Lesson 1.4 · Unit 1 · CED topic 1.5

Atomic structure and electron configuration

Almost everything in chemistry, from why sodium explodes in water to why diamond is hard, comes down to how electrons are arranged around nuclei. The arrangement is not random. Electrons occupy a definite set of energy levels, fill them in a predictable order, and the pattern of that filling is exactly what the shape of the periodic table records. In this lesson you learn to write that arrangement, the electron configuration, for any atom or ion, and the physical law that explains why it takes the form it does.

Learning objective · 1.5.A

Represent the ground-state electron configuration of an atom of an element or its ions using the Aufbau principle.

Required content · EK 1.5.A.1 to 1.5.A.4

The atom is composed of negatively charged electrons and a positively charged nucleus that is made of protons and neutrons.
Coulomb’s law is used to calculate the force between two charged particles: \(F \propto \dfrac{q_1 q_2}{r^2}\).
In atoms and ions, the electrons can be thought of as being in “shells (energy levels)” and “subshells (sublevels),” as described by the ground-state electron configuration. Inner electrons are called core electrons, and outer electrons are called valence electrons. The configuration is explained by quantum mechanics, as delineated in the Aufbau principle and exemplified in the periodic table.
The relative energy required to remove an electron from different subshells of an atom or ion, or from the same subshell in different atoms or ions (ionization energy), can be estimated through a qualitative application of Coulomb’s law. This energy is related to the distance from the nucleus and the effective (shield) charge of the nucleus.
Exclusion: assigning quantum numbers to electrons in subshells is not assessed.

Particles in the atom

An atom has a tiny, dense nucleus of protons (charge +1, mass about 1 amu) and neutrons (no charge, mass about 1 amu), surrounded by electrons (charge −1, mass about 1/1836 amu). The number of protons is the atomic number, Z, and defines the element. A neutral atom has equal numbers of protons and electrons. An ion has gained or lost electrons: a cation (positive) has lost them, an anion (negative) has gained them. A sodium atom has 11 electrons; the Na⁺ ion has 10.

Coulomb’s law

The force between two charged particles depends on the size of the charges and the distance between them: \[ F \propto \dfrac{q_1\, q_2}{r^2} \] Opposite charges attract and like charges repel. The attraction grows when the charges are larger and when the particles are closer, and it falls off with the square of the distance. This single relationship, used qualitatively, explains the whole of Unit 1: how strongly an electron is held depends on the charge pulling it in and how far away it is.

Figure 1.4a Coulomb’s law: the force between charged particles is proportional to the product of the charges and inversely proportional to the square of the distance. Doubling the distance cuts the force to one fourth; quadrupling the charge product quadruples the force.

Worked example · scaling with Coulomb’s law

Two ions attract each other with force \(F\). How does the force change if (a) the charges change from +1 and −1 to +2 and −1, and (b) the distance is also doubled?

(a) The product of the charges goes from 1 to 2, so the force doubles: \(2F\). (b) Doubling \(r\) divides the force by \(2^2 = 4\), so the force becomes \(2F / 4 = F/2\).

Shells and subshells

Electrons are found in shells, numbered \(n = 1, 2, 3, \ldots\) with higher numbers farther from the nucleus and higher in energy. Each shell is divided into subshells labeled s, p, d and f. Shell 1 has only s; shell 2 has s and p; shell 3 has s, p and d; shell 4 has s, p, d and f. A subshell holds a fixed number of electrons because it contains orbitals, each holding at most two electrons:

Subshell	Orbitals	Maximum electrons
s	1	2
p	3	6
d	5	10
f	7	14

The inner electrons are core electrons; the electrons in the outermost shell are valence electrons, and they are the ones that take part in bonding.

The Aufbau principle

The ground state is the lowest-energy arrangement. The Aufbau principle (German for “building up”) says electrons fill the lowest-energy subshell available first. The order of increasing energy is \[ 1s,\ 2s,\ 2p,\ 3s,\ 3p,\ 4s,\ 3d,\ 4p,\ 5s,\ 4d,\ 5p,\ 6s,\ 4f,\ 5d,\ 6p,\ 7s,\ 5f,\ldots \] Note that 4s fills before 3d. You do not need to memorize the list: the periodic table is the memory aid, because its blocks are the subshells (two columns of s, six of p, ten of d, fourteen of f) and its rows run along the filling order.

Figure 1.4b The order in which subshells are filled in the ground state of an atom, read left to right and then on the second row. The periodic table is organized to follow this order.

A configuration is written as subshell labels with the electron count as a superscript: sodium (Z = 11) is \(1s^2\,2s^2\,2p^6\,3s^1\), where the sum of superscripts (2 + 2 + 6 + 1) is 11. The shorthand replaces the core with the previous noble gas in brackets: Na is [Ne] 3s¹. Here are more examples:

Species	Electrons	Configuration
Oxygen, O	8	1s² 2s² 2p⁴
Chlorine, Cl	17	[Ne] 3s² 3p⁵
Iron, Fe	26	[Ar] 4s² 3d⁶
Sodium ion, Na⁺	10	1s² 2s² 2p⁶ (same as Ne)
Chloride ion, Cl⁻	18	[Ne] 3s² 3p⁶ (same as Ar)
Iron(II) ion, Fe²⁺	24	[Ar] 3d⁶

Ions and the order of removal

To write an anion’s configuration, add the extra electrons to the next available spots. For a cation, remove electrons from the outermost shell first, which is the highest value of \(n\), not the last subshell filled. That is why Fe²⁺ loses its two 4s electrons (the outer shell) and not two 3d electrons, giving [Ar] 3d⁶. Transition metals follow this rule.

Orbital diagrams: Hund’s rule

An orbital diagram draws each orbital as a box and each electron as an arrow. Two electrons in the same orbital must have opposite spins (one up, one down). When filling a subshell with several orbitals, Hund’s rule says electrons occupy separate orbitals with parallel spins before any orbital gets a second electron. This minimizes repulsion between electrons. Nitrogen (2p³) has three unpaired electrons; oxygen (2p⁴) has two unpaired electrons and one pair.

Figure 1.4c Orbital diagrams. Electrons fill the boxes of a subshell one at a time with parallel spins (Hund’s rule) before pairing, and no box holds more than two electrons with opposite spins (the Pauli exclusion principle).

The number of unpaired electrons tells you whether an atom is paramagnetic (attracted to a magnet; has one or more unpaired electrons) or diamagnetic (weakly repelled; all electrons paired). Nitrogen and oxygen atoms are paramagnetic. Neon, with every orbital filled, is diamagnetic.

Worked example · configuration, valence electrons and unpaired electrons

Write the configuration of phosphorus (Z = 15), count its valence electrons, and say how many are unpaired.

Fill in order. 1s² (2) → 2s² (4) → 2p⁶ (10) → 3s² (12) → 3p³ (15). The configuration is \(1s^2\,2s^2\,2p^6\,3s^2\,3p^3\), or [Ne] 3s² 3p³.

Valence electrons. Those in shell 3: 2 + 3 = 5.

Unpaired. The three 3p electrons occupy three orbitals singly (Hund’s rule), so there are 3 unpaired electrons.

Worked example · identifying an element from its ion

An ion with charge 2+ has the configuration 1s² 2s² 2p⁶ 3s² 3p⁶. Which element is it?

The ion has 18 electrons. A 2+ charge means two electrons were lost, so the neutral atom had 20 electrons and Z = 20: calcium, Ca²⁺.

One note on scope: chromium and copper (and a few others) do not follow the Aufbau pattern exactly, because a half-filled or filled 3d subshell is slightly more stable. Writing the configurations of these exceptions will not be assessed on the AP Exam.

Exam focus

Check the total. The superscripts must add to the number of electrons (not the atomic number) of the species. For an ion, count the electrons first.
4s before 3d to fill; 4s before 3d to empty. Cations lose the outermost-shell electrons first.
Valence electrons are in the highest shell (for main-group elements, the group number tells you how many).
Coulomb’s law is the reason. Free-response explanations of why one electron is held more tightly than another should name the nuclear charge and the distance.
Draw unpaired electrons separately in a p, d or f subshell until each orbital has one.

Practice

Write the ground-state configuration of sulfur (Z = 16) and state the number of valence electrons.
Show answer
1s² 2s² 2p⁶ 3s² 3p⁴ (or [Ne] 3s² 3p⁴). Valence electrons: 2 + 4 = 6.
Write the configuration of the calcium ion, Ca²⁺, and name the noble gas it matches.
Show answer
Ca has 20 electrons ([Ar] 4s²). Removing two 4s electrons gives 18 electrons: 1s² 2s² 2p⁶ 3s² 3p⁶, the same as argon.
Write the configuration of Fe³⁺ (Z = 26) and state the number of unpaired electrons.
Show answer
Fe is [Ar] 4s² 3d⁶. To make Fe³⁺, remove the two 4s electrons and then one 3d electron: [Ar] 3d⁵. Five d electrons in five orbitals means 5 unpaired electrons.
How many unpaired electrons does an atom of nitrogen have, and is it paramagnetic or diamagnetic?
Show answer
Nitrogen is 1s² 2s² 2p³. By Hund’s rule the three 2p electrons are in separate orbitals, so there are 3 unpaired electrons and the atom is paramagnetic.
Particle X has a charge of +2 and particle Y has −2 at a separation of \(r\). The particles are moved to a separation of \(3r\). By what factor does the attractive force change?
Show answer
The charges are unchanged, but \(r\) triples, so the force is divided by \(3^2 = 9\). It becomes one-ninth of the original.
Explain why the 1s electron in a helium atom is held more tightly than the 1s electron in a hydrogen atom, even though both are in the 1s subshell.
Show answer
Helium has two protons (+2 nuclear charge) while hydrogen has one (+1). The 1s electrons are at about the same distance, so by Coulomb’s law the greater nuclear charge in helium produces a stronger attraction. (The second electron repels only partly, so the net pull is still larger.)