Successive ionization energies (HL)

The big idea: You can pull electrons off an atom one at a time. The energy to remove each one is a successive ionization energy — the 1st IE, 2nd IE, 3rd IE, and so on.

Every successive IE is larger than the one before it. Once you have removed an electron the particle is a positive ion, and the next electron is held by an ion with one fewer electron and the same nuclear charge — so the pull on it is stronger and it costs more energy to remove.

The pattern of those rising energies is a fingerprint of how the atom's electrons are arranged.

The vocabulary: - 1st ionization energy — energy to remove one mole of electrons from one mole of gaseous atoms: X(g) → X⁺(g) + e⁻. - 2nd ionization energy — energy for X⁺(g) → X²⁺(g) + e⁻, and so on. - Successive IEs — the whole sequence (1st, 2nd, 3rd …), always measured for the gaseous species. - Each one is bigger than the last because the electron leaves an increasingly positive ion — more protons pulling on fewer electrons.

Why each step costs more: Two reasons the energy rises with every electron removed:

1. Greater effective nuclear pull — the same number of protons now holds fewer electrons, so each remaining electron feels a stronger net attraction. 2. Less electron–electron repulsion — fewer electrons means the survivors are pulled in tighter.

Both make the next electron harder to remove. The interesting part is how much harder — that is what tells us about shells.

Most successive IEs rise gently. But every so often there is a sudden large jump — the next electron costs several times more than the last. That jump is the key piece of evidence in this topic.

A big jump = a new, inner shell: A large rise in successive IE happens when the next electron must be pulled from a new, inner (lower) main energy level — a shell closer to the nucleus.

Electrons in an inner shell are:

- closer to the nucleus (stronger attraction), and - less shielded by other electrons.

So breaking into a new inner shell costs a large jump of energy. The existence of these jumps is direct evidence that electrons are arranged in shells at different distances from the nucleus.

Reading sodium's pattern: Sodium is 2, 8, 1. Look at the jumps in its successive IEs:

- The 1st electron (the lone n = 3 electron) leaves easily — 496 kJ mol⁻¹. - The 2nd electron must come from the full n = 2 shell → a huge jump to 4 562 kJ mol⁻¹ (about nine times larger). - Electrons 2nd → 10th all come from n = 2 and rise only gently. - The 11th electron comes from the innermost n = 1 shell → another big jump.

Two big jumps → three shells → 2, 8, 1. The pattern is the electron arrangement.

Big jumps vs small rises: - A BIG jump (several-fold) = the next electron comes from a new inner main shell → evidence for shells. - A small extra rise (within a shell) can mark a change of sub-shell (e.g. moving from a p to an s sub-shell) → finer evidence for sub-shells.

For deducing the group you only need the big jumps; the small rises are the subtler sub-shell evidence.

The rule that wins marks: For a main-group element, count the electrons removed before the first big jump.

Number of electrons before the first big jump = number of outer-shell electrons = the GROUP number.

- 1 electron, then a big jump → Group 1. - 2 electrons, then a big jump → Group 2. - 3 electrons, then a big jump → Group 13 (3 outer electrons).

The outer electrons leave relatively easily; the first big jump marks the point where you start breaking into the full inner shell.

Watch the position of the jump, not its size: It is where the first big jump falls (after how many electrons), not how big it is, that gives the group.

A Group 1 element has its big jump after 1 electron; a Group 13 element after 3 electrons. Count carefully: the jump is the step into the next-lower shell, so the outer electrons are the ones removed before it.

How this is tested: Successive IEs are a favourite HL Paper 2 data question.

- Paper 1A (MCQ): pick the element / group that matches a short list of successive IEs, or spot which jump is the big one. - Paper 2: you are given a table or a log-scale graph of successive IEs and asked to deduce the group, identify the element, or explain a particular jump in terms of shells.

Graphs are usually plotted as log₁₀(IE) against electron number so that all the values fit on one axis — the big jumps then show up as clear steps.

Why the graph is logarithmic: Successive IEs span a huge range (hundreds to hundreds of thousands of kJ mol⁻¹). Plotting log₁₀(IE) compresses that range so the whole sequence fits on one graph.

On a log plot, electrons from the same shell sit on a roughly flat step; a step up to a higher level marks a new inner shell. The number of points on the first (lowest) step = the number of outer electrons = the group.

Reading the graph above for magnesium (2, 8, 2): the curve climbs in three flat steps with a sharp jump between each. The lowest step has 2 points (the two outer n = 3 electrons), the middle step has 8 (the n = 2 shell), and the top step has 2 more (the n = 1 shell). Counting the points on the first step gives 2 → Group 2. The same numbers are laid out in the table below.