Electrons energy levels and atomic orbitals

Shells, Sub-shells and Orbitals

Electrons in an atom occupy specific energy regions called shells, sub-shells and orbitals, arranged in a strict hierarchy that determines chemical behaviour.

A shell is a main energy level labelled by the principal quantum number (n), where n = 1, 2, 3, 4… As n increases, the shell lies further from the nucleus and holds electrons of higher energy. Each shell contains one or more sub-shells of slightly different energies, labelled s, p, d and f.

Each sub-shell is made up of one or more orbitals. An orbital is a region of space where there is a high probability [usually ≥ 95%] of finding an electron. Each orbital holds a maximum of two electrons with opposite spins.

The ground state is the lowest-energy arrangement of electrons in an atom. Electrons fill the lowest available energy levels first, giving the atom its most stable configuration.

Examiner InsightWhen defining an orbital, state it as “a region of space where there is a high probability of finding an electron”. Saying “where electrons go” or “an electron path” loses the mark. Exam cue: Lock the phrase “high probability of finding an electron”.

Number of Orbitals and Electron Capacity

Each sub-shell contains a fixed number of orbitals, and each orbital holds a maximum of two electrons, giving each sub-shell a defined electron capacity.

The total electron capacity of shell n is 2n². So shell 1 holds 2 electrons, shell 2 holds 8, shell 3 holds 18, and shell 4 holds 32.

The first shell contains only a 1s sub-shell. The second shell adds a 2p sub-shell. The third shell adds a 3d sub-shell, and the fourth shell adds a 4f sub-shell, although 4f is beyond syllabus scope.

Order of Increasing Sub-shell Energy

Sub-shells fill in order of increasing energy, not strictly in order of increasing n, because the 4s sub-shell lies below the 3d sub-shell in energy.

The order up to 4p is:

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p

The 4s sub-shell fills before 3d because 4s is at a lower energy than 3d in the neutral atom. Once filling begins, 3d electrons are added before 4p.

MisconceptionStudents often write 3d before 4s because 3 < 4. This is wrong for filling order. 4s fills first because it has the lower energy. However, when removing electrons to form positive ions, 4s electrons are removed before 3d. Exam cue: Fill 4s first, but ionise 4s first too.

Writing Electronic Configurations

An electronic configuration lists every occupied sub-shell with the number of electrons shown as a superscript, in order of increasing energy.

For example, sodium (Z = 11) has the configuration 1s²2s²2p⁶3s¹. The superscripts give the electrons in each sub-shell, and the sum of superscripts equals the total number of electrons.

The configuration shows:

• The shell each electron occupies (the number, e.g. 3 in 3s¹).
• The sub-shell each electron occupies (the letter, e.g. s in 3s¹).
• The number of electrons in that sub-shell (the superscript).

To deduce the orbital occupation, divide the sub-shell electrons across its orbitals using Hund’s rule: electrons occupy separate orbitals of the same sub-shell singly before pairing up.

Explaining Configurations Using Energy and Repulsion

Electronic configurations follow two principles: electrons fill the lowest energy sub-shells first, and electrons in the same sub-shell occupy separate orbitals before pairing.

Filling lower energy sub-shells first gives the atom its most stable, lowest-energy ground state. This is why 1s fills before 2s, and 4s fills before 3d.

Within a sub-shell containing more than one orbital, electrons spread out across the orbitals singly first. This minimises inter-electron repulsion because two electrons in the same orbital repel each other more strongly than electrons in separate orbitals. Once each orbital has one electron, further electrons must pair up with opposite spin.

Determining Configurations of Atoms and Ions

For any atom from hydrogen to krypton, fill sub-shells in increasing energy order until all electrons are placed. For ions, add electrons for negative charge or remove them for positive charge.

For neutral atoms, the proton number equals the number of electrons. For example, iron (Z = 26) has the full configuration 1s²2s²2p⁶3s²3p⁶3d⁶4s², or in shorthand [Ar] 3d⁶4s².

The shorthand notation uses the symbol of the previous noble gas in square brackets to represent its full configuration. This is followed by the remaining sub-shells.

For positive ions of d-block elements, remove electrons from the 4s sub-shell before 3d, even though 4s filled first. For example:

• Fe: [Ar] 3d⁶4s²
• Fe²⁺: [Ar] 3d⁶ (remove both 4s electrons first)
• Fe³⁺: [Ar] 3d⁵ (then remove one 3d electron)

For negative ions, add electrons to the next available sub-shell. For example, O (1s²2s²2p⁴) becomes O²⁻ (1s²2s²2p⁶).

Examiner InsightFor transition metal cations, always remove 4s electrons before 3d electrons. Writing Fe²⁺ as [Ar] 3d⁴4s² is a common error that loses the mark. Exam cue: 4s fills first, but 4s ionises first.

Worked Example: Electronic Configuration of Cu and Cu²⁺

Scenario

Copper has proton number 29. Deduce the full electronic configuration of a Cu atom and of the Cu²⁺ ion.

Step-by-step solution:

Step 1 — Configuration of Cu (Z = 29): Filling 29 electrons in order would suggest 1s²2s²2p⁶3s²3p⁶3d⁹4s². However, copper is a known exception because a fully filled 3d¹⁰ sub-shell is more stable than 3d⁹4s². The correct ground-state configuration is:

1s²2s²2p⁶3s²3p⁶3d¹⁰4s¹

Step 2 — Configuration of Cu²⁺: Remove two electrons. The 4s electron is removed first, then one 3d electron:

1s²2s²2p⁶3s²3p⁶3d⁹

Interpretation

The Cu atom adopts the unusual 3d¹⁰4s¹ arrangement because the extra stability of a full 3d sub-shell outweighs the small energy gap. Forming Cu²⁺ removes the lone 4s electron first, then a 3d electron.

Electrons in Boxes Notation

The electrons-in-boxes notation shows each orbital as a single box and each electron as an arrow, with the arrow direction indicating spin.

A pair of electrons in the same orbital is shown as one box with two arrows pointing in opposite directions (↑↓). This represents the requirement that paired electrons have opposite spins.

When filling a sub-shell with multiple orbitals (such as p or d), electrons enter separate orbitals first with parallel spins (↑ ↑ ↑) before pairing. This is Hund’s rule, and it minimises inter-electron repulsion.

For nitrogen (1s²2s²2p³), the 2p sub-shell has three boxes, each containing one upward-pointing arrow. For oxygen (1s²2s²2p⁴), one of the three 2p boxes contains a paired ↑↓, while the other two contain a single ↑.

Shapes of s and p Orbitals

Orbitals have characteristic three-dimensional shapes. The s orbital is spherical and the p orbital is dumb-bell shaped, oriented along the x, y or z axis.

An s orbital has the same probability of finding the electron in all directions from the nucleus. As n increases, the s orbital remains spherical but becomes larger.

A p sub-shell contains three p orbitals of equal energy, labelled pₓ, $p_{\mathrm{y}}$ and $p_{\mathrm{z}}$. Each is a dumb-bell shape with two lobes on opposite sides of the nucleus, separated by a node at the nucleus. The three p orbitals are oriented at 90° to each other along the three Cartesian axes.

Free Radicals

A free radical is a species containing one or more unpaired electrons, which makes it highly reactive.

Free radicals form when a covalent bond breaks evenly, with one electron going to each atom (homolytic fission). A common example is the chlorine radical, Cl•, formed by UV light splitting Cl₂ into two Cl atoms, each with seven valence electrons including one unpaired.

The unpaired electron is shown as a single dot next to the species symbol, for example •CH₃ or H•. Radicals seek to pair their unpaired electron, which is why they react readily with other molecules.