Electron Configurations & Periodic Properties

Electron Spin and the Pauli Exclusion Principle

Electrons possess an intrinsic property called spin, quantized as mₛ = +½ or −½, which behaves like a tiny magnetic moment. The Pauli exclusion principle states that no two electrons in the same atom can have identical values for all four quantum numbers, which means at most two electrons — with opposite spins — can occupy any single orbital. This principle is the foundation for understanding why orbitals hold a maximum of two electrons and why atoms build up the way they do.

• •mₛ = +½ or −½ describes electron spin
• •No two electrons in an atom share all four quantum numbers (n, ℓ, mℓ, mₛ)
• •Maximum of 2 electrons per orbital, with paired (opposite) spins
• •Underpins the structure of the periodic table's orbital-filling pattern

Shielding, Penetration, and Effective Nuclear Charge

In multielectron atoms, inner electrons shield outer electrons from the full attractive pull of the nucleus, so outer electrons experience a reduced effective nuclear charge (Zeff) rather than the full nuclear charge Z. Different subshells within the same principal energy level penetrate toward the nucleus to different extents — s orbitals penetrate more than p, which penetrate more than d — so electrons in s orbitals experience less shielding and are held more tightly, resulting in the energy ordering ns < np < nd for a given n. This shielding/penetration interplay explains why 4s fills before 3d, despite 3d having a lower n.

• •Zeff = Z − shielding (approximately), the net positive charge felt by an outer electron
• •Penetration order within a shell: s > p > d > f
• •Greater penetration means lower energy and tighter binding
• •Explains why 4s orbitals fill before 3d orbitals in neutral atoms

The Aufbau Principle and the Periodic Table as a Map

The Aufbau ('building up') principle states that electrons fill orbitals starting from the lowest available energy level and proceeding upward. The periodic table itself is organized to mirror this filling order: the s-block (groups 1–2), p-block (groups 13–18), d-block (transition metals), and f-block (lanthanides/actinides) each correspond to the type of subshell being filled for elements in that region. Reading across the table left to right, top to bottom, reproduces the correct orbital-filling sequence (1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, ...).

• •s-block: groups 1–2, filling ns orbitals
• •p-block: groups 13–18, filling np orbitals
• •d-block: transition metals, filling (n−1)d orbitals
• •f-block: lanthanides/actinides, filling (n−2)f orbitals

Hund's Rule and Orbital Diagrams

Hund's rule states that when filling degenerate (equal-energy) orbitals within a subshell, electrons occupy separate orbitals singly, with parallel spins, before any orbital receives a second electron. This minimizes electron–electron repulsion and results in the lowest-energy (most stable) configuration for a given electron count. Orbital-box diagrams visually represent this rule, showing individual orbitals as boxes with up/down arrows representing paired or unpaired electron spins.

• •Fill each orbital in a subshell singly before pairing any electrons
• •Unpaired electrons in singly-filled orbitals have parallel spin
• •Minimizes repulsion, giving the ground-state configuration
• •Orbital diagrams: boxes for orbitals, arrows (↑↓) for electron spins

Writing Full and Condensed Electron Configurations

A full electron configuration lists every occupied subshell in order of filling with its electron count as a superscript, such as 1s²2s²2p⁶3s²3p⁴ for sulfur. A condensed (noble-gas core) configuration abbreviates the filled inner shells using the preceding noble gas symbol in brackets, then lists only the remaining electrons, e.g., sulfur becomes [Ne]3s²3p⁴. Condensed configurations are especially useful for quickly identifying valence electrons, which are the outermost electrons involved in bonding.

• •Full configuration: list all subshells in filling order with electron counts
• •Condensed configuration: [previous noble gas] + remaining subshells
• •Valence electrons: electrons in the outermost n level (plus outermost d/f if relevant for transition metals)
• •Core electrons: all electrons in the noble-gas core, not involved in typical bonding

Anomalous Configurations: Chromium and Copper

Chromium and copper (and some heavier congeners) deviate from the expected Aufbau filling pattern because half-filled and fully-filled d subshells confer extra stability due to favorable exchange energy and symmetry. Instead of [Ar]4s²3d⁴, chromium adopts [Ar]4s¹3d⁵, achieving a half-filled 3d subshell; instead of [Ar]4s²3d⁹, copper adopts [Ar]4s¹3d¹⁰, achieving a completely filled 3d subshell. These are the two classic anomalies students must memorize for general chemistry.

• •Chromium: [Ar]4s¹3d⁵ (not [Ar]4s²3d⁴) — half-filled d subshell is extra stable
• •Copper: [Ar]4s¹3d¹⁰ (not [Ar]4s²3d⁹) — fully-filled d subshell is extra stable
• •Analogous anomalies occur for Mo, Ag, Au among heavier transition metals
• •The exception arises from subtle energy differences, not a violation of quantum rules

Configurations of Ions and Magnetic Behavior

When forming cations from transition metals, electrons are removed from the highest-n orbital first — meaning ns electrons are lost before (n−1)d electrons, even though ns filled first — because once occupied, the d orbitals drop below the s orbital in energy. Anions gain electrons following the normal Aufbau order to complete a subshell. An atom or ion is paramagnetic if it has one or more unpaired electrons (weakly attracted to a magnetic field) and diamagnetic if all electrons are paired (weakly repelled by a magnetic field).

• •Transition metal cations: remove ns electrons before (n−1)d electrons
• •Example: Fe → Fe²⁺ removes both 4s electrons first, giving [Ar]3d⁶
• •Paramagnetic: has unpaired electrons, attracted weakly to magnetic fields
• •Diamagnetic: all electrons paired, weakly repelled by magnetic fields

Isoelectronic Species

Isoelectronic species are atoms or ions that share the identical electron configuration, even though they may have different numbers of protons. For example, Na⁺, Mg²⁺, F⁻, O²⁻, and Ne are all isoelectronic with the noble gas neon, each having the configuration 1s²2s²2p⁶. Although isoelectronic species share electron arrangement, their sizes still differ because they have different nuclear charges pulling on the same number of electrons.

• •Isoelectronic species have identical electron configurations
• •Example: O²⁻, F⁻, Ne, Na⁺, Mg²⁺, Al³⁺ are all isoelectronic (10 electrons, Ne configuration)
• •More protons pulling on the same electron count means a smaller ionic radius
• •Isoelectronic comparisons are a common tool for ranking ionic sizes

Periodic Trends: Atomic and Ionic Radius

Atomic radius decreases across a period (left to right) because increasing Zeff pulls the same-shell electrons in more tightly, while it increases down a group because each successive row adds a new, larger principal energy level. Cations are always smaller than their parent atom because removing electrons decreases electron–electron repulsion, and losing an entire shell can shrink the radius dramatically; anions are always larger than their parent atom because added electrons increase repulsion and electron cloud spread. These trends are consistent and can be predicted directly from an element's position on the periodic table.

• •Atomic radius decreases left to right across a period (increasing Zeff)
• •Atomic radius increases top to bottom down a group (new occupied shells)
• •Cations are smaller than their neutral atom; anions are larger than their neutral atom
• •Among isoelectronic species, radius decreases as nuclear charge (Z) increases

Ionization Energy and Electron Affinity

Ionization energy (IE), the energy required to remove an electron from a gaseous atom or ion, generally increases across a period and decreases down a group, mirroring the same Zeff/shielding logic as atomic radius trends. Successive ionization energies (IE₁, IE₂, IE₃, ...) always increase, but a very large jump occurs once electrons must be removed from a lower, more stable core shell rather than the valence shell — a signature used to identify an element's number of valence electrons. Electron affinity, the energy change when an electron is added to a gaseous atom, generally becomes more negative (more energy released) across a period, though trends are less regular than for ionization energy, and metallic character (tendency to lose electrons and form cations) increases down a group and decreases across a period, opposite to the ionization energy trend.

• •Ionization energy increases across a period, decreases down a group
• •Large jump in successive IEs occurs when a core (inner-shell) electron must be removed
• •Anomalies: group 13 has lower IE than group 2 (filled s vs. starting p); group 16 has lower IE than group 15 (paired p electron easier to remove than breaking a half-filled set)
• •Electron affinity generally becomes more negative (exothermic) across a period, with irregular exceptions
• •Metallic character increases down a group and decreases across a period (opposite of ionization energy)

Write the full and condensed electron configurations for phosphorus (Z = 15).

1. 1Determine total electrons: Z = 15, so 15 electrons must be placed.
2. 2Fill in Aufbau order: 1s² 2s² 2p⁶ 3s² 3p³ (2+2+6+2+3 = 15).
3. 3Full configuration: 1s²2s²2p⁶3s²3p³.
4. 4Identify the preceding noble gas: neon (Ne, Z=10) has configuration 1s²2s²2p⁶.
5. 5Condensed configuration: [Ne]3s²3p³.

Full: 1s²2s²2p⁶3s²3p³; Condensed: [Ne]3s²3p³

Write the condensed electron configuration for chromium (Z = 24), noting its exception.

1. 1Determine total electrons: Z = 24.
2. 2Expected Aufbau filling would give [Ar]4s²3d⁴ (18+2+4 = 24).
3. 3Recall the chromium exception: a half-filled 3d subshell is more stable, so one 4s electron shifts to 3d.
4. 4Correct configuration: [Ar]4s¹3d⁵ (18+1+5 = 24).

[Ar]4s¹3d⁵

Write the electron configuration of the Fe²⁺ ion (Fe, Z = 26).

1. 1Write neutral iron's configuration: [Ar]4s²3d⁶ (18+2+6 = 26).
2. 2To form Fe²⁺, remove 2 electrons.
3. 3For transition metals, remove ns electrons before (n−1)d electrons.
4. 4Remove both 4s² electrons first, leaving 3d⁶ untouched.
5. 5Final configuration: [Ar]3d⁶ (18+6 = 24 electrons, matching Fe²⁺'s charge of +2 from 26).

Fe²⁺: [Ar]3d⁶

Rank the following isoelectronic species by increasing ionic radius: Mg²⁺, O²⁻, Na⁺, F⁻.

1. 1Confirm all species have the same electron count (10 electrons, Ne configuration): Mg²⁺ (12−2), Na⁺ (11−1), F⁻ (9+1), O²⁻ (8+2), all equal 10.
2. 2For isoelectronic species, ionic radius decreases as nuclear charge (Z, i.e., number of protons) increases.
3. 3List protons: O²⁻ has Z=8, F⁻ has Z=9, Na⁺ has Z=11, Mg²⁺ has Z=12.
4. 4More protons pull the same 10 electrons in more tightly, so radius decreases as Z increases.
5. 5Order from smallest Z (largest radius) to largest Z (smallest radius): O²⁻ > F⁻ > Na⁺ > Mg²⁺.

Increasing radius: Mg²⁺ < Na⁺ < F⁻ < O²⁻

Explain why the second ionization energy of sodium is drastically higher than its first ionization energy, and estimate which shell is involved.

1. 1Write sodium's configuration: [Ne]3s¹, valence electron in 3s.
2. 2First ionization removes the lone 3s valence electron: Na → Na⁺ + e⁻, relatively low energy (loosely held, well-shielded).
3. 3Second ionization must remove an electron from the filled, lower-energy 2p core (the [Ne] core), since the valence shell is now empty.
4. 4Core electrons are much closer to the nucleus and experience far less shielding, so removing them requires drastically more energy.
5. 5This produces a large jump between IE₁ and IE₂, characteristic of removing a core electron after the valence electrons are gone.

IE₂ >> IE₁ because IE₂ removes a tightly-held core (2p) electron rather than the loosely-held valence 3s electron.

Q1. According to the Pauli exclusion principle, a single orbital can hold at most:

Q2. Why does the 4s orbital fill before the 3d orbital in neutral atoms?

Q3. Which of the following correctly applies Hund's rule to three electrons in a p subshell?

Q4. What is the condensed electron configuration of chlorine (Z = 17)?

Q5. Which element shows an anomalous electron configuration due to the extra stability of a half-filled d subshell?

Q6. When forming the Fe³⁺ ion from neutral iron ([Ar]4s²3d⁶), which electrons are removed?

Q7. An atom or ion with all electrons paired is described as:

Q8. Which pair of species is isoelectronic?

Q9. Atomic radius generally decreases across a period from left to right because:

Q10. Which of the following correctly ranks the ions by increasing size: Na⁺, Na, Na⁻(hypothetical)?

Q11. The large jump between the first and second ionization energies of sodium is best explained by:

Q12. Which trend correctly describes ionization energy across the periodic table?

Q13. The slightly lower first ionization energy of aluminum (group 13) compared to magnesium (group 2) is best explained by:

Q14. Metallic character across a period (left to right) and down a group behaves in which pattern?