Why don't hydrogen atoms -> neutron + neutrino?

[Relain]

Hey all, I'm a Theoretical Physics undergrad and so far I've only done one course in QM. Mainly playing with the TISE pushing wavefunctions around.

Anyway after some trolling on here I've gotten to wondering, in a hydrogen atom why doesn't the electron just collapse into the nucleus? The coulomb potential is pretty strong, i don't think that the Pauli exclusion principle would apply as electrons have lepton number right? So they can both occupy the same QS? So i got to thinking it must be related to the angular momentum of the electon, similar to closed gravitational orbits in a classical system, but this didn't seem like a nice enough solution.

I think that for the atomic L = 0 state the <r> = 0, but yet I'm sure there are plenty of hydrogen atoms like this that haven't just decayed into a neutron and neutrino. this can happen though , electron capture, in multi electron atoms.

Is this related to the spin of the proton / electon and their respective compatability or otherwise?

Can you use the TDSE to show that the wavefunction of the electron won't collapse over time?

Thanks for any help you can give, I've just about lost all faith in my brian right now. :)

 

[sridhar_n]

Hey all, I'm a Theoretical Physics undergrad and so far I've only done one course in QM. Mainly playing with the TISE pushing wavefunctions around.Anyway after some trolling on here I've gotten to wondering, in a hydrogen atom why doesn't the electron just collapse into the nucleus?

Are you sure that you have studied Quantum Mechanics.

if you have, then u must have come across Stationary orbits... That is the answer to your question.

 

[Relain]

well I've come across stationary orbits in a classical sense, how's this relate to the Qm? someone Convince me

 

[chroot]

This is what particles do in central potentials. You can consider it an effect of the uncertainty principle -- the electron gets as close as it can to the nucleus, thus localizing itself, but its concomittant increase in momentum prevents it from staying there. The stable electronic orbits are a balance between the two.

The dissection of the quantum mechanical model of the hydrogen atom should be done in any quantum mechanics course. The basic examples of discretized energy states, like the infinite square well, come early in the course.

What kind of QM course have you taken that did not discuss these topics?

- Warren

 

[turin]

I think that for the atomic L = 0 state the <r> = 0, ...

I've been out of QM for a year now, and I'm already starting to forget everything (never stop studying!). Anyway, for some reason, the above does not look correct. I'm pretty sure that in a zero angular momentum state, the expectation value for the radius is non-zero. I don't have my QM book with me, but I'll check when I get it (I need to refresh my brain with the book).

One thing to add: don't forget that <r> is not the same thing as <x>, but is more closely related to <|x|>, which is to say, something like &radic;<x²>.

 

[Relain]

hey guys, yeah that's pretty much cleared it up. see i knew all that, i just didn't put it together in a way that would convince me i was right. If you know what i mean.
Hehe don't worry, i did cover all that. potentials, the HUP, communtators and operators etc etc but i guess I'm just on a no brain weekend.

Thanks for the help folks

Chris

 

[Njorl]

This is what particles do in central potentials. You can consider it an effect of the uncertainty principle -- the electron gets as close as it can to the nucleus, thus localizing itself, but its concomittant increase in momentum prevents it from staying there. The stable electronic orbits are a balance between the two.

The dissection of the quantum mechanical model of the hydrogen atom should be done in any quantum mechanics course. The basic examples of discretized energy states, like the infinite square well, come early in the course.

What kind of QM course have you taken that did not discuss these topics?

- Warren

I went to a school that used terms, not semesters. I believe we started the second term of QM with the hydrogen atom.

Njorl

 

[mathman]

The obvious answer to the original question is that a neutron has more mass than a hydrogen atom. Free neutrons decay.

 

[Janitor]

Mathman gives the reason why the process of "electron capture" (as it is called) does not work for hydrogen, at least for the lightest isotope of hydrogen.

Electron capture, meaning an orbital electron being captured by a proton, with conversion to a neutron and the release of a neutrino, actually is an important type of radioactivity. In one of its modes, the element which results from the shift of one position in the periodic table is argon, and by measuring argon in a sample of rock or whatever, one can date the material, using the assumption that the argon got there entirely by this radioactive process.

I think the cross section for electron capture--at least as a rule of thumb--rises with atomic number. But it has been observed even in as light an element as beryllium, element number four.

 

[chasingwind]

Electron capture, meaning an orbital electron being captured by a proton, with conversion to a neutron and the release of a neutrino, actually is an important type of radioactivity. In one of its modes, the element which results from the shift of one position in the periodic table is argon, and by measuring argon in a sample of rock or whatever, one can date the material, using the assumption that the argon got there entirely by this radioactive process.

Janitor, could you please tell me what course of physics can handle such phenomena you have described above? Quantum field theory??

 

[Janitor]

Chasingwind,

While I personally have never taken a class that covered that topic, I would think that a course in quantum field theory might cover it, if only briefly.

 

[chasingwind]

While I personally have never taken a class that covered that topic, I would think that a course in quantum field theory might cover it, if only briefly.

Janitor, thanks for your hint. I am about to start my Ph.D studies and I think I will have that course. It is really a shame for a student of theoretical physics who doesn't know quantum field theory.

 

[Reflector]

Why do a proton and electron stay apart?... To compensate for the destruction of space through gravity by the CONSTRUCTION of space.

 

[Janitor]

Reflector-

Is that your final answer?

 

[Reflector]

What do you mean? Do you want me to explain more? I just had this idea, I can't really remember it but it did seem to make a lot of sense (according to all my previous ideas). If I tell everyone my ideas that could cost me profit and credit potentially. So I need to save them if I am to develop my own theory like everyone else. Do you think it is a good idea though? It probably is not my final answer because there is a heap of stuff I don't know. I just thought I'd drop it into see what would happen.

 

[Janitor]

Well, I don't have the credentials to say if it has promise or not, but on the other hand I've done quite a bit of reading in my spare time, and I can say that I have never encountered an idea remotely like yours.

 

[Reflector]

Maybe gravity causes the proton-electron separation from a neutron. Think of a Neutron in remote space. It has gravity because it has mass but who is it going to share it with?... so out comes an electron and then it works.