Learning objectives
State the relative masses and charges of protons, neutrons and electrons, deduce the numbers of each in atoms and ions, and describe how beams of these particles behave in an electric field
Write electronic configurations of atoms and ions in full, shorthand and electrons-in-boxes notation, and sketch the shapes of s and p orbitals
Define first ionisation energy, write equations for successive ionisation energies, and explain the trends down a group and across a period
Use isotope notation, explain why isotopes have the same chemical properties, and explain the trends in atomic and ionic radius across a period and down a group
Key definitions
Isotopes
Atoms of the same element with the same number of protons but different numbers of neutrons.
First ionisation energy
The energy required to remove one mole of electrons from one mole of gaseous atoms to form one mole of gaseous 1+ ions.
Orbital
A region of space around the nucleus in which there is a high probability of finding an electron; each orbital holds a maximum of two electrons with opposite spins.
Free radical
An atom, molecule or ion that has at least one unpaired electron, such as a chlorine atom, Cl•, or the methyl radical, CH₃•.
Isoelectronic species
Atoms or ions with the same number of electrons, e.g. Na⁺, Mg²⁺ and Al³⁺, which all have the configuration 1s²2s²2p⁶.
Explanation
An atom is mostly empty space. Almost all its mass is in a tiny, dense nucleus of protons (relative mass 1, charge +1) and neutrons (relative mass 1, charge 0); electrons (relative mass 1/1836, charge −1) occupy shells around it. The proton number Z defines the element; the nucleon number A is protons plus neutrons, so neutrons = A − Z. A neutral atom has equal numbers of protons and electrons; a 2+ ion has lost two electrons, a 1− ion has gained one. In isotope notation the nucleon number is written at the top left of the symbol and the proton number at the bottom left: ³⁷₁₇Cl has 17 protons, 37 − 17 = 20 neutrons and 17 electrons. When beams of the three particles travel at the same speed through an electric field, the neutrons pass straight through undeflected because they have no charge; the protons curve towards the negative plate and the electrons towards the positive plate, and the electron beam is deflected far more because its charge-to-mass ratio is about 1836 times that of a proton. Isotopes such as ³⁵Cl and ³⁷Cl have the same chemical properties because they have the same number and arrangement of electrons, but different physical properties, such as mass and density, because their nuclei contain different numbers of neutrons.
Atomic and ionic radius. Across a period the atomic radius decreases: the proton number rises but each extra electron enters the same shell, so shielding hardly changes and the greater nuclear charge pulls the outer electrons closer. Down a group the atomic radius increases, because each element has one more occupied shell, further from the nucleus and shielded by more inner electrons. A positive ion is smaller than its atom: a metal atom usually loses its whole outer shell, and the remaining electrons are held more tightly by the same nuclear charge. A negative ion is larger than its atom: the extra electrons increase the repulsion between electrons in the outer shell while the nuclear charge stays the same. In a set of isoelectronic ions the radius falls as the proton number rises: Na⁺ (0.102 nm) > Mg²⁺ (0.072 nm) > Al³⁺ (0.053 nm), because all three have the configuration 1s²2s²2p⁶ but 11, 12 and 13 protons attract those ten electrons. Down a group, ions with the same charge get larger, just as the atoms do.
Electrons occupy shells (principal quantum number n), which are split into sub-shells made of orbitals; each orbital holds at most two electrons, with opposite spins. An s sub-shell has one orbital and holds 2 electrons, a p sub-shell has three orbitals and holds 6, and a d sub-shell has five orbitals and holds 10. An s orbital is spherical; the three p orbitals are dumbbell-shaped along the x, y and z axes. Sub-shells fill in order of increasing energy, 1s 2s 2p 3s 3p 4s 3d 4p: the 4s sub-shell fills before 3d because it is lower in energy, but 4s electrons are also lost first when transition-metal ions form. Within a sub-shell, electrons occupy the orbitals singly, with parallel spins, before they pair up, because two electrons in the same orbital repel each other more strongly. Electrons-in-boxes notation shows this: each box is an orbital and each arrow an electron, so nitrogen’s 2p³ is three boxes with one arrow in each, while oxygen’s 2p⁴ has one box holding a pair of opposite arrows and two boxes with single arrows. A configuration can be written in full (Fe: 1s²2s²2p⁶3s²3p⁶3d⁶4s²) or in shorthand using the previous noble gas (Fe: [Ar]3d⁶4s²; Na: [Ne]3s¹). For an ion, start from the atom and remove electrons from 4s before 3d: Fe²⁺ is [Ar]3d⁶, Fe³⁺ is [Ar]3d⁵ and Cu²⁺ is [Ar]3d⁹. Chromium ([Ar]3d⁵4s¹) and copper ([Ar]3d¹⁰4s¹) are the exceptions to remember, because a half-filled or full d sub-shell is unusually stable. Any species that has at least one unpaired electron, such as a chlorine atom (Cl•) or a methyl radical (CH₃•), is a free radical.
Ionisation energy depends on three factors: nuclear charge, distance of the electron from the nucleus (shielding by inner shells), and the repulsion between paired electrons. Down a group the outer electron is further away and more shielded, so first ionisation energy falls. Across Period 3 it generally rises as nuclear charge increases with the same shielding, but with two dips: aluminium is lower than magnesium because its outer electron is in the higher-energy 3p sub-shell, and sulfur is lower than phosphorus because the electron removed is one of a spin-paired pair in a 3p orbital and repulsion makes it easier to remove. Second and later ionisation energies each remove one more electron from a gaseous positive ion: the second ionisation energy of magnesium is Mg⁺(g) → Mg²⁺(g) + e⁻ and the third is Mg²⁺(g) → Mg³⁺(g) + e⁻. Each is larger than the one before, because the electron is removed from an increasingly positive ion; successive values rise steadily within a shell and jump sharply when a new inner shell is broken into, so the position of the big jump tells you the group.
Mass spectra are taught in the topic Analytical techniques: infrared spectroscopy and mass spectrometry, including how to calculate Aᵣ from isotopic abundances and how to use the molecular ion and the [M+1]⁺ and [M+2]⁺ peaks.
Formulae
Neutrons = nucleon number − proton number
Isotope notation: nucleon number top left, proton number bottom left, e.g. ³⁷₁₇Cl
Aᵣ = Σ(isotopic mass × % abundance) ÷ 100
X(g) → X⁺(g) + e⁻ (first ionisation energy)
X⁺(g) → X²⁺(g) + e⁻ (second ionisation energy)
Sub-shell capacities: s 2, p 6, d 10 electrons (1, 3 and 5 orbitals)
Worked examples
q: Iron has proton number 26 and copper 29. Write the shorthand electronic configurations of Fe, Fe²⁺, Cu and Cu²⁺, and use electrons-in-boxes notation to find the number of unpaired electrons in Fe²⁺.
steps: Fe has 26 electrons: [Ar]3d⁶4s², because 4s fills before 3d.
Fe²⁺ loses the two 4s electrons first: [Ar]3d⁶.
Cu is one of the exceptions: [Ar]3d¹⁰4s¹, with a full 3d sub-shell. Cu²⁺ loses the 4s electron and then one 3d electron: [Ar]3d⁹.
For Fe²⁺, draw five 3d boxes. The first five electrons go in singly with parallel spins, which keeps repulsion to a minimum; the sixth pairs up in the first box.
So Fe²⁺ has one box with a pair and four boxes with a single arrow: 4 unpaired electrons.
In context
Carbon dating relies on the radioactive isotope ¹⁴C behaving chemically exactly like ¹²C in living tissue.
Free radicals, species with unpaired electrons, start the chain reactions that make plastics and rubber crack in sunlight; manufacturers add stabilisers that react with the radicals and stop the chain.
Common misconceptions
Thinking 3d fills before 4s: 4s fills first (lower energy) but is also emptied first on ionisation.
Explaining the Mg → Al dip by "aluminium has an extra shell" — both have three shells; the point is that the 3p electron is higher in energy than 3s (and partly shielded by the 3s pair).
Believing isotopes of an element react differently — they have the same electron arrangement and so the same chemistry.
Removing 3d electrons before 4s when writing the configuration of a transition-metal ion — the 4s electrons are lost first, so Fe²⁺ is [Ar]3d⁶, not [Ar]3d⁴4s².
Thinking a positive ion is larger than its atom — losing the outer shell makes a cation smaller; it is anions that are larger than their atoms.
Study tips
Ionisation energy explanations need all three factors named: nuclear charge, shielding, distance (and paired-electron repulsion for the P → S dip).
When a question shows successive ionisation energies, count the electrons removed before the first large jump — that is the group number.
In deflection questions state three things: neutrons are undeflected, protons and electrons curve in opposite directions, and electrons are deflected more because of their much larger charge-to-mass ratio.
Evaluate the idea
The Bohr shell model explains ionisation-energy trends well enough for A Level, but only the orbital model explains the Mg/Al and P/S dips.
Reasoning
Higher nuclear charge → same shielding → stronger attraction of outer electron → higher first ionisation energy
Summary
Protons define the element; neutrons vary between isotopes; electrons determine chemistry.
In an electric field neutrons are undeflected and electrons are deflected more than protons, in the opposite direction.
Sub-shells hold s 2, p 6, d 10 electrons; fill 1s 2s 2p 3s 3p 4s 3d, remove 4s before 3d for ions; Cr and Cu are exceptions.
First ionisation energy falls down a group and rises across a period, with dips at Al and S; successive ionisation energies jump when a new shell is broken into.
Atomic radius falls across a period and rises down a group; cations are smaller and anions larger than their atoms.
Check your understanding
Question 1: How many neutrons are in ⁵⁶Fe³⁺?
1. 29
2. 30
3. 26
Question 2: Which element has the electronic configuration [Ar] 3d⁵ 4s¹?
1. Manganese
2. Chromium
3. Vanadium
Question 3: Which of these isoelectronic ions has the smallest radius?
1. Mg²⁺
2. Na⁺
3. Al³⁺