How big an atom is

Cut a sliver of magnesium ribbon half a millimetre wide, about the width of a full stop. You can see it, and you can hold it between two fingers. The puzzle is how many magnesium atoms sit side by side across that width. It takes one number you learn and three lines of working - and the number comes first.

This is video three of seven in Atomic structure. If the particles inside an atom are not solid yet, Protons, neutrons and electrons comes before this one.

Right, the number to learn is the size of an atom. The radius of an atom is about nought point one nanometres. A nanometre is a billionth of a metre. In metres, that radius is one times ten to the minus ten metres. As a decimal it is nought point, then nine zeros, then a one. The nucleus, though, is far smaller. Its radius is about one times ten to the minus fourteen metres. When you divide one power of ten by another, you take the second power away from the first. Put the atom's radius on top, the nucleus's radius underneath, and divide. How many times wider is the atom than its nucleus? Ten thousand times. Minus ten take away minus fourteen is plus four, and ten to the power four is ten thousand. Picture it. If an atom were blown up to the size of a football stadium, its nucleus would be about the size of a pea on the centre spot. That gives two facts that come as a pair. Almost all of an atom's mass is in the nucleus. Almost all of its volume is empty space. So every drawing of an atom you meet, with a nucleus big enough to see, is not to scale. The real nucleus would be too small to see.

Now, the magnesium ribbon. The width is nought point five millimetres. The radius of a magnesium atom is one point six times ten to the minus ten metres. Before any division, write a convert line. Every length goes into metres, in standard form, on a line of its own. What is nought point five millimetres in metres, in standard form? Five times ten to the minus four metres. A metre is a thousand millimetres, so divide nought point five by a thousand. Next, atoms side by side: does each one take up its radius, or its diameter? Its diameter. Touching atoms sit edge to edge, so each one takes up its full width, which is twice the radius. Divide by the radius, and you count twice as many atoms as there are. So double it. Two times one point six times ten to the minus ten is three point two times ten to the minus ten metres. Now, divide the width by the diameter. Five times ten to the minus four, divided by three point two times ten to the minus ten. Five divided by three point two is about one point five six. And minus four take away minus ten is plus six. That makes about one point six times ten to the six. About one point six million magnesium atoms lie across a strip you can hold between two fingers. One examiner's report describes a question about fitting atoms across a sample of magnesium. Students who recalled the radius "often then did not ensure that the values for atomic radius and the width of magnesium metal were in the same units". The same report goes on. Among those who got that far, "the most common error was then not recognising that the atomic radius needed to be doubled". Both slips live in the two lines written before the division. So write both lines every time: the convert line, then the radius or width question. Here is your handle for this video, and it is those two lines in order: metres first, then radius or width.

Atoms, though, are not the only things this size. In diamond, the bond between two carbon atoms is about nought point one five nanometres long. A carbon atom has a radius of about nought point nought seven nanometres. One nanometre is ten to the minus nine metres. Two lengths, then, and the convert line comes first. Convert both to metres. Is the bond longer or shorter than one atom is wide? The bond is one point five times ten to the minus ten metres. The radius is seven times ten to the minus eleven metres, so one atom is one point four times ten to the minus ten metres wide. The bond is a shade longer than one atom's width, by about one times ten to the minus eleven metres. That fits: a bond runs from nucleus to nucleus, and two touching atoms have nuclei about one width apart. Atoms, small molecules and the bonds between atoms are all around ten to the minus ten metres. That is the size to carry in your head.

Right, time to see if it has stuck. The last question is a calculation you have not seen. What is the typical radius of an atom, in metres? About one times ten to the minus ten metres, which is nought point one nanometres. Now the pair: where is an atom's mass, and what is most of its volume? The mass is almost all in the nucleus. The volume is almost all empty space. Last, a new metal. A gold wire is nought point one millimetres wide. A gold atom has a radius of one point four times ten to the minus ten metres. How many gold atoms fit side by side across that wire? About three hundred and sixty thousand. Convert first, then double, then divide. Nought point one millimetres is one times ten to the minus four metres. The diameter is two point eight times ten to the minus ten metres. Dividing gives about three point six times ten to the five - just like the magnesium ribbon at the start.

If you could now fit atoms across any width without a prompt, converting and doubling first, that's in the bag, so give it a thumbs up. Still wobbly on the powers of ten? Save it; three questions in, the working starts to feel normal.

Next in the chapter: Atomic number, mass number and isotopes.

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