Cambridge International AS & A Level Chemistry 9701 · Topic 1

Atomic structure

One question runs through the whole of this topic: how tightly is a particular electron held? Answer that and everything else follows — the size of an atom, the size of its ion, how much energy it takes to pull an electron off, and why the periodic table has the shape it has. The topic gives you four tools for answering it: nuclear charge, distance, shielding, and the repulsion between two electrons sharing an orbital.

Inside the atom1.1.1–1.1.2

An atom is almost entirely empty space. Essentially all of its mass sits in a nucleus of protons and neutrons, and that nucleus is about 10⁻¹⁵ m across while the atom is about 10⁻¹⁰ m across — a factor of a hundred thousand. Scale the nucleus up to a marble on the centre spot of a football pitch and the nearest electrons are somewhere in the stands. The electrons are found in shells surrounding it.

These are relative values, which is the whole point of them: you never need the absolute figures (a proton is 1.673 × 10⁻²⁷ kg and carries 1.602 × 10⁻¹⁹ C) to answer a question about atomic structure. What matters is that a proton and a neutron have the same mass as each other, that a proton and an electron carry equal and opposite charge, and that an electron is roughly two thousand times lighter than either nuclear particle.

Atomic number, mass number and notation1.1.3, 1.2.2

The atomic number (or proton number), Z, is the number of protons in the nucleus. It is what makes an element that element: change it and you have a different element. In a neutral atom it is also the number of electrons, because the atom has no overall charge.

The mass number (or nucleon number), A, is the total number of protons and neutrons. "Nucleon" simply means "particle in the nucleus", so nucleon number is the more descriptive of the two names. Neither number counts electrons, since an electron contributes almost nothing to the mass.

The standard notation puts the mass number above the atomic number, both to the left of the symbol:

Number of neutrons = A − Z. That is the only arithmetic in this part of the topic, and one thing about it is worth saying out loud: the mass number is not the number of neutrons, it is the number of neutrons plus protons. Subtract, every time.

Where the mass and the charge sit1.1.4

Take ²³Na, with 11 protons, 12 neutrons and 11 electrons. The 23 nucleons carry all but a fraction of the mass: the eleven electrons together weigh 11/1836 ≈ 0.6% of one nucleon, or about 0.026% of the atom. So mass is concentrated in the nucleus, in a volume something like 10⁻¹⁵ of the atom's volume. Nuclear matter is correspondingly dense — of the order of 10¹⁷ kg m⁻³.

Charge is distributed differently. All the positive charge is in the nucleus (+11 for sodium), and all the negative charge is spread through the electron shells (−11), so the atom is neutral overall but strongly polarised at short range: the centre is intensely positive and the outside is negative. Every explanation in this topic is a consequence of an electron sitting somewhere in that field.

Beams of protons, neutrons and electrons in an electric field1.1.5

Fire the three particles between a pair of charged plates, all at the same velocity, and each behaves in the way its charge and mass dictate. There are only two things to decide: which way a particle bends, and how far.

• Which way is decided by the sign of the charge. A proton is positive, so it is attracted to the negative plate. An electron is negative, so it deflects the opposite way, towards the positive plate. A neutron is uncharged, so it is not deflected at all and carries straight on.
• How far is decided by the charge-to-mass ratio. The force on a particle of charge q in a field E is qE, and the acceleration that force produces is qE/m — so the deflection goes with q/m. Proton and electron carry the same size of charge, but the electron has 1/1836 of the mass, so it deflects 1836 times further.

Notice what the model does with the neutron: no charge means no force, whatever the field strength, so the deflection stays exactly zero rather than becoming very small. That distinction — zero versus small — is what separates the neutron answer from the electron answer.

Counting particles in atoms and ions1.1.6

For a neutral atom, protons = electrons = Z, and neutrons = A − Z. For an ion, only the electron count changes, because ions are made by moving electrons, not nucleons:

• electrons in a cation = Z − (charge), so ²⁷Al³⁺ has 13 − 3 = 10 electrons;
• electrons in an anion = Z + (charge), so ³²S²⁻ has 16 + 2 = 18 electrons.

Protons and neutrons are untouched in both cases. This is worth stating because the commonest slip in the whole topic is adjusting the proton count to make the charge work.

Isotopes1.2.1–1.2.4

Because the proton number is the same, isotopes are the same element and sit in the same place in the periodic table — which is where the word comes from, isos topos, "same place". Because the neutron number differs, they have different mass numbers. Chlorine, for instance, occurs as ³⁵₁₇Cl (17 protons, 18 neutrons) and ³⁷₁₇Cl (17 protons, 20 neutrons); carbon occurs as ¹²C, ¹³C and ¹⁴C.

Why the chemistry is identical

Chemical reactions are a rearrangement of electrons. Isotopes of an element have the same number of protons, therefore the same number of electrons in a neutral atom, therefore the same electron configuration — and the extra neutrons are electrically neutral, so they do not alter how tightly those electrons are held. Same electrons, same chemistry: ³⁵Cl and ³⁷Cl both form Cl⁻, both react with sodium to give a chloride, both have the same electronegativity.

Why the physics differs — and only in two ways

The syllabus is precise about this, and so should you be. Isotopes differ in physical properties limited to mass and density. A ³⁷Cl atom is about 5.7% heavier than a ³⁵Cl atom, and a sample of ³⁷Cl₂ is correspondingly denser than a sample of ³⁵Cl₂ of the same volume, because the atoms occupy the same space — the electron cloud sets the size — but each one weighs more.

Run through a few elements in the model and watch the electron configuration column: it never changes within an element, however many neutrons you add. That column is the reason the chemistry is identical, and saying so is what earns the explanation mark rather than the recall mark.

Atomic radius across a period and down a group1.1.7

An atom has no hard edge — the electron cloud fades out rather than stopping — so "the radius of an atom" has to be defined by measurement. Two definitions are used, and both appear in questions:

• the covalent radius, half the distance between the nuclei of two identical atoms joined by a single covalent bond (so half the Cl–Cl distance in Cl₂);
• the metallic radius, half the distance between the nuclei of two neighbouring atoms in the metal lattice.

Neither can be measured for a noble gas, which forms no bonds and no lattice at room temperature. What is quoted for argon instead is a van der Waals radius, measured between atoms merely touching: 192 pm, nearly double chlorine's 99 pm. That is not a real jump in atomic size, it is a change of ruler, and it is why the period 3 trend is quoted from Na to Cl with argon set to one side rather than plotted at the end of the line.

The same caution applies within period 3 itself: sodium, magnesium and aluminium are quoted as metallic radii and silicon to chlorine as single covalent radii, because those are the measurements that exist for each. The trend they show is real and the syllabus expects you to explain it, but be aware you are reading two quantities on one axis.

Across a period: the radius falls

Going from Na to Cl, each step adds one proton to the nucleus and one electron to the same outer shell (n = 3). The number of inner-shell electrons doing the shielding stays at ten throughout. So:

• nuclear charge rises steadily, +11 to +17;
• shielding is essentially unchanged, because the added electrons go into the shell being pulled in, not underneath it;
• the outer electrons are therefore attracted more strongly and pulled closer in, and the atom gets smaller: 186 pm at sodium down to 99 pm at chlorine.

The quantity that captures "nuclear charge minus shielding" is the effective nuclear charge — the resultant attraction an outer electron actually feels. At this level you estimate it as the nuclear charge minus the number of inner-shell electrons, so it climbs from +1 at sodium to +7 at chlorine while the outer electrons stay in the same shell.

Down a group: the radius rises

Be → Mg → Ca → Sr → Ba runs 112, 160, 197, 215, 217 pm, all measured the same way as metallic radii. Each step down adds a whole new shell, so the outer electrons are in a higher principal quantum number and further from the nucleus. The nuclear charge rises a great deal too, from +4 to +56, but each new shell brings a full complement of inner electrons with it, so the extra shielding very nearly cancels the extra nuclear charge. Distance is left as the deciding factor, and the atoms get bigger.

Notice in the model that the increases get smaller as you descend — 48, 37, 18, 2 pm — because the added shells are progressively better shielded from a nucleus that is also getting much more positive. "Increases down a group" is the trend; "by a decreasing amount" is the detail that shows you know why.

The case that proves the rule

Run the model on Sc to Zn. Ten elements, ten added protons — the same as period 3 — and yet the radius falls by only about 19 pm instead of 87, almost all of it in the first three, and then goes flat. The difference is which sub-shell is filling. In period 3 the electrons are added to the outer shell, where they shield badly. Across the d block they are added to 3d, which lies inside the 4s electrons that set the size of the atom, so each added electron shields the 4s pair from each added proton almost perfectly and the two effects cancel. Filling an inner sub-shell is not the same as filling an outer one, and this is the evidence.

Ionic radius1.1.7

Ions are a different size from their parent atoms, and always in a predictable direction.

Cations are smaller than their atoms

Na 186 pm → Na⁺ 102 pm; Mg 160 → Mg²⁺ 72; Al 143 → Al³⁺ 54. Two things happen at once when a metal atom in period 3 loses its outer electrons. The whole outer shell (n = 3) is removed, so the ion's outermost electrons are now in n = 2 — genuinely closer in. And the same nuclear charge now holds fewer electrons, so each remaining one is pulled harder. Both effects shrink the ion, which is why the drop is so large: more than half, in the case of aluminium.

Anions are larger than their atoms

Cl 99 pm → Cl⁻ 181 pm; S 104 → S²⁻ 184; F 72 → F⁻ 133. No new shell is added — the added electrons go into the existing 3p sub-shell — but the same nuclear charge is now holding more electrons, so the attraction per electron is weaker and inter-electron repulsion is greater. The cloud expands.

Across an isoelectronic series

N³⁻, O²⁻, F⁻, Na⁺, Mg²⁺ and Al³⁺ all have exactly ten electrons, in the configuration 1s² 2s² 2p⁶. Their radii run 171, 140, 133, 102, 72 and 54 pm. Ions with the same electron configuration are called isoelectronic, and a series like this one is the cleanest experiment in the topic: the electron count is held constant, the shells are the same, and the only variable left is nuclear charge, which climbs from +7 to +13. More protons pulling on the same ten electrons gives a smaller ion, every time. (The nitride figure is an estimate rather than a direct measurement, which is why it is flagged in the model.)

Shells, sub-shells and orbitals1.3.1–1.3.2

Three words that students use interchangeably and examiners do not. They nest inside one another:

Each row is just "orbitals × 2". Shell n contains n sub-shells, so shell 1 has only 1s, shell 2 has 2s and 2p, shell 3 has 3s, 3p and 3d, and the shell capacities come out as 2, 8, 18 and 32.

Where the evidence comes from

None of this is assumed. The evidence that electrons occupy distinct energy levels at all, and that those levels are subdivided, comes from ionisation energy data: remove electrons from an atom one at a time and the energies come in groups, with large jumps between the groups and smaller steps within them. Section 21 goes through exactly how a set of successive ionisation energies reveals the arrangement. Keep it in mind while reading the next few sections — the configurations are a conclusion drawn from measurements, not a convention.

The order of sub-shell energies1.3.3

Sub-shells fill from the lowest energy upwards. Within a shell the order is always s < p < d, but the shells overlap, and one overlap matters at this level:

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

The 4s sub-shell is slightly lower in energy than 3d, so it fills first. That single inversion is why period 4 begins with potassium and calcium filling 4s, then scandium to zinc filling 3d, and only then gallium onwards filling 4p. It is also why the d block sits where it does in the periodic table, one period below where a naive shell count would put it.

The blocks of the periodic table

Which sub-shell an element is filling is what its block means. Groups 1 and 2 are filling an s sub-shell, so they are the s block. Groups 13 to 18 are filling p, so they are the p block. The ten columns between them are filling d, and the f block is the two long rows pulled out underneath. Read that backwards and the periodic table becomes a lookup table for electron configurations: an element's position tells you which sub-shell it is filling and how many electrons are in it.

Writing an electron configuration1.3.4, 1.3.6

An electron configuration says how many electrons are in each sub-shell. Building one is mechanical:

1. Find the number of electrons. For a neutral atom that is the atomic number.
2. Fill sub-shells in energy order — 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p — filling each to capacity before starting the next. Filling the lowest available level first is the Aufbau principle (German aufbauen, to build up).
3. Stop when you run out of electrons, and write the sub-shells in shell order.

A long configuration can be abbreviated with the previous noble gas in square brackets: iron is [Ar] 3d⁶ 4s², chlorine is [Ne] 3s² 3p⁵. Use it to save time, but write the full version if a question says "full electron configuration".

This builder replaces an activity that the source file could not supply — its data was missing, not merely unplayable — and it does rather more than the original: as well as the configuration it shows the filling order beside the written order, the electron count in every shell and sub-shell, the noble-gas shorthand, and the electrons-in-boxes diagram for the outer shell.

Why the configurations come out that way1.3.5

The syllabus asks you to explain configurations "in terms of energy of the electrons and inter-electron repulsion", which means two competing effects.

Energy of the electrons. An electron falls to the lowest-energy orbital available, because that arrangement is the most stable. Sub-shell energies are set by how close the orbital lets an electron get to the nucleus and how well it is shielded — which is why 2s is below 2p, and why 4s slips below 3d.

Inter-electron repulsion. Electrons all carry the same charge and repel one another. Two electrons in the same orbital are especially close together, so the repulsion between them — spin-pair repulsion — is significant. It costs energy to pair electrons up, so an electron entering a sub-shell with empty orbitals available will occupy one of those instead of pairing.

That last point is Hund's rule: within a sub-shell, electrons occupy the orbitals singly, with parallel spins, until every orbital has one electron; only then do they start pairing. Nitrogen's three 2p electrons therefore sit one in each of the three 2p orbitals, unpaired; oxygen's fourth 2p electron has no choice but to pair with one of them.

Electrons in boxes1.3.7

The electrons-in-boxes notation makes Hund's rule visible. One box per orbital, one arrow per electron, arrow up or down for the two possible spins, and two electrons in the same box must be drawn with opposite arrows — the Pauli exclusion principle: no two electrons in an atom can be identical, so two sharing an orbital must have opposite spin.

Chromium and copper1.3.5

Two elements in period 4 do not follow the plain filling rule, and both are worth knowing by name.

The 4s and 3d sub-shells are extremely close in energy, so a small gain elsewhere can outweigh the cost of promoting a 4s electron. In both cases the gain is a more even, lower-repulsion arrangement of the d electrons: chromium reaches a half-filled 3d sub-shell with five unpaired electrons spread one per orbital, and copper reaches a completely filled one. Spreading electrons out over five orbitals rather than doubling up in four reduces spin-pair repulsion, and that is what tips the balance.

Electron configurations of ions1.3.6

One rule covers every ion you will be asked about: electrons are removed from the outermost shell first — the highest n — and within a shell from the highest sub-shell. Electrons added to make an anion go into the lowest available space, continuing the filling order.

For a d-block metal this means the 4s electrons are removed before the 3d electrons, even though 4s filled first. There is no contradiction: 4s is marginally lower in energy in the neutral atom, but it is in the shell further out, and it is the outer shell that ionises. So:

This builder also replaces an activity whose data was missing from the source file. Pick an element and a charge and it applies the outer-shell-first rule and shows what was removed or added, so you can check your own reasoning against it rather than against an answer list.

Shapes of s and p orbitals1.3.8

An orbital is a region of high probability, not a track, so its "shape" is the shape of the volume inside which the electron is very likely to be found. Two shapes are examinable, and you need to be able to sketch both.

• An s orbital is spherical, centred on the nucleus. There is one per shell, and it gets larger as n increases — a 2s orbital is a bigger sphere than a 1s orbital.
• A p orbital is dumb-bell shaped: two lobes on opposite sides of the nucleus. There are three of them per p sub-shell, identical in shape and energy but pointing along three mutually perpendicular axes, so they are labelled p_x, p_y and p_z.

The rotatable model is there for one reason: the three p orbitals are genuinely perpendicular in three dimensions, and a flat diagram makes them look like a flower in a plane. Drag it until the p_z dumb-bell points at you and the other two go edge-on.

Free radicals1.3.9

That is the whole definition, and it is about the electrons rather than the charge: a radical can be neutral (Cl•, •CH₃, NO), and a species can be charged without being a radical (Na⁺, Cl⁻). The convention is to write the unpaired electron as a dot next to the symbol.

An unpaired electron is chemically expensive: pairing electrons up lowers the energy, so a radical will react to find a partner, which makes radicals short-lived and highly reactive. A chlorine molecule split by ultraviolet light gives two chlorine radicals, Cl₂ → 2Cl•, and each of those goes on to attack whatever it meets — the opening step of the radical substitution mechanism you will meet in organic chemistry, and of ozone depletion.

First ionisation energy1.4.1–1.4.2, 1.4.5

Four details in that wording each carry a mark:

• one mole — because the unit is kJ mol⁻¹, the definition is per mole of electrons removed, not per electron;
• gaseous — atoms must be isolated, with no neighbours attracting or repelling them, otherwise you would be measuring lattice or intermolecular effects as well. Every equation therefore carries (g) on both species;
• atoms → 1+ ions — the first ionisation energy starts from a neutral atom. Starting from an ion makes it a second or later ionisation energy;
• the electron removed is the most loosely held one, that is, the outermost.

The equation for the first ionisation energy of sodium is

Na(g) → Na⁺(g) + e⁻

and the second and third are

Na⁺(g) → Na²⁺(g) + e⁻
Na²⁺(g) → Na³⁺(g) + e⁻

Ionisation energy exists at all because of the attraction between the nucleus and the outer electron. Everything that follows is an argument about how strong that attraction is.

Trends in ionisation energy1.4.3

Plot first ionisation energy against atomic number for the first few periods and the graph repeats: a peak at every noble gas, a trough at every alkali metal, and a general climb in between. That repeating pattern is the original evidence for shells.

Across a period: a general increase

Na 496 → Mg 738 → Al 578 → Si 787 → P 1012 → S 1000 → Cl 1251 → Ar 1521 kJ mol⁻¹. Ignoring two dips for a moment, the value rises. The reasoning is the same as for atomic radius, applied to an electron being removed:

• nuclear charge increases across the period;
• the outer electron stays in the same shell, and the number of inner shielding electrons does not change;
• the atomic radius therefore falls, so the outer electron is both closer in and more strongly attracted, and more energy is needed to remove it.

Down a group: a decrease

Li 520 → Na 496 → K 419 kJ mol⁻¹. Nuclear charge is rising, so why does ionisation energy fall? Because the outer electron is in a new shell each time: it is further from the nucleus, and the extra inner shells shield it. Those two effects between them outweigh the increase in nuclear charge, so the outer electron is less firmly held and comes off more easily.

The two dips, and why they are not exceptions to the physics

Within period 3 the increase is interrupted twice, and Cambridge expects the reason for each.

The four factors1.4.6

Every ionisation energy explanation in this syllabus is assembled from four factors. Learn them as a checklist and work through it in order.

The first three combine into the effective nuclear charge — the net pull an outer electron actually experiences. At this level you estimate it by subtracting the inner-shell electrons from the nuclear charge, giving the core charge: +1 for sodium, +2 for magnesium, rising to +8 for argon, then back to +1 at potassium. That reset at the start of each period is the shape of the ionisation energy graph.

Successive ionisation energies1.4.4, 1.4.7–1.4.8

Keep pulling electrons off the same atom and each removal costs more than the last. Sodium goes 496, 4562, 6910, 9543, 13 354, 16 613, 20 117, 25 496 kJ mol⁻¹. Two reasons, both worth stating:

• each electron is being removed from an increasingly positive ion, so the attraction holding it is stronger;
• with fewer electrons left, there is less inter-electron repulsion and the remaining electrons are pulled closer in, reducing the radius.

So successive ionisation energies always increase. What makes them useful is how much they increase at each step.

Reading the jumps

Look at sodium again. From the first to the second value the energy rises by a factor of nine. After that each step is a modest increase. That enormous jump happens because the first electron came from the outer shell (n = 3) while the second had to come from the shell beneath it (n = 2) — much closer to the nucleus and far less shielded. A big jump marks the point where you break into a new shell.

Which gives the standard method: count the electrons removed before the big jump, and that is the number of electrons in the outer shell — the group number. One easy electron means group 1; two means group 2; seven means group 17 (group VII in the older numbering the method is usually taught in).

A second, smaller feature is readable too. Chlorine is 3s² 3p⁵, so the first five electrons come out of 3p and the sixth and seventh out of 3s. Its ratios run ×1.84, 1.66, 1.35, 1.27, 1.43, 1.18 — nothing like the ×3.05 at the shell boundary, but the fifth step is clearly larger than its neighbours, and that small bump is the 3p sub-shell running out. Reading both features is how successive ionisation energies reveal sub-shells and not merely shells, and it is the evidence the configurations in part two rest on.

Self-test1.1–1.4

Thirty-two questions across the whole topic, in random order, each with the reasoning behind the answer rather than just the answer. Work out your response before revealing it — the explanation is written to be read after you have committed to a choice.

Definitions to learn1.1–1.4

These are the sentences worth knowing word for word, because a paraphrase usually loses a mark somewhere.

Data used on this pagereference

First ionisation energies, hydrogen to krypton / kJ mol⁻¹

Successive ionisation energies / kJ mol⁻¹

Atomic radii / pm

Ionic radii / pm (six-coordinate)

Bracketed values are estimates rather than measurements.