The mass of neutrons versus protons? The existence of matter?

January 16, 2008 5:33 PM

Why do neutrons have more mass than protons?

My fascinating, if frustrating, chemistry professor posed this question to the class. "Have you ever asked yourself that? You have to ask these questions. There is a reason for everything, and those reasons are important. The fact that neutrons have more mass than protons is vital to the very existence of matter."

But then he didn't explain, and I'm dying to know the answer, and why the answer is so significant. I've tried to figure it out on my own but so far, no luck.

posted by bookish to science & nature (30 comments total)

It's an interesting thing to say that "there is a reason for everything," because in biology it is generally understood that there really is a reason for everything, because natural selection causes to wash away useless stuff. In matter itself, though?
posted by rxrfrx at 5:40 PM on January 16, 2008

There seems to be an answer here.
posted by suedehead at 5:46 PM on January 16, 2008

A quick Google search found this quote from this site:

Heavyweight neutrons are required for long-lived stars. If the mass of a neutron were less than that of a proton plus an electron, then the Big Bang would have produced a profusion of very heavy elements. There would be no lack of chemicals in that alternate universe. However, all hydrogen would be in a form that would burn rapidly in stars. Therefore all stars would be short-lived. The fact that neutrons are heavier depends on details of subnuclear physics. If they were 0.1 % lighter than they are, there would be no long-lived stars in our universe.
posted by burnmp3s at 5:48 PM on January 16, 2008

I think your chemistry professor has his causality backwards.

No one knows why protons and neutrons have the mass ratio they have, but the universe we live in is configured the way it is because of that mass ratio.

A better way to phrase the question is "what are the consequences of protons and neutrons having a mass ratio other than 1:1?"
posted by b1tr0t at 5:52 PM on January 16, 2008 [2 favorites]

Can you ask him?
posted by Count Ziggurat at 5:58 PM on January 16, 2008

My old physics teacher: "Neutrons are great value. They weigh more, and there's no charge!"

A stupid joke, but I remember it, and the fact that neutrons weigh more and have no charge, so I suppose it worked. Then I studied medieval history at university.
posted by WPW at 6:01 PM on January 16, 2008 [2 favorites]

@b1tr0t: Your question seems to me to be quite different from the professor's question. He isn't asking, what if? He's asking, why? Or, as I read it, what are the natural laws whose governance results in neutrons being massier than protons? I doubt he has an answer in mind; I don't think we know this. I think he just is trying to instill the spirit of inquiry.
posted by bricoleur at 6:18 PM on January 16, 2008

The reason is that a down quark weighs more than an up quark. A proton is two up quarks and a down quark; a neutron is one up quark and two down quarks.

But of course, in a sense that just begs the question, because then you could ask, OK, why is a down quark heavier than an up quark? No one knows the answer to that, and it may be that the only answer we'll ever have is, "That's just the way it is."

And no one knows why both protons and neutrons in iron atoms weigh less than they do in uranium atoms, and in helium atoms.
posted by Steven C. Den Beste at 7:16 PM on January 16, 2008 [2 favorites]

Why, if the mass of the electron were different, the pyramids could not have been built. The ratio between the mass of the neutron and the number of ways that article is crazy are left to the reader.
posted by jepler at 7:36 PM on January 16, 2008

I think SCDB's answer is the closest you're going to get. The reason the neutron is heavier is because it's comprised of heavier, even closer-to-fundamental particles. (Whether quarks are actual nothing-possibly-smaller fundamental particles is a matter of dispute.) But *why* are down quarks heavier than up quarks? I don't think there's any answer to that.

This same question could be posed about any fundamental physical characteristic of space. Why is the speed of light what it is? Why is pi 3.14159..., instead of, say, 3.0? Why is the 'strong interaction' stronger than the 'weak interaction', instead of the other way around?

I'm not sure physics is really in a position to answer any of those questions. At best, physics can explain what would happen if one of those values wasn't what it is -- and generally the results are bad news. Hence you end up with fairly glib responses like the anthropic principle, which sort of dodge the why by simply stating that it must.
posted by Kadin2048 at 8:05 PM on January 16, 2008

without reading anyone else's reply, (yet) I always thought it was because a neutron was a proton plus an electron, or more accurately, the subatomic particles that make up each of them.
posted by skybolt at 8:30 PM on January 16, 2008

While we're on the subject, and maybe this should just be a new post - I've been wondering lately about the arrangement of protons and neutrons within a nucleus. I've heard it said the reason for neutrons in a nucleus is to keep the protons far enough apart so the tendency of the protons to repel each other (strong force?) is cancelled out by the tendency of the nucleus to hold together (or is THIS one the strong force?). More protons and you need an ever increasing number of neutrons to keep things peaceful. This is why so many large atoms need a proportionately HUGE number of neutrons. For example, uranium has 92 or so protons, but 137 or more neutrons. So, here's my question: if we arrange the neutrons in a regular, say, crystalline formation, and THEN put the protons in the intervening space, why then can we create huge, but stable, NPN-radioactive elements much larger than 107 on the periodic scale?

I'm not sure what use these heavy elements would be, or how to manipulate the neutrons, bit the idea seems promising anyway.
posted by skybolt at 8:42 PM on January 16, 2008

Skybold, when a neutron decays, it produces a proton, an electron, and a neutrino. But that doesn't mean it's what a neutron is made of before it decays. A high energy gamma ray can spontaneously convert into an electron and a positron, but a photon isn't made of electrons and positrons.

In a sense, you've got it backwards. Because a neutron is heavier, it becomes possible for it to break down in that way. Were it not heavier, the conservation laws would prevent it. But what's actually happening is that a down quark is being converted into an up quark, an electron, and a neutrino, which is only possible because a down quark masses more than an up quark + electron + neutrino. Because a down quark changes to an up quark, that means the neutron becomes a proton.

As to what holds a nucleus together, it's the strong force. The strong force is actually a force that causes quarks to attract to one another and its primary function in the universe is holding the quarks inside of protons and neutrons. But quarks in neighboring hadrons also attract one another.

The mediating particle for the strong force is called a "gluon", and because it has nonzero mass, it means that the range of the strong force is finite. In fact, the gluon is quite massive so the range is extremely short.

Protons are also electrically charged, and since they're all positively charged, they try to repel. But in a He 4 nucleus, the attractive strong force of four hadrons is greater than the repulsive force of two protons, so the nucleus holds together.

The mediating particle for the electric force is the photon, and since photons have no mass the range of the electric force is infinite.

As nuclei get larger, the radius of the nucleus exceeds the range of the strong force, so it takes a greater and greater ratio of neutrons to protons to hold the nucleus together. Protons on opposite edges of the nucleus no longer attract one another via strong force, but they still repel due to the electric force.

In really large atoms, depending on the proton/neutron ratio, the hold is still a bit tenuous. Shifting of the hadrons around can cause the nucleus to pull apart due to electric repulsion, which is known as "fission". Or just a tiny piece can fly away, alpha radiation. So if a large atom has too low a ratio of neutrons, you get fission or alpha decay with a shorter and shorter half life as the ratio of neutrons is lower and lower. In some extreme cases you're talking picoseconds or even less.

On the other hand, if the ratio of neutrons is too great, the chance of neutron decay rises drastically because of the weak force. Beta decay is how a neutron turns into a proton; the ejected electron is the beta ray. (I have tried several times to figure out how the weak force works, and I have never succeeded, so while it does what I just said, I don't have the slightest idea why.)

So your infinite matrix of neutrons wouldn't be stable. Before you could finish creating it and start plugging in your protons, a lot of those neutrons would spontaneously decay into protons.

I think that above a certain size, there's no longer any sweet spot between the tendency of the electric force to cause fission or alpha decay and the tendency of the weak force to cause neutron decay, which is why Bismuth 209 is the heaviest nucleus that's stable. For anything heavier than that, you're either going to get fission, alpha decay, or beta decay, either blitz fast, somewhat fast, somewhat slow, or achingly slow (e.g. thorium 232).
posted by Steven C. Den Beste at 9:51 PM on January 16, 2008

... the radius of the nucleus exceeds the range of the strong force...

That should have been "the diameter of the nucleus" etc.
posted by Steven C. Den Beste at 9:53 PM on January 16, 2008

Part of what I have never understood about that is why it is that there isn't a clean line for some element's isotopes, above which everything beta decays and below which you get fission or alpha decay. That isn't how it works. Thorium, for instance:

Th 228 alpha
Th 229 alpha
Th 230 alpha
Th 231 beta
Th 232 alpha
Th 234 beta

Probably that would be clear if I really did understand how the weak force worked. Anyone care to try to explain that part to me?
posted by Steven C. Den Beste at 9:59 PM on January 16, 2008

Part of what I have never understood about that is why it is that there isn't a clean line for some element's isotopes, above which everything beta decays and below which you get fission or alpha decay.

Because nobody really understands atom stability?
posted by vacapinta at 11:32 PM on January 16, 2008 [1 favorite]

Strikes me that the anthropic principle applies, as burnmp3 and b1tr0t suggest. Neutrons have more mass than protons. If they didn't, then we'd be talking about a universe whose physical laws were totally different from our own. Most likely different enough so as to preclude our existing to make the observation or ask the question.
posted by mumkin at 1:10 AM on January 17, 2008

Nuclear physics is difficult, as vacapinta said. There's lots of quantum mechanics involved - for example it'd be unwise to think of alpha decay as some bit of the nucleus getting too far from the rest randomly, as there's quantum tunnelling going on. There's all sorts going on to hold the nucleus together, and it's not sitting in a rigorous structure either, and calculations of the actual physics are ridiculously hard as you have large numbers of strongly interacting particles, and the interactions are hard enough to calculate as it is.
Broadly speaking though, the lattice idea probably doesn't work simply because the lattice isn't actually a stable way for the baryons to sit together. It's much more a quantum mechanical mishmash than the atoms in a crystal for example.
Lastly I'd also caution against thinking that SCDB is absolutely right to say that it's because a down quark is heavier. A proton and neutron differ by about 1.3 MeV. Look at the mass estimates on the quark wikipedia page and while the down is heavier, the upper end of the scale allows for it to be 4 or more MeV heavier than the up. So how could you put in 4 MeV more mass in the quark and only end up 1.3 MeV more massive in the resulting neutron? And why do three ~4 MeV quarks add up to a 938 MeV mass baryon? It's because the binding energy between the quarks is absolutely immense, and isn't something you can forget about. There must be binding energy differences between a proton and neutron, otherwise the top end of the down quark mass estimate range would only be 1.3 MeV above the up's, not 4.
posted by edd at 2:33 AM on January 17, 2008

OK, I suspect that what your professor is really trying to get at is that if neutrons were lighter than protons, protons would decay into a positron, neutron and neutrino, and neutrons would be stable. As it is protons are stable, and neutrons decay into an electron, proton and antineutrino in a matter of minutes, unless bound up in a nucleus.

If protons decayed like neutrons did then there might be a slight hydrogen shortage. As it is, if protons decay at all then they've a lifetime that's about a hundred trillion trillion times the age of the universe, and there's plenty of hydrogen to go round.
posted by edd at 3:38 AM on January 17, 2008

SCDB, I thought the reason the Uranium nucleus weighed more (per proton/neutron) than an Iron nucleus is because there is more energy (per proton/neutron) holding the U nucleus together, and E=mc²?
posted by Xoder at 6:29 AM on January 17, 2008

SCDB said "The mediating particle for the strong force is called a "gluon", and because it has nonzero mass, it means that the range of the strong force is finite. In fact, the gluon is quite massive so the range is extremely short."

Also, gluons are massless.
posted by vacapinta at 7:41 AM on January 17, 2008

This is a question for a priest or a philospher, not a physicist. It's one of a kind of question that isn't accessible to physics. Physics can answer questions like "what is a neutron?" and "how does it behave?", but it can't answer "why?" questions.

Your question is better recast as the closely related "what implications does a heavy neutron have for cosmology?", but that's still not your teacher's question "why?".

Science is descriptivist, not presciptivist. If more conservatives understood that, we wouldn't have book bannings in Kansas.
posted by bonehead at 7:55 AM on January 17, 2008

Vacapinta, if the gluon was massless, wouldn't the strong force have infinite range?
posted by Steven C. Den Beste at 8:00 AM on January 17, 2008

The strong force is limited in range because of confinement - which is itself a result of the gluon interacting with other gluons due to them having colour charge.

Since you never see exposed colour due to confinement, how would you know if the strong force has infinite range or not?
posted by edd at 8:02 AM on January 17, 2008

The correct answer for "why is this so?" is not that physics "can't answer 'why?' questions." It's that nobody knows. Just as nobody knew "why" the binding energy of electrons in Hydrogen is 13.6 eV before Schroedinger came along. It certainly was not that this value could not be predicted by a fundamental theory.

The mediating particle for the strong force is called a "gluon", and because it has nonzero mass, it means that the range of the strong force is finite. In fact, the gluon is quite massive so the range is extremely short.

While this is the case for the W and Z bosons of the weak force, the gluon is exactly massless. The strong force is "short range" because of confinement.

The reason is that a down quark weighs more than an up quark. A proton is two up quarks and a down quark; a neutron is one up quark and two down quarks.

This is oversimplifying, as edd pointed out. Here's another way to see why: We know the masses of both the neutron and the proton, so if we assume that their masses were just the sum of their parts, we can find both the up and down quark mass. We'll get 312.3 MeV and 313.6 MeV for the up and down, respectively.

Now we can ask about the mass of a pi+ meson, made of an up and an anti-down. The anti-down must have the same mass as the down (by CPT invariance), so we'd expect the pi meson to have a mass of around 626 MeV. In fact, it is much less: 139.6 MeV [pdf]. The origin of nucleon mass is a lot more interesting and complicated than just shifting the problem over to the quarks. Indeed, as you start to look inside a proton, you don't just see 3 quarks floating around. You find a sea of quarks, anti-quarks, and gluons moving around, and the fraction of each that you find changes the closer and closer you look. (I can't seem to find a good, accessible link about parton evolution, but it's mentioned in this Wikipedia entry.)

Furthermore, you not only get downs turning into ups such as in the reaction d -> u + e + anti-nu, (as in neutron decay), you can also have ups going to downs, as in the fundamental reaction involved in solar fusion: p + p -> H2 + (e+) + nu, where e+ is a positron. So, even if neutrons were lighter than protons, we'd still get solar fusion and all that, but we'd be burning neutrons instead of protons (because their would be more neutrons around, as described above and immediately below).

A very important difference involves what edd noted in his second comment. The proton would decay into a neutron plus a positron--and the positron may then go off and annihilate with an electron to form a photon. "Hydrogen," from a chemist's perspective, would now be deuterium--a nucleus containing 1 neutron and 1 proton--with an electron orbiting it, because a neutron isn't going to attract an electron, our lone, stable neutrons are chemically inert.

Most of the deuterium that's around today is from shortly after the big bang -- it didn't come from stars, because stars fuse it into helium nuclei quickly. Cosmically, there's something like a few deuterium nuclei for every 100,000 hydrogen nuclei. On Earth, it's a bit higher--a little more than 1 per every 10,000 hydrogen atoms in the oceans. This would be all of the chemically active hydrogen. Assuming everything else went the same and we still got a planet like Earth to appear, instead of vast oceans, we'd have a bunch of free neutron gas floating around in the atmosphere (with Oxygen and Nitrogen, and then perhaps some puddles of heavy water here and there.
posted by dsword at 8:05 AM on January 17, 2008 [1 favorite]

Excellent points dsword. But would neutrons be sufficiently penetrating that the neutron gas wouldn't sit around in the atmosphere but fall through the ground or undergo reactions with other nuclei? I don't know enough about how slow moving neutrons behave, but I can't see them just acting like a gas made of atoms.
posted by edd at 8:16 AM on January 17, 2008

Actually, I would expect the neutrons to tend to float off into space, much as molecular hydrogen does. But you're right, they're still not charged, so there's still no repulsive force keeping them from running into other nuclei (in the ground or atmosphere). I also don't know enough to answer that, but I think you're probably right that they'd interact quickly, so that we'd have a very different zoo of chemicals/isotopes on Earth. I'm happy to sweep all that under the, "assuming everything else went the same" rug.

Also, I guess the oceans would be about 10-20 inches deep. A big puddle!
posted by dsword at 8:36 AM on January 17, 2008

On second thought, maybe they would just fall. My brain needs food, I think. Ugh.
posted by dsword at 9:08 AM on January 17, 2008

OK, so we can't BUILD a nucleus of crystallyine nuegtoms, as the neutrons would decay. But, because there are examples of non-decaying neutrons (such as the high gravity environment of a neutron star), let's assume no issues with creating our large (but less than infinite) nucleus. Can we have a stable, large lattice of neutrons that holds protons properly due to the gluonic force?

And what happens if we start adding a huge number of protons to a neutron star?
posted by skybolt at 11:31 AM on January 17, 2008

To your second question, they come with electrons, which they're going to be able to capture. They're not going to act fundamentally differently to the nucleons already there.
posted by edd at 3:42 AM on January 18, 2008