Ionisation Energy

Ionisation energy is one of the few properties in chemistry that is measured directly, precisely, and for essentially every element. That makes it unusually good evidence — it is how we know atoms have shells at all — and it makes the small deviations from the expected trend genuinely informative rather than annoying.

The definition hides three conditions

The first ionisation energy is the energy needed to remove one electron from each atom in a mole of gaseous atoms:

X(g) → X⁺(g) + e⁻

Three details in that line are doing work.

Gaseous. The atoms must be isolated. Ionise an atom sitting in a solid and you would also be paying to overcome its attraction to its neighbours, which is a property of the substance rather than of the atom.

Per mole. The value is an energy per mole of atoms, quoted in kJ/mol. Atomic physicists more often quote per atom in electronvolts, and the conversion is 1 eV = 96.485 kJ/mol. Hydrogen's 13.60 eV becomes 1,312 kJ/mol, which is the figure chemistry courses use.

Always positive. Pulling a negative electron away from a positive nucleus costs energy in every case, for every element, without exception. An ionisation energy is never released, and a negative value is an error.

An older name, ionisation potential, still appears in physics literature. It survives from the days when the quantity was determined by finding the accelerating voltage at which electrons began to ionise a gas, and it means the same thing measured in volts.

Every successive removal costs more, and one costs enormously more

Take electrons off one at a time and each is harder to remove than the last, because you are pulling a negative charge away from an increasingly positive ion.

The interesting part is that the increases are not smooth. Magnesium, in kJ/mol:

The second costs about twice the first — a normal step. The third costs more than five times the second. Something changes qualitatively at that point, and what changes is which shell the electron comes from. The first two are magnesium's outer-shell electrons; the third has to be prised out of a filled inner shell that lies much closer to the nucleus and is not screened by anything above it.

Aluminum shows the same signature one place later: 577.5, then 1,816.7, then 2,744.8, then 11,577. Three moderate values, then a jump by a factor of four.

This pattern is the direct experimental evidence that electrons are arranged in shells rather than distributed smoothly, and plotting the logarithm of successive ionisation energies against electron number for a single element makes the shell structure visible as a staircase.

Reading an element's group off a list of numbers

Because the big jump falls immediately after the valence electrons are exhausted, a list of successive ionisation energies identifies an element's group without naming the element.

Consider these successive values in kJ/mol: 1,000 · 2,252 · 3,357 · 4,556 · 7,004 · 8,496 · 27,107.

Work along looking for the largest proportional step. Each of the first five increases is a factor of one to two. Between the sixth and the seventh, the value more than triples. So this element has six electrons that come off comparatively easily, and it belongs to group 16. The numbers are sulfur's.

Two habits make this reliable. Compare ratios, not differences — the absolute gaps grow throughout, so the largest gap is not necessarily the jump you want. And count the removals before the jump; the jump itself is the first core electron, not the last valence one. The connection between that count and the group is set out under valence electrons.

Two dips in period 2, for two different reasons

Across a period, ionisation energy rises, because effective nuclear charge rises while the shell stays the same. Period 2, in kJ/mol:

lithium 520 · beryllium 900 · boron 801 · carbon 1,087 · nitrogen 1,402 · oxygen 1,314 · fluorine 1,681 · neon 2,081

The overall climb is dramatic — neon takes four times what lithium takes — but two elements come in below their left-hand neighbour. Both dips have specific causes, and they are not the same cause.

Beryllium to boron. Beryllium's outermost electron is a 2s electron. Boron's is a 2p electron, which lies at higher energy and is partly screened by the filled 2s pair beneath it. A 2p electron is easier to remove than a 2s electron even though boron has one more proton.

Nitrogen to oxygen. Nitrogen's 2p subshell holds three electrons in three separate orbitals, all unpaired. Oxygen's fourth 2p electron has no empty orbital left and must share one, and two electrons crowded into a single orbital repel each other. That repulsion makes the paired electron the cheapest one in the atom to remove. The orbital-filling rule behind it is Hund's, covered under orbitals and subshells.

The same two dips recur in period 3, at magnesium-to-aluminum and at phosphorus-to-sulfur, for the same two reasons. When a question asks you to explain an anomaly in this trend, naming which of the two you are looking at is most of the answer.

Cesium, not francium, is the easiest to ionise

Down a group the value falls, because the outer electron sits in a shell further from the nucleus while the effective nuclear charge stays roughly constant — the mechanism set out under periodic trends. Group 1, in kJ/mol: lithium 520, sodium 496, potassium 419, rubidium 403, cesium 376.

Extrapolate and francium should be lower still. It is not. Francium's first ionisation energy has been measured at about 393 kJ/mol — higher than cesium's, breaking the trend at the very last element in the group.

The cause is relativistic. With 87 protons, francium's innermost electrons move fast enough for relativistic effects to matter, and the consequence is a contraction and stabilisation of the 7s orbital that holds the outermost electron more tightly than its position implies. Cesium therefore holds the record for the lowest first ionisation energy of any element, and francium is not, as many sources still claim, the most reactive metal.

At the other end, helium's 2,372 kJ/mol is the highest of any element — two protons pulling on two electrons in the smallest shell there is, with no screening from anything.

The flat middle of the fourth period

Across the first transition series the trend nearly disappears. Scandium's first ionisation energy is 633 kJ/mol and iron's is 763 — a rise of about 20% across eight elements, where period 2 managed a fourfold rise across the same span. The values are also not monotonic: copper's 745 sits below iron's.

The cause is the same one that flattens the atomic radii across this series: each newly added electron joins an inner subshell rather than the outer one being stripped, so most of the extra nuclear charge is neutralised before it ever reaches the 4s level.

Zinc breaks upward to 906 kJ/mol, because with 3d completely full and 4s completely full it has no partly filled subshell at all — a configuration that resists disturbance in much the same way a noble gas does.

Where the marks go

• Omitting "gaseous" from a definition. It is not decoration; a definition without it describes a different quantity.
• Assuming the trend across a period is smooth. It is not, in either period 2 or period 3, and the two exceptions are examinable precisely because they require a reason rather than a direction.
• Applying a first-ionisation trend to a second ionisation. Sodium has a very low first ionisation energy and one of the highest second ionisation energies in the periodic table. Each removal must be reasoned about separately, using the configuration of the ion it starts from, not the atom.