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How Big Is a Proton Anyway? This Decade-Long Debate May Have Just Been Solved

The correct proton size

The subatomic realm can be a confusing place, but you would think that we’ve studied atoms long enough to at least understand their most basic properties. Things like how big a proton is. And based on several experiments, scientists had thought they had a pretty good handle on it too. Until an ingenious 2010 experiment came back with a very different number for the size of a proton, calling what we thought we knew into question. Now, after almost a decade of reexamination, scientists think they’ve solved what’s known as the proton radius puzzle. Before we really dive into the details of the latest findings, I have to set the record straight on atoms. A lot of the things you were taught about them in grade school are oversimplified.
Scientists thought they knew the approximate size of a proton until a 2010 experiment came back with a very different number, creating the proton-radius puzzle.
The correct proton size
The proton itself is not a smooth billiard-ball, but more like a cloud of quarks held together by gluons. The quarks a proton is made up of giving it its positive charge, and the threshold of that positive charge can be thought of as the proton’s size. For decades, scientists have used two approaches to find the radius of a proton’s boundary. One method involves firing electrons at atoms, often hydrogen, which in its simplest form is a single proton in the nucleus with one orbiting electron. Based on how the electrons bounce off the nucleus, scientists can determine where the proton’s positive charge starts to fade. The other method measures how much energy it takes to excite an atom’s electron from one state to the next, and again, hydrogen is often the atom of choice.

In its lower energy state, hydrogen’s electron doesn’t just orbit around the proton but actually spends some time inside the proton. I told you your grade school ideas about atoms are all wrong. Anyway, because electrons have a negative charge, when one is inside the proton, the proton’s positive charge pulls it in opposite directions, reducing the electrical attraction between them. This lowers the energy needed to excite the electron to its next energy level. So the thinking goes that the bigger the proton, the more time an electron will spend inside it, and the weaker the atom will be bound together. By measuring just how much energy it takes for an electron inside a proton to hop to the next energy state, scientists can deduce the size of the proton.

Over the years, these two methods came more or less to the agreement that the proton’s radius was about 0.8768 femtometers, and all was well until about a decade ago when someone had the bright idea of artificially swapping out hydrogen’s electron with a muon. Muons are like electrons in every way, except they’re 207 times more massive. That added weight means that the moon spends more time inside the proton, making its switch to a higher energy state millions of times more sensitive to the proton’s size than the electron is in regular hydrogen. By measuring the proton using muonic hydrogen, they came back with a result 4% smaller than the previously accepted size, a difference that’s not insignificant. But the sensitivity of the method was too much to ignore.

So scientists had a problem. Were their previous measurements off? Or was this a hint at something more tantalizing? Maybe muons and protons interacted in ways that made the protons shrink, or muons somehow behaved differently than electrons. Maybe the discrepancy would reveal some heretofore unknown physics or even new elementary particles. Which brings us to September of 2019, when scientists at York University in Toronto announced the results of an experiment that used regular, electronic hydrogen-like most experiments before.

Like those past experiments, they excited the electron into a higher energy state. Only this time, the scientists used a high-precision measuring technique called frequency-offset separated oscillatory fields, which they modified for this experiment. Their results showed the proton’s radius was right around 0.833 femtometers, consistent with the muonic hydrogen experiment from 2010. So the results are bittersweet. It looks like the discrepancy in the proton’s size was just down to measurement error, and not a hint of some undiscovered realm of particle physics. But at least the proton’s size is finally settled.

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