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How Many Atoms Fit on the Head of a Pin?

After all this time, we still don’t know exactly what stuff is made from or precisely how gravity works. This whole debate about “settled science?” Ha! We know things are made from molecules, and molecules are made from atoms. The next level is pretty “settled,” too; atoms are made from protons, electrons, and neutrons. But what are they made from? Scraggly-haired physicists talk about quarks and the gluons holding them together. The Standard Model says quarks are fundamental particles, not made of anything smaller. But science marches on, so who knows? Plenty of smart people are talking about subcomponents of quarks. Anyway, before migraines set in, just how big are atoms? And more importantly, how many atoms fit on the head of a pin?

Squishy Measurement Approximations

The head of a pin is easy to measure. Being solid, at least at the scale we see and touch, we can stick calipers across it and come up with a diameter somewhere in the neighborhood of a millimeter, depending on your particular tastes in pins.

Atoms, on the other hand, are more like measuring our solar system. There are no hard edges, nor do we have calipers small enough. The simple Hydrogen atom has a proton in the middle and an electron in orbit, so we need to measure the orbital diameter. To visualize the scale of the proton and electron, think of the center of a Hydrogen atom as a pea (the garden variety) and the orbital space as a large football stadium. Plop the pea on the 50-yard line, and the electron orbits around the upper deck. That’s what our Hydrogen atom looks like in itty-bitty scale. Even with its “solar system” measurement, a Hydrogen atom is just about .1 nanometers in diameter. That’s .1 billionths of a meter.

That’s just Hydrogen. Other atoms are of different sizes and with different weights. For example, an Oxygen atom has eight protons, eight electrons and eight neutrons, so it’s somewhat larger.

So, How Many Atoms Fit on the Head of a Pin?

We’ll use round numbers as this stuff gets hairy. Let’s assume a pinhead is 1 millimeter across. Doing the old geometry math, it should have a surface area of about 0.000000007853975 meters.

Now for the Hydrogen atom. Since it’s a “ball,” we have to slice it in half and measure the cut surface area to get an idea of how many can rest on the pinhead or else they’ll just roll off while we’re counting. That “half” is about 0.000000000000000000007853975 meters. If you do the long division, carry the one, and all that, we’re estimating 1,000,000,000,000 will fit on the pinhead. What a handy number to memorize, huh? Like your old math teacher said, “You’ll use that one day!”

How Many Atoms Do You Have?

We’ve figured out atoms vary in size depending on their type, so we have to consider what type of atoms make up the average human body. Most people consist almost entirely of Hydrogen, Oxygen, and Carbon, although I maintain a higher percentage of Reese’s Peanut Butter Cups atoms than average folk. Those first three atom types represent about 99 percent of our mass. But I digress.

Given the balance of these three elements, we can calculate the number of atoms we’ve got hanging around our midsection and the rest as follows. We’re about 2/3 Hydrogen, 1/4 Oxygen and 1/10 Carbon. I’ll spare you the math of figuring out the relative size of each of those percentages and offer up the answer directly.

7,000,000,000,000,000,000,000,000,000

If I’m counting all those 27 zeroes correctly, you can also say that as seven billion, billion, billion. If each atom represented one dollar, that’s almost as much money as politicians have bamboozled in the past 250 years.

Ever wonder about...

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