So, how thick is gold leaf?

Very thin, obviously, but it is surprisingly difficult to find out exactly. So how about going back to basics and working it out. The place to start is with the manufactures and distributors, who have an interest in being precise about such a delicate and valuable material. Gold leaf is sold in books of 25 sheets, and usually each sheet is 3 3/8 inches square. The manufactures, quite sensibly, use the weight of the gold to define the quality of their product. The standard being how much gold for a thousand sheets.

For example the German Monarch company produces a book of pure gold leaf, 24kt, and 19 grams per 1000 leaves. Pure gold leaf isn't as common as you might think, Monarch make another twenty varieties of gold leaf, from 23 3/4kt, to 9kt. Alloying with copper makes the leaf a darker and redder colour, and with silver, whiter. The Monarch range has descriptive names; Rosenoble, Red Gold, French Pale, Moon Gold, Lemon. And Edible Gold; owing to possible amounts of copper, not all gold leaf is food safe.

So a thousand leaves of 3 3/8... each leaf is 85.725mm each side and has an area of 7348.7 square millimetres, so a thousand of them gives an area of 7,348,775 square millimetres. Next to find the volume of this large thin sheet of gold, we know the weight of it, 19 grams, and as the density of gold is 19.32 grams per cubic centimetre, (or 0.01932 grams per cubic millimetre) our volume is 983.4 cubic millimetres. As volume is area times thickness, division by the area gives the thickness of the gold leaf as, 0.000134 mm. This is more usually expressed in microns, which are a thousandth of a millimetre.

So the thickness of this variety of gold leaf is 0.134 microns. Which is very thin, too thin to see. Literally. It is thinner than the wavelength of light.

Monarch makes gold leaf in many weights, but lets turn to the long established French brand Dauvet and one of it's coloured gold leaves, 'Rouge', it's 23kt, which means that one part in 24 isn't gold, certainly copper in this case. And 14 grams per thousand sheets, but that's just the gold, so the total weight is 14.6 grams. This time it's the French metric standard of 84 mm square, so the total area is 7,056,000 square millimetres. Having one twenty-fourth copper drops the density to 18.88, so volume is 773 cubic millimetres. Divided by area gives 0.1096 microns.

To reach the thickness of a millimetre, 9,123 sheets would have laid on top of each other.

That was the easy bit, now to work out how many atoms thick it is. Imagine we have a leaf of the pure gold, the 0.134 micron one, and we manage to cut a tiny cube, with sides the thickness of the leaf. This is impossible of course, as the cube would be the size of a virus. And the volume of this tiny cube; 2.39 times ten to the power of minus twelve, which is another way of saying there are twelve zeros between the decimal point and the 2.39. So a small number then. Multiply by the density to find out that our tiny cube weighs 4.63 times ten to the power of minus fourteen grams.

Time for a bit of chemistry, back in the day chemists worked out that a certain amount of a substance would react with another amount of another substance. For example to make gold iodide, AuI, you could combine 196.967 grams of gold with 126.904 grams of iodine. They soon worked out (two hundred years ago) that these two amounts contained the same number of atoms, they are now called the atomic weights of these elements. And a lot later the actual number of atoms in these quantities was determined, and it is 6.022 times ten to the power of 23. Yes it's a number that has 23 zeros... The amount of a substance that has that amount of atoms is called a mole, we need to work how many moles are in are tiny cube, so divide the weight of our cube by the atomic weight of gold, 196.967, which is 2.35 times ten to the power of minus 16. We know how many atoms are in a mole, so now it's time to multiply an enormously big number by a ridiculously small number.

141,565,233, the number of atoms in that tiny cube, more or less. The atoms in gold are arraigned in a cubic structure, which is handy for us, because what we need to do now is to find the cube root of the above number to find the number of atoms on each side of the cube, which is how many atoms thick our gold leaf is.

521. That's it. That many atoms. The same calculation done on the thinner French gold leaf gives the result of 427 atoms. And it's hard to imagine how small an atom is; and to imagine that piece of gold leaf on your finger is only a few hundred atoms thick.

There is another way to find the number of atoms, slightly less satisfying though as it involves looking up the size of gold atoms and dividing into the thickness of the leaf. Atoms are fuzzy things, and there seem to be many definitions of their size. 'Empirically measured radii', sounds as good as any, the figure being 135 pm. That's picometres, which are of course, very, very small, a millionth of a micron in fact. Multiply by two to get the diameter of the atom, 270 pm.

The 19 gram gold leaf, 133,823 pm thick, divided by 270 pm; 495.6 atoms.

And the 14 gram one; 406 atoms.

Amazed how close these figures are to the calculated ones above.