Atoms are the building blocks of matter. Pretty much everything around us is made of atoms — starts, the earth, air, clouds, your body, your computer, a tennis ball.

You can think of an atom as a tiny tiny ball. That’s not exactly accurate, but it is a fine picture when thinking about certain qualities of the atom, like its size.

How small is an atom?

A single atom it so small, that it pushes the limits of our imagination to visualize. But here’s a way to picture it. You will need a tennis ball. If you don’t have a tennis ball, try a baseball. A golf ball, an apple or an orange will do. Or you can use this picture:

Imagine picking an atom out of the air. Pick an oxygen molecule, which is two oxygen atoms joined together. Pull it apart into a single oxygen atom and place that atom gently on the top of your tennis ball. There. What does that look like? Well, we know that atom it much too small to see. And that’s an understatement.

Here’s how small it is. Imagine growing the tennis ball. Grow it until it’s the size of the entire earth. At the same time, your atom on the ball is growing. When the tennis ball has reached the size of the earth, your atom will have grown to be the size of — a tennis ball.

The earth is pretty big. Think about how far a drive it is to the ocean, and once you get there how big the ocean itself is. Think of how long it might take to fly to Honolulu or Sydney or London. Think of how much rock and magma there is deep under your feet.

Put your tennis ball down on the ground. Look at it and compare it to the size of the earth. That tennis ball is one atom.

Using a tennis ball as reference, the earth is as big as an atom is tiny.

The math

The diameter of a ball is its width.

let a = diameter of an atom

b = diameter of a tennis ball = 0.065 meters

e = diameter of the earth = 12,700,000 meters (7,900 miles)

a / b = b / e

Our model claims that these two ratios, atom divided by ball, and ball divided by earth, are equal.

solving for a, we get diameter of an atom = a = b^2 / e = 3.3 x10^-10 meters = 3.3 Angstroms = 0.00000000033 meters

Notes

The size of the earth: http://solarsystem.nasa.gov/planets/profile.cfm?Object=Earth

I measured the diameter of a tennis ball with a metric ruler; 65 mm or 0.065 meters.

Determining a good measurement for the “diameter of an atom” is a slightly hazy task. We usually talk about an atomic radius, where a radius is half of a diameter. For our tennis ball model, we are looking for an atomic radius of roughly 1.6 Angstroms. One measurement is the van der Waals radius. For the first 10 elements, the range of van der Waals radii is about 1.2 to 1.8 Angstroms.

Here is a table of the van der Waals radii for the elements in picometers: http://www.periodictable.com/Properties/A/VanDerWaalsRadius.v.html. A picometer is one trillionth of a meter. An Angstrom is 100 picometers.