What is a neutron? (if not an electron inside a proton)

[davidyanni10]

Simple question, please help. I think it belongs in this forum, though I apologize if there's a nuclear physics forum or somewhere else I should put this.

I came across this thread when trying to figure out why electrons don't rest at zero distance away from the nucleus of an atom.

So as I understand it (please correct me if I'm wrong) HUP says $$\Delta x \Delta p \geq \frac{\bar{h}}{2}$$ so if you try to confine an electron to the nucleus Δx becomes small so that Δp becomes large, and an increased spread in p leads to an increased kinetic energy so there's an energy requirement or "pressure" involved in confining an electron to within, say, a proton.

Now, the above thread outlines a problem (homework probably) that is meant, I believe, to show that thinking of a neutron as an electron embedded into a proton waiting to tunnel away as Beta radiation is incorrect. There is too large a deviation between the emission energy of an electron in Beta decay and the hypothetical electron's kinetic energy while bound inside a proton.

So my question is twofold:
1) Is my reasoning correct so far?
2) How ought I to think about a neutron and the process of Beta decay?

 

[mfb]

1) Is my reasoning correct so far?

It is.

2) How ought I to think about a neutron and the process of Beta decay?

A neutron is a hadron (a particle made out of quarks and hold together by the strong force), very similar to the proton. The electron is produced in a beta decay, it does not exist before.

 

[davidyanni10]

Thanks! (for some reason I never considered that an electron could spring into being during a beta decay, that's pretty nifty.)

 

[jtbell]

[I posted this before I realized that you had already gotten a response in a duplicate thread in another forum. I've merged the two threads together and deleted the duplicate opening post. This is why we frown on multi-posting: parallel answers in multiple threads waste people's time.]

1) Is my reasoning correct so far?

Yes, pretty much.

2) How ought I to think about a neutron and the process of Beta decay?

A neutron consists of two down-quarks and an up-quark. In beta decay, one of the down-quarks converts to an up-quark and a virtual W boson. The virtual W in turn "decays" into an electron and an antineutrino.

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/proton.html#c4

 

[soothsayer]

1) Your reasoning is somewhat correct so far within the framework of a Bohr model of the atom, in which electrons "orbit" around the nucleus in discrete orbitals. I think the use of the Uncertainty Principle is a more or less acceptable explanation of why the electron cannot just crash into the nucleus, but it's usually better to think of atoms within the framework of a more accurate model, using electron "clouds"; the idea being that the wavefunction of the electron is such that the electrons are effectively "smeared out" across certain areas of the atom. The probability distribution of the electron in an atomic potential dictates where those electrons are most likely to be. Simply looking at the wavefunctions show that hey have zero probability of being found at r=0. It's tempting to search for a somewhat classical reason behind this, but truthfully, the quantum explanation is all that is needed, though we can argue about interpretations of the wavefunction until the cows come home.

2. As for the idea of a neutron being an electron inside a proton, you're right about the energy disparity, that's a big red flag that should right away prove to you that model is incorrect. Let's go inside the proton and the neutron--neither of these are fundamental particles, they are actually made of even smaller particles called quarks, which are fermions, just like the electron, another fundamental particle. One thing fermions all have in common is that they take part in the "weak interaction", or "weak nuclear force". This force is responsible for radioactive decay. I would do some research into quarks and weak interactions between them, as well as fundamental conservation laws in particle physics to see why electrons come out of Beta decay.

Again, we don't really know HOW particles turn into other particles, we just know that they DO, and for now, that'll have to do. Perhaps String Theory might shed some light on that in the future, that's beyond my pay grade though!

- Soothsayer

 

[davidyanni10]

Thanks for the responses and links, sorry about the double posting (wasn't sure which forum my question fit into.)

@soothsayer, What is classical about the uncertainty principle though? Aren't HUP and Schrodinger's equation saying essentially the same thing about the energy of an electron at r=0 away from the nucleus? I understand that the energy levels are quantized and spherical harmonics give us the "shape" of the orbitals, but position isn't quantized (right?) and the energy for an inner electron an r=0 (if it were allowed) is greater than the energy for an electron at the bohr radius away from the nucleus. So you see energy decreasing as we move an electron away from the nucleus. In this sense shcrodinger's equation shows a prohibitive energy increase for placing an electron at r=0 away from the nucleus just the same as HUP does no?

In fact, thinking about smeared out electrons in orbitals relies on an interpretation of the wavefunction, which like you said, we could debate. There's no two ways around HUP though.

Thanks again, now I'm off to try to research the weak force!

 

[e.chaniotakis]

Well, if you consider the neutron as an electron-proton bound state then you have two problems:
1) The energy of the beta decay is of order 1 MeV, whereas the energy of an electron emitted by tunneling would be E~hbar/1fm which will correspond to ~200 MeV
2) The spin of the neutron is 1/2 whereas a bound electron-proton state would be spin0 or 1.
3)The continuous beta spectrum cannot be explained this way!

As very enlightingly explained above, the reason is the weak interaction.
A neutron decay is a (udd) decay where one gets to :
(udd)->(ud[u+W])->(udu+ e+ neutrino)

 

[soothsayer]

@soothsayer, What is classical about the uncertainty principle though? Aren't HUP and Schrodinger's equation saying essentially the same thing about the energy of an electron at r=0 away from the nucleus?

Of course, I didn't mean to imply that the UP was somehow classical, it just seemed like you were kind of looking at the atom from a somewhat classical perspective, with well defined energies and positions and electron orbits. Rereading your post, I think I may have just made that up, though XD It seemed like you were forgetting about the wavefunction nature of the electron, but you were probably just looking for some reasons as to why the wavefunction of an electron behaved the way it did in the r → 0 limit. Certainly, the UP and Schrodinger equation come from the same basic principle. Yes, the HUP is definitely the reason as to why an r→0 electron configuration is energetically unfavorable.

I also meant to say that analyzing the wavefunction was a more quantitative way of analyzing electron radii than the UP. Both will tell you something about the energy of an electron at a given radius, but the probability distribution will give you added information, like where an electron is actually most likely to be found in the atom. I'm sure you know this, though.

Good luck with the Weak force research! It's definitely the strangest of the forces, to me. Doesn't really seem like much of a "force" in the traditional sense, but it is an interaction mediated by virtual bosons and can break apart an atom.