How large is the broad side of a barn, anyway?

Of course you know the idiom “can’t hit the broad side of a barn” of someone who has poor aim. That’s from 1852.

But how large is the broad side of a barn, anyway? Would you be surprised to learn that scientists have actually worked that out? And why do I know this??

Some time ago, I was trying to find a way to remember my license plate that ends with the letters “FB”. I don’t like a particular social media site so I was googling for other things that use those letters and discovered that it is also a unit of measurement used in particle physics: fb means femtobarn. I immediately chose that as my mnemonic simply because of its nerdy obscurity.

What I want to share here is its ridiculous back story: what the hell is a femtobarn?!

Okay, stay with me, we’re going to dive into particle physics now:

In the 1940s, physicists working on the Manhattan Project used a particle accelerator in their research. As it turns out, “particle accelerator” is what it does, but not what it’s for: it accelerates particles all right, but it does that to smash those particles into a target so that the collision effects can be measured: that target is an atomic nucleus. It being during World War II, the physicists needed a secretive unit to describe the approximate cross-sectional area presented by the typical nucleus. It goes without saying that such a nucleus is ridiculously small in our everyday world, but for particle accelerators that is actually considered a large target.

Hitting … Large … Target … Hmmm …

The challenge of hitting a large target is nicely contained in that “broad side of a barn” idiom, so they adopted “barn” as their secret unit: a barn is defined as the size of a typical target: the approximate cross sectional area presented by the typical nucleus, or 10^-28 m².

I’m sure they all laughed nerdily about their clever idea.

Now, the prefix femto means one quadillionth. So a femtobarn is 10^-43 m², or one quadillionth of a barn. That is a tenth of a sextillionth of a sextillionth of a square meter!

And that’s a pretty good description of the size of my car, too…