatic.
⚠️ The AP exam regularly asks: "Explain why the first IE of element X is greater/less than that of element Y." You must use Z_eff, distance, shielding, or electron-electron repulsion in your answer, not just state the trend.
⚠️ Know the two IE exceptions (IIA→IIIA and VA→VIA) and be able to explain both using the correct argument (penetration for the first, electron-electron repulsion from pairing for the second).
⚠️ Successive IE questions: identify the huge jump that signals you have broken into a core energy level. That jump tells you the element's group.
⚠️ Isoelectronic comparisons ("rank these ions by size") appear frequently. Remember: same electron count, more protons = smaller ion.
⚠️ Never write that a half-filled subshell has "special stability." The AP exam penalises this.
Fill in the blank: The Aufbau principle states that electrons fill orbitals from ________ to ________ energy. (lowest, highest)
True or false: When forming Fe²⁺, the two 3d electrons are removed first. (False. The two 4s electrons are removed first.)
Fill in the blank: Atomic radius decreases across a period because ________ increases. (effective nuclear charge / Z_eff)
True or false: Fluorine has a more negative electron affinity than chlorine. (False. Chlorine's EA is more negative because F's small 2p orbitals create unusually strong electron-electron repulsion.)
Rank in order of increasing ionic radius: Na⁺, F⁻, O²⁻. (Na⁺ < F⁻ < O²⁻)
Q: Write the electron configuration for cadmium (Cd, Z = 48) and determine whether it is diamagnetic or paramagnetic.
A: Cd: [Kr] 4d¹⁰ 5s². All d orbitals are fully paired, and the 5s orbital is fully paired. Cd is diamagnetic.
Q: The first ionisation energy of phosphorus (1060 kJ/mol) is higher than that of sulfur (1005 kJ/mol), even though sulfur has a higher Z_eff. Explain.
A: Phosphorus has a 3p³ configuration (three unpaired p electrons, no pairing). Sulfur has 3p⁴, meaning one p orbital now contains a paired electron. The electron-electron repulsion from this pairing makes it easier (less energy required) to remove that fourth p electron from sulfur, despite sulfur's higher Z_eff.
Q: Predict the trend in radius for Be²⁺, Mg²⁺, Ca²⁺, and Sr²⁺. Explain.
A: Be²⁺ < Mg²⁺ < Ca²⁺ < Sr²⁺. All are +2 cations in the same group. Moving down the group, each ion has an additional principal energy level, so the ionic radius increases. Distance from the nucleus and shielding by more inner shells both increase.
Q: Consider atoms with configurations (a) 1s² 2s² 2p⁶, (b) 1s² 2s² 2p⁶ 3s¹, (c) 1s² 2s² 2p⁶ 3s². Which has the largest first IE? Which has the smallest second IE?
A: (a) is Ne, (b) is Na, (c) is Mg. Ne has the largest first IE: it has a full valence shell and the highest Z_eff among these three for its valence level. Mg has the smallest second IE: removing the second 3s electron still leaves it in the same subshell (3s² → 3s¹ → 3s⁰), so no huge energy jump. Na's second IE, by contrast, requires breaking into the 2p core.
Q: Why is fluorine the most electronegative element?
A: Fluorine has the highest Z_eff among the halogens (7 for its valence shell) and the smallest atomic radius, so its nucleus is very close to the bonding electrons. This combination produces the strongest pull on shared electrons in a bond.
Q: Explain why the Cr atom has the configuration [Ar] 4s¹ 3d⁵ rather than [Ar] 4s² 3d⁴.
A: Placing one electron in 4s and five in the 3d orbitals (one per orbital) minimises electron-electron repulsions more effectively than having two electrons paired in 4s and four spread across 3d. The total energy is lower with [Ar] 4s¹ 3d⁵.
Electron configurations are the foundation for understanding chemical bonding (Chapter 8 and 9). The number and arrangement of valence electrons determine whether atoms form ionic, covalent, or metallic bonds.
Periodic trends in ionisation energy and electronegativity directly predict bond polarity, which in turn governs molecular polarity and intermolecular forces (Chapter 11).
The concept of effective nuclear charge and shielding reappears in discussions of transition metal chemistry, coordination compounds, and colour (Chapter 21).
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