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91. An Amazing Number

In their calculations scientists often have to do with what they call constants, i.e., numerical values characterizing some quality or property. We wish to draw your attention to one of them.

It is called Avogadro’s number, after the famous Italian scientist who put this constant into use. Avogadro’s number is the number of atoms in a gram-atom of any element.

It will be recalled that a gram-atom is the number of grams of an element equal to its atomic weight. For example, a gram-atom of carbon is (roundly) 12 g, that of iron, 56 g, and of uranium, 238 g.

The number of atoms in each of the quantities named is exactly equal to Avogadro’s number.

Written on paper it can be represented approximately by a “one” followed by twenty-three naughts; more exactly, it is 6.025×1023.

That is how many atoms are contained in twelve grams of carbon, fifty-six grams of iron, or two hundred and thirty-eight grams of uranium.

Avogadro's number is so monstrously large that it is difficult even to imagine.

Still, let us try.

The human population of the globe is about three thousand million. Now suppose all the inhabitants of the Eaith decided to count up the number of atoms in a gram-atom of some element. Suppose each man worked eight hours daily and made one count each second.

How much time would it take for all the inhabitants of the Earth to count up all the 6.025×1023 atoms?

A very simple calculation, which you can easily do yourself, shows that it would take about 20 million years. Impressive, isn’t it?

The immensity of Avogadro’s number is evidence that the idea of the omnipresence of all the chemical elements has a sound footing. We can always detect at least a few atoms of any chemical element everywhere.

Avogadro’s number being so large, it is obvious that all attempts to obtain an absolutely pure substance containing no impurities at all would be futile. It is utterly impossible to catch a single atom of an impurity among 1023 atoms without introducing new impurities in the process.

Indeed, a gram of, say, iron, contains about 1022 atoms. If it contains only one per cent (10 milligrams) of copper atoms as the impurity, that still makes not less than 1020 atoms. Even if the impurity content is reduced to one ten-thousandth of a per cent, the number of atoms of the impurity per 1023 atoms of the principal substance remains 1016 atoms. If the impurity includes all the elements of the Periodic System, there will be an average of 1014, i.e. one hundred trillion atoms of each element.

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by Ian Ellis