Isotopes

Take an atom of hydrogen — a single proton with a single electron whizzing round it. Now imagine quietly slipping one extra neutron into its nucleus. You haven't added any protons, so it is still hydrogen: it still reacts the same way, still makes water with oxygen, still sits in the same box on the periodic table. But it is now twice as heavy. Chemists give this heavier hydrogen its own name — deuterium — and it is real: a spoonful of it is floating in every glass of water you drink.

Atoms of the same element that carry different numbers of neutrons are called isotopes. They are the same element wearing different weights. This one idea — same protons, different neutrons — explains heavy water, radioactive decay, carbon dating, and why the atomic masses on the periodic table are almost never whole numbers.

Same protons, different neutrons

In our lesson on the atom we met the three particles in the nucleus and its cloud: protons (positive), neutrons (no charge), and electrons (negative). The single most important number about an atom is its atomic number Z — the number of protons. It is this number, and only this number, that decides which element you have: every atom with 6 protons is carbon, every atom with 8 is oxygen, every atom with 92 is uranium.

The number of neutrons, though, is free to vary. Two atoms with the same number of protons but a different number of neutrons are isotopes of each other. They are the same element, but with different masses.

Isotopes are atoms of the same element that differ only in their neutron count:

They have the same atomic number Z (same number of protons), so they are the same element.
They have different numbers of neutrons, and therefore different mass numbers A.
They behave identically in chemical reactions — chemistry is run by the electrons, and a neutral atom's electron count matches its proton count, which isotopes share.
They can differ in mass and in nuclear stability — some isotopes are steady forever, others are radioactive.

The two counts that describe any nucleus are the atomic number and the mass number:

A = Z + N,

where A is the mass number (protons + neutrons — the total count of heavy particles in the nucleus), Z is the atomic number (protons), and N is the number of neutrons. Rearranged, the neutron count is just N = A - Z.

Standard notation: numbers on the left

Scientists write an isotope with two small numbers stacked on the left of the element symbol — the mass number on top and the atomic number on the bottom:

{}^{A}_{Z}\text{X} \qquad\longrightarrow\qquad {}^{12}_{\;6}\text{C}, \quad {}^{14}_{\;6}\text{C}.

Both of those are carbon — you can tell instantly because the bottom number is 6 in each. The top number differs: carbon-12 has a mass number of 12, carbon-14 has 14. Because N = A - Z, carbon-12 carries 12 - 6 = 6 neutrons, while carbon-14 carries 14 - 6 = 8. Two extra neutrons, same element.

In everyday writing we usually drop the bottom number (it is fixed by the element's name anyway) and just say carbon-12 or carbon-14 — the number after the dash is the mass number.

Good spot — the bottom number really is redundant once you know the element. It is kept because it makes the bookkeeping of nuclear equations foolproof. When a nucleus decays or particles smash together, the top numbers must add up to the same total on both sides, and so must the bottom numbers (charge is conserved). Writing both means you can balance a nuclear reaction just by checking two columns of sums — a trick you will lean on the moment you meet radioactive decay.

Worked example 1 — reading an isotope symbol

An atom is written {}^{23}_{11}\text{Na}. How many protons, neutrons and electrons does this neutral atom have?

Step 1 — read off the two numbers. The bottom number is the atomic number, Z = 11; the top number is the mass number, A = 23.

Step 2 — protons. Protons = atomic number, so there are 11 protons. (Eleven protons means it is sodium, Na — the symbol confirms it.)

Step 3 — neutrons. Use N = A - Z:

N = 23 - 11 = 12 \text{ neutrons.}

Step 4 — electrons. A neutral atom has as many electrons as protons, so 11 electrons.

Worked example 2 — the same element, two isotopes

Chlorine comes in two common isotopes, {}^{35}_{17}\text{Cl} and {}^{37}_{17}\text{Cl}. Show that they really are isotopes of each other, and find how their neutron counts differ.

Step 1 — check the atomic numbers. Both have Z = 17 protons. Same proton number → same element → they are isotopes of chlorine.

Step 2 — neutrons in chlorine-35. N = 35 - 17 = 18 neutrons.

Step 3 — neutrons in chlorine-37. N = 37 - 17 = 20 neutrons.

Step 4 — compare. They share 17 protons and 17 electrons — so they are chemically the same stuff, both forming salt with sodium — but chlorine-37 carries 20 - 18 = 2 more neutrons, making it a touch heavier.

Build your own isotope

Here is a carbon nucleus. Carbon always has 6 protons — take any of those away and it stops being carbon — but you can add or remove neutrons freely. Drag the neutron slider and watch the nucleus grow, the mass number change, and the atom flip between stable and radioactive. Notice you are always making a different isotope of carbon — never a different element.

Two of the settings are stable (carbon-12 with 6 neutrons and carbon-13 with 7); the rest are radioactive. Carbon-14, with 8 neutrons, is the famous unstable one — hold that thought for the story about dating ancient bones below.

Stable and radioactive isotopes

Neutrons act like glue in the nucleus, helping the mutually-repelling protons stick together. Get the balance of neutrons to protons just right and the nucleus sits there, unchanged, essentially forever — it is stable. Get it wrong — too many neutrons, or too few — and the nucleus is unstable: sooner or later it will spit out a particle or a burst of energy to fix the imbalance. Unstable isotopes are exactly what we mean by radioactive.

Some elements you may know by their isotopes:

Hydrogen: {}^{1}_{1}\text{H} (ordinary, no neutrons, stable), {}^{2}_{1}\text{H} (deuterium, 1 neutron, stable), and {}^{3}_{1}\text{H} (tritium, 2 neutrons, radioactive).
Carbon: carbon-12 and carbon-13 are stable; carbon-14 is radioactive.
Uranium: uranium-238 is the common, only weakly radioactive form, while the rarer uranium-235 is the one that splits in a nuclear reactor or bomb — same element, wildly different jobs, separated only by three neutrons.

The key point: whether an isotope is stable or radioactive is set by what is happening in the nucleus. It has nothing to do with the electrons, so it does not change the atom's chemistry one bit — radioactive carbon-14 forms exactly the same carbon dioxide as ordinary carbon-12.

Why atomic masses aren't whole numbers

Glance at the periodic table and chlorine's mass is listed as 35.5 — a strange half-number, when every individual atom must have a whole number of protons and neutrons. The reason is isotopes. A real sample of chlorine is a mixture: about three-quarters chlorine-35 and one-quarter chlorine-37. The number on the table is the relative atomic mass A_r — the weighted average of the isotope masses, weighted by how common each one is.

A_r = \frac{\sum (\text{isotope mass} \times \text{percentage})}{100}.

Worked example 3 — the relative atomic mass of chlorine

Chlorine is 75\% chlorine-35 and 25\% chlorine-37. Find its relative atomic mass.

Step 1 — multiply each isotope's mass by its abundance.

(35 \times 75) + (37 \times 25) = 2625 + 925 = 3550.

Step 2 — divide by 100 (the total percentage):

A_r = \frac{3550}{100} = 35.5.

So the "impossible" half-number is really just the average pull of a crowd of two whole-numbered isotopes — closer to 35 than 37 because the lighter isotope is three times as common. That is why A_r lands between the isotope masses and rarely comes out whole.

It's the neutrons that differ, not the protons. Isotopes of an element share the same number of protons (the same atomic number) — that is what keeps them the same element. If you change the number of protons, you have made a different element, not an isotope. Protons name the element; neutrons only change the weight.
Don't mix up mass number and atomic number. The top-left number is the mass number A (protons + neutrons); the bottom-left number is the atomic number Z (just the protons). Neutrons are the difference, N = A - Z — never read the top number as the neutron count.
Adding a neutron does not change the chemistry. Carbon-14 reacts exactly like carbon-12 — same electrons, same bonds, same everything a chemist cares about. It is only heavier and, in this case, radioactive. An isotope is a heavier (or lighter) twin, not a new substance.

The air is full of ordinary carbon-12, but cosmic rays constantly brew a tiny, steady trickle of radioactive carbon-14 high in the atmosphere. Living things — plants, and the animals that eat them — keep swapping carbon with the air, so while they are alive they hold the same small fraction of carbon-14 as everything else. The instant an organism dies, the swapping stops, and its trapped carbon-14 begins to decay away at a perfectly known, clockwork rate (half of it vanishes every 5,730 years).

So archaeologists measure how much carbon-14 is left in a scrap of ancient wood, bone or cloth, compare it with a fresh sample, and read off how long ago the thing was alive — like an hourglass that started running the moment it died. It works precisely because carbon-14 is chemically identical to carbon-12, so a living body can't tell them apart and stores them in the same proportion. One rare isotope, and we can read the age of the pharaohs.

Swap the ordinary hydrogen in a water molecule for its heavier isotope deuterium ({}^{2}_{1}\text{H}, with an extra neutron) and you get heavy water, written \text{D}_2\text{O}. It looks and tastes almost exactly like normal water — it is chemically the same, after all — but it is about 11\% denser, so an ice cube of it sinks in a glass of ordinary water instead of floating. Heavy water is no laboratory curiosity: because those extra neutrons slow stray neutrons down without swallowing them, it is used inside some nuclear reactors to keep the chain reaction ticking over. A single neutron per atom, and the same old water gets a brand-new job.