### Sidebar: properties of atoms

So, how do you measure the size and mass of individual atoms?

Chemists discovered long ago that various substances combine in exact relative amounts during chemical reactions. For example, 16 grams of Oxygen will combine with 2 grams of Hydrogen to form 18 grams of Water. From the vast catalog of reactions such as that, you can work out the relative masses of each type of atom. Carbon weighs 12 times as much as Hydrogen, and 0.75 times as much as Oxygen, and so on. So, if you can figure out the exact weight of any

Actually, all you really need to know is how many atoms there are in a particular lump of stuff. Then you can divide the mass of that lump by the number of atoms in it, and estimate the mass of a single atom. Nowadays, we have several tools for figuring out how many atoms there are in something (at least one of which is a Discovery in its own right), but in the 1800s your choices were more limited. I've heard that one way it was done was through kinetic theory, which I don't have the details of. Another was to look at the way air scatters light. Electromagnetic theory was well developed, and there was already an equation governing the scattering of light passing through air, which depended, among other things, on the number of atoms or molecules in a cubic centimeter of air. So, in 1890 Lorenz did the math, weighed a cubic centimeter of air, and came up with a pretty good estimate of the masses of all the different types of atoms.

With this information in hand, it becomes relatively easy to estimate the volume of an atom too: just divide the volume of a lump of stuff by the number of atoms in it, which in turn can be worked out by dividing the lump's mass by the mass of a single atom. Of course, atoms aren't perfectly packed together in solid matter, but it's within a factor of 2 or so, which is good enough for some purposes.

Quite a chain of logic, eh? Anyway, once these ballpark estimates were well known, lots of work got done on refining the numbers to the point at which we find them today.

Chemists discovered long ago that various substances combine in exact relative amounts during chemical reactions. For example, 16 grams of Oxygen will combine with 2 grams of Hydrogen to form 18 grams of Water. From the vast catalog of reactions such as that, you can work out the relative masses of each type of atom. Carbon weighs 12 times as much as Hydrogen, and 0.75 times as much as Oxygen, and so on. So, if you can figure out the exact weight of any

*one*type of atom, you've got them*all*.Actually, all you really need to know is how many atoms there are in a particular lump of stuff. Then you can divide the mass of that lump by the number of atoms in it, and estimate the mass of a single atom. Nowadays, we have several tools for figuring out how many atoms there are in something (at least one of which is a Discovery in its own right), but in the 1800s your choices were more limited. I've heard that one way it was done was through kinetic theory, which I don't have the details of. Another was to look at the way air scatters light. Electromagnetic theory was well developed, and there was already an equation governing the scattering of light passing through air, which depended, among other things, on the number of atoms or molecules in a cubic centimeter of air. So, in 1890 Lorenz did the math, weighed a cubic centimeter of air, and came up with a pretty good estimate of the masses of all the different types of atoms.

With this information in hand, it becomes relatively easy to estimate the volume of an atom too: just divide the volume of a lump of stuff by the number of atoms in it, which in turn can be worked out by dividing the lump's mass by the mass of a single atom. Of course, atoms aren't perfectly packed together in solid matter, but it's within a factor of 2 or so, which is good enough for some purposes.

Quite a chain of logic, eh? Anyway, once these ballpark estimates were well known, lots of work got done on refining the numbers to the point at which we find them today.

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