According to the Wikipedia article on neutrons ( http://en.wikipedia.org/wiki/Neutron ) the following decay scenarios are possible (for the sake of simplicity I am ignoring the neutrinos; perhaps I shouldn’t!):
neutron → electron + proton
proton → positron + neutron
I.e. a neutron can emit an electron to become a proton, and a proton can emit a positron to become a neutron.
Two questions occur to me:
A proton is less massive than a neutron. How can it become a neutron by losing the mass of a positron?
The above scenario suggests a perpetual energy machine: a neutron becomes a proton, which then becomes a neutron, and so on ad infinitum, and if you can keep the electrons and positrons generated in the process, you can mutually annihilate them to produce mass and energy from nothing.
Clearly I am missing something fundamental here. Over to our resident physics experts…
In essence, by adding sufficient energy to make up the mass deficit. Remember E = mc²? On the ordinary macroscopic scale, it’s convenient to talk of mass and energy as distinct properties, and macroscopic physics problems can usually be separated into their mass conservation, their energy conservation and their momentum conservation aspects, basically because mass/energy conversion effects are normally negligible on the macroscopic scale. On the atomic scale, this is no longer true, and we must conserve (relativistic) momentum and mass-energy (rather than mass and energy separately). In the neutron/proton case in question, neutrons bound in atoms in certain isotopes can decay in so-called beta decay events, emitting an electron and capturing an additional proton in the nucleus. In other atoms, the neutrons are stable because the nucleus’s binding energy keeps them tightly bound. (It’s a bit more complicated than that but close enough.) Free neutrons, on the other hand, decay quite readily with a surplus of energy. The neutrinos balance both the mass-energy account and the momentum account. In contrast, protons are rock-solid, stable and extremely dependable customers. You have to smash them at very high energies into assorted targets in a particle accelerator to get them to do their positron thing.
No, see the answer to your first question. You’ll have to keep adding at least as much energy to keep making positrons as you can theoretically recover from the mutual electron-positron annihilations. The laws of thermodynamics never sleep.
I am aware of the notion of mass-energy, but it is still not clear to me where the extra mass-energy comes from. When a proton emits a positron, isn’t it LOSING mass-energy? Where does it pick up the mass-energy to become a neutron?
No, see the answer to your first question. You’ll have to keep adding at least as much energy to keep making positrons as you can theoretically recover from the mutual electron-positron annihilations. The laws of thermodynamics [i]never[/i] sleep.
Of that I have no doubt, but that was precisely why I couldn’t understand what’s going on with neutron and proton decay.
It is part of the energy the proton gets when sent down a particle accelerator before smashing into a target. Alternatively, it could be part of the energy the proton receives from another sufficiently energetic particle that smashes into it.
Yes, indeed it does, but you seem to be forgetting that the proton must have a comparatively large excess of mass-energy before it will decay. Not only that, a trigger such as colliding with another particle is also required to prompt the decay.
It already has it by virtue of the energy added to it that will get it into a state where it has the potential to decay, e.g. in an accelerator or by a collision with another high-energy particle. An essentially free proton simply doesn’t decay spontaneously into positron/neutron/neutrino without the addition of copious amounts of energy. Your bafflement is similar to the supposition that we can dissociate water into hydrogen and oxygen, and by burning the latter, get some free energy. This hypothetical scenario rests on the erroneous assumption that dissociating water needs little or no energy.
In the nucleus of a (stable) atom, the situation is slightly different. Here, any proton decay event is almost instantly offset by a corresponding neutron decay event (and vice-versa!), and so the mass-energy and momentum accounts remain balanced (within the limits of Heisenberg Uncertainty). Within the nucleus, we have three other conservation laws that apply, namely charge, spin and quantum number. That is why I added the parenthetical remark “It’s a bit more complicated than that but close enough” in my first reply. Among other things, Heisenberg Uncertainty means that within certain precise limits, a particle can “borrow” energy for a short period of time without anyone being any the wiser. Nobody knows how exactly this works; it’s an integral part of quantum weirdness and explains many observable quantum effects. The salient points are that such “borrowed” energy can be sufficient to precipitate a decay event, and that it is returned in short order without affecting the overall energy account.
Ah, now the world makes sense again. I assume that in the inside of the sun, where positrons are emitted during nuclear fusion, something similar also happens: protons are smashed into one another with great force because of the great heat and pressure, and that is where they get the energy to emit positrons AND turn into neutrons in helium.
Incidentally, I assume that in the sun, the emitted positrons very quickly run into electrons, with which they then mutually annihilate and produce energy?
I am still looking for a book or web page that explains all this quantum stuff in terms that an idiot can understand, but apparently it is actually difficult to do without delving into some fearsome math, a subject which I find beautiful and fascinating, but alas, for which I also lack the necessary neural equipment to ever master.
I am especially perplexed by all the gazillions of fundamental particles discovered, and can’t work out whether those particles are sitting around in the nucleus, waiting for it to smash open so they can come swarming out, or whether they are created de novo out of the energy of the collisions with the mass of the particles depending on the energy involved. Or perhaps something else altogether.
I agree my layman understanding stopped at the neutron, proton and electron.
When all these other things like quarks and who knows what else came falling out,
I fell out of the bus.
Excellent, although sometimes I wonder about that…
Correct. The principal source of the energy that keeps the fusion process going and which manifests as heat and pressure is in fact the conversion of mass into energy. The mass of a helium nucleus is less than the sum of the individual masses of two protons and two neutrons. One is tempted to say that in this case, the whole is less than the sum of its parts.
Yes, that’s one possibility. Another is that they are absorbed by neutrons, forming new protons, which process also emits energy. But there’s a veritable zoo of other particles with which they can interact. Such particle interactions have been described, not inaccurately, as “a free-for-all, barnyard dance”: You have a fairly good idea what’s happening overall, but it’s impossible to predict what’s going to happen at a specific time and place in the barnyard.
Many science popularisers have sought to provide such but none has really succeeded. If interested, I suggest reading as many such popular accounts by different authors as you can lay your hands on. With familiarity comes understanding of sorts, and what one author explains really well, others might misfire on and vice versa. The difficulty is not so much explaining as interpreting the mathematics. The maths is clear and unambiguous but porting it into everyday familiar terms is the really hard part. It’s a case of much being lost in translation and so most physicists don’t fret about translating.
Most of them exist in fairly narrow energy ranges and conditions that don’t obtain in normal circumstances. The real point, however, is that it’s not the multitude of different particles that can be produced per se that’s interesting, but rather that the Standard Model of particle physics not only explains their “construction” from a handful of elementary building blocks, but also predicts their existence at the energy levels and conditions at which they have been found. In other words, all those particles are stunning experimental confirmation for the superb accuracy of the Standard Model, and that’s what’s truly amazing.
Yup, I have read popular accounts that sounded pretty much like post-modernism: analogy piled on analogy until you cannot make head or tails of it anymore. Alas, reality is under no obligation to make sense to the layman.
Most of them exist in fairly narrow energy ranges and conditions that don’t obtain in normal circumstances. The real point, however, is that it’s not the multitude of different particles that can be produced per se that’s interesting, but rather that the [url=http://en.wikipedia.org/wiki/Standard_Model]Standard Model of particle physics[/url] not only explains their “construction” from a handful of elementary building blocks, but also predicts their existence at the energy levels and conditions at which they have been found. In other words, all those particles are stunning experimental confirmation for the superb accuracy of the Standard Model, and that’s what’s truly amazing.
So does God, or does he not, play dice with the universe?
A new question has now occurred to me. Or actually, as usual, several new questions.
As I understand it, inside stars atoms are ripped to pieces, and instead of polite hydrogen and helium gas, you actually have a sort of soup of subatomic particles and electrons and stuff whizzing about. Now seeing as protons are positive and electrons negative, who don’t they promptly all stick together? What happens anyway when you squeeze a proton and electron together? A neutron? Is this what happens in neutron stars, i.e. electrons and protons are squeezed into one another? But if there is an electrostatic attraction between them, why do you have to squeeze them together, as opposed to them spontaneously bonding by themselves?
Actually, in the interior of stars heavier elements are forged by fusing lighter ones. Towards the surface of the star, the fusion of lighter elements (chiefly hydrogen & its isotopes deuterium, tritium) into helium, thence into lithium, beryllium up to carbon and oxygen occurs. The deeper into the star’s interior one goes, the heavier the elements that are formed up to iron.
However, owing to the high temperature, these elements are in a plasma state — that is, the nuclei and electrons are in a sort of soup state, rather than the electrons being captured by individual nuclei.
It takes less energy to fuse nuclei (protons and neutrons) than to produce neutrons from protons and electrons. This does not mean that neutrons are not produced. Protons and electrons must be squeezed together very tightly for them to fuse into neutrons, and, as indicated earlier in this thread, free neutrons are unstable and decay into protons and electrons (and a neutrino) very quickly.
When a star begins running out of lighter elements to fuse (its main source of fuel), the outward radiation pressure from its core begins to weaken and the star contracts under its own gravity. If the star is massive enough, the gravitational contraction may be sufficient to squeeze the nuclei and electrons together sufficiently for all the protons and electrons to fuse into neutrons, producing a neutron star that is one homogeneous mass consisting entirely of neutrons. These neutron stars are extremely dense at around 5×1017 kg/m3, which means that one teaspoonful would have a mass of around 2.5 billion tons.
The reason protons and electrons need to be squeezed together despite their mutual electrostatic attraction to form neutrons is the same reason that an ordinary hydrogen atom doesn’t simply collapse into a neutron: The stable quantum states in which the system is allowed to be. Squeezing them together eventually produces another semi-stable quantum state (i.e. a neutron) but this requires the input of energy. The so-called ground sate of an atom is its most stable and lowest-energy state.
Okay, and this is my understanding of it too - I just didn’t put it this elegantly.
When a star begins running out of lighter elements to fuse (its main source of fuel), the outward radiation pressure from its core begins to weaken and the star contracts under its own gravity. If the star is massive enough, the gravitational contraction may be sufficient to squeeze the nuclei and electrons together sufficiently for all the protons and electrons to fuse into neutrons, producing a neutron star that is one homogeneous mass consisting entirely of neutrons. These neutron stars are extremely dense at around 5×1017 kg/m3, which means that one teaspoonful would have a mass of around 2.5 billion tons.
And it appears that I had this bit more or less right as well.
The reason protons and electrons need to be squeezed together despite their mutual electrostatic attraction to form neutrons is the same reason that an ordinary hydrogen atom doesn’t simply collapse into a neutron: The stable quantum states in which the system is allowed to be. Squeezing them together eventually produces another semi-stable quantum state (i.e. a neutron) but this requires the input of energy. The so-called ground sate of an atom is its most stable and lowest-energy state.
This bit I don’t really get, and I suspect I won’t get it either, at least not without spending several years studying math.
The reason I asked is that I got asked a very good question by a bright grade five kid: why doesn’t the Earth collapse under its own gravity, i.e. shrink smaller and smaller until it disappears? Kids can ask amazingly perceptive questions! I more or less know the answer, but the bit with electrons and protons was what bothered me.
Consider the difference between cotton balls and table tennis balls.
Cotton balls can be squeezed together gradually as the force acting on them increases. Table tennis balls can’t be squeezed smaller as the force increases. Instead, they will resist all forces up to a point and then break suddenly.
Due to their quantum nature, atoms are like table tennis balls.
