Category Archives: Atomic Physics

Celebrating the Standard Model: Atoms, Quarks and the Strong Nuclear Force

For the general reader:

Last week I showed you, without any technicalities, how to recognize the elementary forces of nature in the pattern of particle masses and lifetimes. This week we’ll start seeing what we can extract just from the particles’ masses alone… and what we cannot. Today we’ll focus on quarks and the strong nuclear force.

A key factor in nature, which plays an enormous role in everyday life, is the mass of a typical atom. [Note: on this website, “mass” always means “rest mass”, which does not increase with a particle’s speed.] This in turn arises mainly from the masses of protons and neutrons, which are about equal, and tiny: about 0.00000000000000000000000000167 kg (or 0.00000000000000000000000000368 pounds). Since those numbers are crazy-small, physicists use a different measure; we say the mass is about 1 GeV/c2, and more precisely, 0.938 GeV/c2. In any case, it’s tiny on human scales, but it’s some definite quantity, the same for every proton in nature. Where does this mass come from; what natural processes determine it?

You may have heard the simplistic remark that “a proton is made of three quarks” (two up quarks and a down quark), which would suggest these quarks have mass of about 1/3 of a proton, or about 0.313 GeV/c2. But something’s clearly amiss. If you look at websites and other sources about particle physics, they all agree that up and down quark masses are less than 0.01 GeV/c2; these days they usually say the up quark has mass of 0.002 GeV/c2 and the down quark has 0.005 GeV/c2. So if the proton were simply made of three quarks, it would naively have a mass of less than 1% of its actual mass.

What’s going on? A first little clue is that different sources sometimes quote different numbers for the quark masses. There are six types of quarks; from smallest mass to largest, they are up, down, strange (u,d,s, the three light quarks), charm, bottom (c,b, the two somewhat heavy quarks) and top (t, the super-heavy quark.) [Their names, by the way, are historical accidents and don’t mean anything.] But some websites say the up quark mass is 0.003 instead of 0.002 GeV/c2, a 50% discrepancy; the bottom quark’s mass is variously listed as 4.1 GeV/c2, 4.5 GeV/c2, and so forth. This is in contrast to, say, the electron’s mass; you’ll never see websites that disagree about that.

The origin of all these discrepancies is that quarks (and anti-quarks and gluons) are affected by the strong nuclear force, unlike electrons, Higgs bosons, and all the other known elementary particles. The strong forces that quarks undergo make everything about them less clear and certain. Among numerous manifestations, the most dramatic is that quarks (and anti-quarks and gluons) are never observed in isolation. Instead they’re always found in special combinations, called “hadrons“. A proton is an example, but there are many more. And the strong nuclear force can have a big effect on their masses.

The Modern Proton and the Masses of Quarks

A proton, in fact, is not simply made from three quarks, the way a hydrogen atom is simply made from a proton and an electron. As I described in this article, it’s vastly more complex; it’s made from three quarks plus lots of gluons plus lots of pairs of other quarks and anti-quarks. So the simple intuition we get from atoms does not apply to hadrons like the proton.

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The Size of an Atom: How Scientists First Guessed It’s About Quantum Physics

Atoms are all about a tenth of a billionth of a meter wide (give or take a factor of 2). What determines an atom’s size? This was on the minds of scientists at the turn of the 20th century. The particle called the “electron” had been discovered, but the rest of an atom was a mystery. Today we’ll look at how scientists realized that quantum physics, an idea which was still very new, plays a central role. (They did this using one of their favorite strategies: “dimensional analysis”, which I described in a recent post.)

Since atoms are electrically neutral, the small and negatively charged electrons in an atom had to be accompanied by something with the same amount of positive charge — what we now call “the nucleus”. Among many imagined visions for what atoms might be like was the 1904 model of J.J. Thompson, in which he imagined the electrons are embedded within a positively-charged sphere the size of the whole atom.

But Thompson’s former student Ernest Rutherford gradually disproved this model in 1909-1911, through experiments that showed the nucleus is tens of thousands of times smaller (in radius) than an atom, despite having most of the atom’s mass.

Once you know that electrons and atomic nuclei are both tiny, there’s an obvious question: why is an atom so much larger than either one? Here’s the logical problem”

  • Negatively charged particles attract positively charged ones. If the nucleus is smaller than the atom, why don’t the electrons find themselves pulled inward, thus shrinking the atom down to the size of that nucleus?
  • Well, the Sun and planets are tiny compared to the solar system as a whole, and gravity is an attractive force. Why aren’t the planets pulled into the Sun? It’s because they’re moving, in orbit. So perhaps the electrons are in orbit around the nucleus, much as planets orbit a star?
  • This analogy doesn’t work. Unlike planets, electrons orbiting a nucleus would be expected to emit ample electromagnetic waves (i.e. light, both visible and invisible), and thereby lose so much energy that they’d spiral into the nucleus in a fraction of a second.

(These statements about the radiated waves from planets and electrons can be understood with very little work, using — you guessed it — dimensional analysis! Maybe I’ll show you that in the comments if I have time.)

So there’s a fundamental problem here.

  • The tiny nucleus, with most of the atom’s mass, must be sitting in the middle of the atom.
  • If the tiny electrons aren’t moving around, they’ll just fall straight into the nucleus.
  • If they are moving around, they’ll radiate light and quickly spiral into the nucleus.

Either way, this would lead us to expect

  • Rnucleus = # Ratom

where # is not too, too far from 1. (This is the most naive of all dimensional analysis arguments: two radii in the same physical system shouldn’t be that different.) This is in contradiction to experiment, which tells us that # is about 1/100,000! So it seems dimensional analysis has failed.

Or is it we who have failed? Are we missing something, which, once included, will restore our confidence in dimensional analysis?

We are missing quantum physics, and in particular Planck’s constant h. When we include h into our dimensional analysis, a new possible size appears in our equations, and this sets the size of an atom. Details below.

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