How Big Is a Proton?

The new measurement puts the proton's radius to around 0.833 femtometers, which is 4 percent less than the previously accepted figure.

Complexity is what gives the subatomic realm its specialty. But given the years of dedication on studying and learning about atoms, it’s about time we know some of their most basic properties at the very least. So how big is a proton?

Based on a large number of experiments, researchers thought they had the size of the proton figured out. But that changed in 2010, when an experiment came back with a value 4 percent less than expected. This might not seem like much, but to scientific community this shrinkage in value is a huge deal. Now after years of re-evaluation, physicists have finally solved the conundrum known as the proton-radius puzzle.

The new measurement puts the size of the proton to around 0.833 femtometers, against the previously accepted figure of 0.842 femtometers.

Contrary to the models of atoms you were taught about in high school, protons bear no sort of resemblance with smooth balls of spheres. In fact, the proton does not have a clearly defined surface; so it’s more like a cloud – a cloud of quarks bound together by gluons. The quarks give proton its positive charge, and it’s size is defined by a threshold of that positive charge.

Just for the sake of reference, we aren’t able to observe quarks and gluons just yet, but theoretical predictions based on their existence have been confirmed experimentally.

This turmoil of quarks and gluons is what scientists imagine a proton is made of. [CERN]

So to measure its size, the electron has to be pushed towards the edge of the cloud. The action can be achieved using one of two approaches.   

The first method involves firing electrons at the nuclei of hydrogen atoms. Based on how the electrons ricochet off the nucleus, scientists can determine where the positive charge of the proton start to fade.

The other is based on how much energy an atom takes to jump from one energy level to the next. When a hydrogen atom is in its lower energy state, the electron not only orbits around the proton, but rather stays inside it. And since electron possesses negative charge, when it’s within the confinement of proton, the positive charge of the proton pulls it in opposite directions, reducing the electrical attraction between them. This is turn reduces the energy the electron needs to go to its next energy level.

So the bigger the size, the more time an electron spends inside. By estimating the amount of energy it takes for an electron inside a proton to get excited, the size of the proton can be measured.

This style of measurement based on shift in electron energies is known as the Lamb Shift, named after Willis Lamb, an American Physicist. All these years, experimentations hinge on this method came more or less to the agreement that the proton’s radius was about 0.8768 femtometers. However, this changed when new study in 2010 introduced the idea of swapping an electron with a muon, a hefty cousin of an electron.

Muons are 207 times the weight of electrons – and more weight means more time spent dipping inside the proton. And the upshot? The added weight make the switch to a higher energy state millions of times more sensitive to the size of the proton than when the electron is in regular hydrogen. In other words, the mouns add more precision to the measurement of proton’s radius.

The experiment using muonic hydrogen suggested 4 percent reduction in the proton’s radius compared to official figure. Not much, but the sensitivity of the methods was too great to pass over.

Then again in 2019, researchers went about performing an experiment using the regular electron, but this time, they used a cutting-edge technique called frequency-offset separated oscillatory fields (FOSOF). The results of the experiment corresponded to that of the muonic hydrogen experiment of 2010, that is – the proton’s radius was right around 0.833 femtometers.

Were the previous measurements flawed? Would the disparity open up new unexplored realm of physics, or even introduce new elementary particles? We don’t know yet. But at least the proton’s size is finally settled.

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