1The idea in one paragraph

An atom is almost entirely empty space. At its centre is a nucleus, tens of thousands of times narrower than the atom but holding nearly all of its mass, made of positive protons and neutral neutrons. Around it, in the space that makes up the rest of the atom, are negative electrons. The number of protons decides which element an atom is. The number of neutrons can vary within one element, which gives isotopes: atoms that behave the same way chemically but have different masses. Because most elements are a mix of isotopes, the "mass of an atom" of an element is an average, the relative atomic mass, and that is why the numbers in the periodic table are not whole.

2Inside the atom

Figure 1 is a lithium-7 atom. It is not to scale, and cannot be: drawn with the nucleus the size shown, the atom would have to be hundreds of metres across.

The three subatomic particles have these relative masses and charges. The data booklet gives their actual masses in kilograms and the actual charge in coulombs; what you must know is the relative values.

Protons and neutrons together are called nucleons. Because an electron's mass is about two-thousandths of a proton's, the mass of an atom is, to a very good approximation, the mass of its nucleons. That is why the nucleus is dense: nearly all the mass is squeezed into a tiny fraction of the volume.

An atom is neutral, so it has as many electrons as protons. The positive charge of the nucleus attracts the negative electrons, and that attraction is what holds an atom together. Almost all of chemistry is about the electrons, which are on the outside where other atoms can reach them. The nucleus is untouched by any chemical reaction.

How we know. Early in the twentieth century the accepted model spread the atom's positive charge evenly through it, with electrons embedded like fruit in a pudding. Figure 2 shows the experiment that ended it. A beam of fast, positive alpha particles was fired at a very thin sheet of gold.

Nearly all the alpha particles went straight through, so most of the atom is empty space. A few were deflected, so there is concentrated positive charge somewhere in it. A very small number bounced back. Spread-out charge could never turn round a fast, heavy particle, so the positive charge and most of the mass had to be packed into something tiny. That something is the nucleus. The model was replaced because it could not explain the data, which is exactly how scientific models are supposed to change.

3The nuclear symbol

Every atom or ion can be written as a nuclear symbol. Figure 3 labels its parts.

• The atomic number, Z, written bottom left, is the number of protons. It defines the element: every atom with 13 protons is aluminium, and the periodic table in the data booklet is arranged in order of Z.
• The mass number, A, written top left, is the number of protons plus neutrons.
• The charge, written top right, is present only for an ion.

In print it looks like ²⁷₁₃Al³⁺, and often the Z is left off, as in ²⁷Al³⁺, because the symbol Al already tells you Z = 13.

Three rules turn a symbol into numbers.

protons = Z · neutrons = A − Z · electrons = Z − charge

"Z − charge" handles both kinds of ion at once. A positive ion has lost electrons, so a charge of 3+ means 13 − 3 = 10 electrons. A negative ion has gained electrons, so a charge of 2− means you subtract −2, which adds 2. Losing or gaining electrons never changes the nucleus, so an ion has the same numbers of protons and neutrons as its atom.

The last row is worth a second look: a hydrogen-1 ion is a bare proton, with no neutron and no electron.

The rules also run backwards. A species with 17 protons, 20 neutrons and 18 electrons has Z = 17, which the periodic table says is chlorine, A = 17 + 20 = 37, and a charge of 17 − 18 = 1−. It is ³⁷Cl⁻.

4Isotopes

Isotopes are atoms of the same element with different numbers of neutrons. Same Z, different A. Figure 4 shows the two isotopes of chlorine found in nature.

Isotopes are named by their mass number: chlorine-35 and chlorine-37, or ³⁵Cl and ³⁷Cl.

Same chemical properties. Chemical reactions involve electrons. Isotopes of an element have the same number of protons, so the same number of electrons, arranged in the same way (S1.3 describes that arrangement). The extra neutrons are buried in the nucleus and take no part. So ³⁵Cl and ³⁷Cl form the same compounds, in the same ratios, in the same reactions. The linking question in the guide points ahead: the chemical properties of an atom are decided by its electrons, which is where S1.3 begins.

Different physical properties. Anything that depends on the mass of the atom differs. A heavier isotope, or a compound made from it, has a higher density, and in a gas its particles move more slowly at the same temperature (S1.1: same average kinetic energy, so a larger mass means a smaller speed), so it diffuses more slowly. Melting and boiling points differ slightly too. Water made with hydrogen-2 in place of hydrogen-1 is denser than ordinary water and boils a little above 100 °C. Some isotopes also have unstable nuclei and are radioactive, while others of the same element are stable. You do not need to learn named examples of isotopes; you need to explain the difference.

A useful consequence (it is a Nature of science link in the guide): because isotopes react identically but can be told apart by mass or by radioactivity, a chemist can build a reactant with one atom swapped for a rare isotope and then find where that labelled atom ends up in the products. These isotope tracers are one way reaction mechanisms are tested, which Reactivity 3.4 returns to.

5Relative atomic mass from isotopes

Most elements are a mixture of isotopes in fixed natural proportions. A sample of chlorine is about three-quarters ³⁵Cl and one quarter ³⁷Cl, so the average mass of a chlorine atom lies between 35 and 37, closer to 35. That average is the relative atomic mass, Ar: the weighted mean mass of the atoms of an element, on a scale on which one atom of carbon-12 has a mass of exactly 12 (S1.4 explains the scale). Because it is a ratio of masses, Ar has no units.

Ar = Σ (isotope mass × abundance) ÷ Σ (abundances)

When the abundances are percentages, the bottom line is 100. Exam questions usually give each isotope's mass as its mass number.

Worked example. Natural chlorine is 75.8% chlorine-35 and 24.2% chlorine-37.

Figure 5 shows why the answer has to look like this. Think of the isotope masses as weights on a beam: the balance point is pulled towards the heavier weight, which here is the more abundant isotope.

Two checks catch most errors. The answer must lie between the smallest and largest isotope masses. And it must lie closer to the more abundant isotope. An answer of 36.0 for chlorine fails the second check straight away.

The data booklet gives chlorine's Ar as 35.45, not 35.48. The small difference is not an error in your method: real isotope masses are not exact whole numbers (chlorine-35 is slightly less than 35), and the booklet uses the precise values. In calculations from S1.4 onwards, always use the values in the data booklet, to two decimal places.

Working backwards to an abundance. If you know Ar and the isotope masses, you can find the abundances. For two isotopes, call the fraction of the lighter one x; the other is then 1 − x.

Boron has Ar = 10.81 and two isotopes, boron-10 and boron-11.

Check it against the balance point: 10.81 is much closer to 11 than to 10, so boron-11 must be the more abundant. It is.