Ionisation energies orbitals and electronic configuration

Defining Ionisation Energies

The first ionisation energy is the energy required to remove one mole of electrons from one mole of gaseous atoms to form one mole of gaseous +1 ions under standard conditions.

The second and third ionisation energies refer to removing the next electron from the +1 and +2 gaseous ions respectively, forming +2 and +3 gaseous ions.

All ionisation energies are endothermic because energy must be supplied to overcome the electrostatic attraction between the negatively charged electron and the positively charged nucleus.

The defining equations use gaseous species and one-electron steps in every case:

• First: M(g) → M⁺(g) + e⁻
• Second: M⁺(g) → M²⁺(g) + e⁻
• Third: M²⁺(g) → M³⁺(g) + e⁻

State symbols are essential. Marks are commonly lost when the (g) is omitted from either side of the equation.

MisconceptionIonisation energy is not the energy “released” when an electron leaves. Energy is always absorbed because the electron is held by the nucleus.

Exam TipAlways state “energy required to remove” and include (g) on both sides.

Orbitals and Electron Spin

An orbital is a region within an atom that can hold up to two electrons with opposite spins.

The two electrons within the same orbital must spin in opposite directions because parallel spins would repel and destabilise the pair.

This pairing of opposite spins is represented in electron-in-boxes notation by two arrows pointing in opposite directions inside one box: ↑↓.

Factors Affecting Ionisation Energy

Three key factors determine the magnitude of an ionisation energy: nuclear charge, shielding, and the sub-shell from which the electron is removed.

A greater number of protons in the nucleus increases the nuclear charge, which strengthens the electrostatic attraction on the outer electron. Therefore more energy is required to remove that electron.

Electron shielding [the repulsion of an outer electron by inner-shell electrons that reduces the effective nuclear pull] decreases the attraction felt by the outer electron. More inner shells therefore lower the ionisation energy.

The sub-shell also matters because electrons in different sub-shells have different average distances and energies. An electron in a p sub-shell is at a slightly higher energy than one in the s sub-shell of the same quantum shell, so it is removed more easily.

A fourth implicit factor is the distance of the electron from the nucleus. Electrons further from the nucleus experience weaker attraction because electrostatic force decreases with distance.

Examiner InsightAlways state all relevant factors when comparing two ionisation energies. Naming only “more protons” without addressing shielding or distance frequently loses marks.

Exam TipStructure comparisons as nuclear charge → shielding → distance → sub-shell.

Evidence from Successive Ionisation Energies

Successive ionisation energies provide evidence for the existence of quantum shells and confirm the group of an element in the Periodic Table.

When the successive ionisation energies of an element are plotted on a logarithmic scale against the number of the electron removed, large jumps appear between certain electrons.

Each large jump corresponds to an electron being removed from a quantum shell closer to the nucleus, which is held more tightly because of less shielding and a shorter distance to the nucleus.

The number of electrons removed before the first large jump equals the number of outer-shell electrons, which equals the group number of the element.

For example, sodium shows a large jump between the first and second ionisation energies. This means sodium has one outer electron and is therefore in Group 1.

Evidence from First Ionisation Energy Trends

The pattern of first ionisation energies across a period provides evidence for the existence of electron sub-shells.

Across Period 3, the first ionisation energy generally rises because nuclear charge increases while shielding stays roughly constant. The outer electrons are pulled more strongly.

However, two distinctive dips appear: between magnesium and aluminium, and between phosphorus and sulfur. These dips reveal sub-shell structure.

The dip from Mg to Al occurs because aluminium’s outer electron is in a 3p sub-shell, which is at a slightly higher energy than magnesium’s 3s sub-shell. Less energy is therefore required to remove it.

The dip from P to S occurs because sulfur has the first paired electron in the 3p sub-shell. The two paired electrons repel each other, making one easier to remove than the unpaired 3p electron in phosphorus.

Shapes of s and p Orbitals

An s orbital is spherical and surrounds the nucleus symmetrically in all directions.

A p orbital has a dumb-bell shape with two lobes on opposite sides of the nucleus, with the nucleus itself at the centre between the lobes.

There are three p orbitals in any p sub-shell, oriented along the x, y and z axes at right angles to one another. They are labelled pₓ, $p_{\mathrm{y}}$ and $p_{\mathrm{z}}$.

Filling Orbitals within Sub-Shells

Orbitals within the same sub-shell follow two key filling rules: the single-electron rule and the pairing rule.

Each orbital in a sub-shell first takes a single electron before any orbital takes a second. This minimises electron-electron repulsion because singly occupied orbitals keep electrons apart.

Once every orbital in the sub-shell holds one electron, further electrons pair up with opposite spins inside the same orbitals.

For example, the three 2p orbitals of nitrogen each hold one electron with parallel spins, while oxygen’s four 2p electrons fill one orbital as a pair and leave the other two singly occupied.

Mnemonic“Singles first, then pair up.”

Predicting Electronic Configurations to Krypton

The electronic configuration of an atom lists the order in which sub-shells fill, starting from the lowest-energy sub-shell.

The order of filling for elements up to krypton is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p. Note that 4s fills before 3d because 4s is at a slightly lower energy than 3d when both are empty.

In s, p, d notation each sub-shell is written with a superscript showing the number of electrons it holds. For example, calcium is 1s² 2s² 2p⁶ 3s² 3p⁶ 4s².

For the d-block elements, two anomalies occur due to the extra stability of half-filled and fully-filled 3d sub-shells. Chromium is 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵ 4s¹, and copper is 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s¹.

When forming positive ions of d-block elements, electrons are removed from the 4s sub-shell before the 3d sub-shell. For example, Fe is [Ar] 3d⁶ 4s², while Fe²⁺ is [Ar] 3d⁶ and Fe³⁺ is [Ar] 3d⁵.

For ions of s- and p-block elements, electrons are removed from or added to the highest-energy outer sub-shell. For example, Mg²⁺ is 1s² 2s² 2p⁶ and O²⁻ is 1s² 2s² 2p⁶.

MisconceptionWhen writing the configuration of a transition metal cation, students often remove 3d electrons first. Always remove 4s electrons before 3d when forming an ion.

Exam Tip4S fills first but is also emptied first.

Worked Example: Electronic Configurations of Iron and Iron(III)

Scenario

Write the full electronic configuration of an iron atom (Z = 26) and its Fe³⁺ ion using s, p, d notation.

Step 1: Determine the total number of electrons in the atom. Iron has 26 protons, so a neutral iron atom has 26 electrons.

Step 2: Fill sub-shells in order of increasing energy until 26 electrons are placed. The order is 1s, 2s, 2p, 3s, 3p, 4s, 3d.

Step 3: Distribute electrons across each sub-shell using their maximum capacities (s = 2, p = 6, d = 10). 1s² (2 electrons), 2s² (4 total), 2p⁶ (10 total), 3s² (12 total), 3p⁶ (18 total), 4s² (20 total), 3d⁶ (26 total).

Step 4: Write the full configuration of Fe: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶ 4s².

Step 5: For Fe³⁺, remove three electrons. Remove 4s electrons before 3d. Removing both 4s electrons gives [Ar] 3d⁶, then removing one 3d electron gives [Ar] 3d⁵.

Step 6: Write the configuration of Fe³⁺: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵.

Interpretation

The half-filled 3d⁵ sub-shell of Fe³⁺ is particularly stable, which helps explain why iron readily forms the +3 oxidation state in its compounds.

Electronic Configuration and Chemical Properties

The electronic configuration of an element determines its chemical properties because outer-shell electrons control how the atom bonds and reacts.

Elements in the same group of the Periodic Table share the same outer-shell configuration, so they undergo similar chemical reactions and form analogous compounds.

For example, all Group 1 elements have an outer ns¹ configuration, which is why they all react vigorously with water to form +1 ions and hydrogen gas.

The number and arrangement of outer electrons also dictate the type of bonding an element forms — whether ionic, covalent or metallic — and the oxidation states it can achieve.

Blocks of the Periodic Table

The Periodic Table is divided into s, p and d blocks based on the sub-shell occupied by the highest-energy electron of each element.

The s block contains Groups 1 and 2 because their outer electron occupies an s sub-shell. The p block contains Groups 3 to 0, where the outer electron occupies a p sub-shell. The d block contains the transition metals, where the outer electron occupies a d sub-shell.

The capacity of each sub-shell is fixed: s holds 2 electrons, p holds 6 electrons, and d holds 10 electrons. These capacities determine the width of each block.