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How much of an atom is empty space?

Very nearly all of it. Let's take a look at an atom of hydrogen to see how empty it really is. Of course, this diagram isn't drawn to scale...

A hydrogen atom.

A hydrogen atom is made from a single proton that's circled by a single electron. How big is a hydrogen atom? The radius of a hydrogen atom is known as the Bohr Radius, which is equal to .529 × 10-10 meters. That means that a hydrogen atom has a volume of about 6.2 × 10-31 cubic meters.

How big is the proton at the center of a hydrogen atom? Recent studies indicate that protons have a radius of about .84 × 10-15 meters, giving them a volume of about 2.5 × 10-45 cubic meters.

We need to do a little more math to find out how much of a hydrogen atom is empty space:

Percent Full = 100 × (Volume Filled / Total Volume)
Percent Full = 100 × (2.5 × 10-45 m3 / 6.2 × 10-31 m3)
Percent Full = 100 × (4 × 10-15)
Percent Full = 4 × 10-13 %
Percent Full = 0.0000000000004%

If 0.0000000000004% of a hydrogen atom is full, then the rest of it must be empty:

Percent Empty = 100% - Percent Full
Percent Empty = 100% - 0.0000000000004%
Percent Empty = 99.9999999999996%

A hydrogen atom is about 99.9999999999996% empty space. Put another way, if a hydrogen atom were the size of the earth, the proton at its center would be about 200 meters (600 feet) across. While I wouldn't want something that big landing on my head, it's tiny compared to the size of the earth.

Author:

Steve Gagnon, Science Education Specialist (Other answers by Steve Gagnon)

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