# Quantum Tunneling in Atoms

Wave functions that produce two lobes of electron probability on opposing sides of the core indicate that our point-like electron must tunnel through the nuclear core when the point charge moves to the opposing lobe. I don't understand what is the driving force for this process? Does this process occur at near light speed?

malawi_glenn
Homework Helper
No, when you derive the wave functions for electron wavefucntions, the nucleus are regarded to be point like (recall how small the nucleus is compared with the 'seize' of an atom).

Then you must take notice of the radial wave functions of the hydrogen atom looks like, only the ground state (n=1, L=0) have a non zero probabilty to be located at r=0 (i.e inside the nucleus). Then you must know your particle interaction rules, the electron interact via the weak force to make the process (electron capture): http://en.wikipedia.org/wiki/Electron_capture
So this process is a weak process, i.e it goes very slow. And in reality, since the nucleus has a certain size, L and M shell electrons can be captured, but that process is quite small compared to K shell capture.

The thing is how the wave function works, and how we really want to interprent everything that the electron is moving around etc. One has to use the formalism and compare with experiments.

I hope I at least shed some light on how atomic electrons interact with the atomic nucleus.

http://www.cyberphysics.pwp.blueyonder.co.uk/graphics/diagrams/Feynman/Feynmanelectroncapture.gif
http://en.wikipedia.org/wiki/Weak_interaction

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malawi_glenn
Homework Helper
Also, the concept of tunneling is this:

If a particle can be located at a classical forbidden region, it has undergone tunneling. I.e let the energy of the particle be E, and the potential energy be V. if E<V, then the region is called classical forbidden.

But in the atom, the potential is attractive (the one that the nucleus are generating) so the electron has no potential barrier to overcome, so tunneling is not occuring in the atom. The nucleus can bind the atom, and there exists an (infinite) number of bound states.

That was the electromagnetic force, the weak force you cannot have potentials since it is a totaly different force than the electromagnetic one.

So the main thing about tunneling is that when you have a region where the particle can't be classically, one can solve the schrodinger equation and find the transmission probabilities and so on. The first example of tunneling is alpha decay, the model is that an alpha particle is inside the nucleus and since it is charged, the repulsive EM potential (that outer lying protons will create) will keep the alpha inside the nucleus. However, there is a small probability of tunneling through this barrier.

If you want, I can give you plenty of material and references for all of this. But I think you know all of this, you are much older than me and you are about to make this theory of everything :-)

Also, the concept of tunneling is this:

If a particle can be located at a classical forbidden region, it has undergone tunneling. I.e let the energy of the particle be E, and the potential energy be V. if E<V, then the region is called classical forbidden.

But in the atom, the potential is attractive (the one that the nucleus are generating) so the electron has no potential barrier to overcome, so tunneling is not occuring in the atom. The nucleus can bind the atom, and there exists an (infinite) number of bound states.

That was the electromagnetic force, the weak force you cannot have potentials since it is a totaly different force than the electromagnetic one.

So the main thing about tunneling is that when you have a region where the particle can't be classically, one can solve the schrodinger equation and find the transmission probabilities and so on. The first example of tunneling is alpha decay, the model is that an alpha particle is inside the nucleus and since it is charged, the repulsive EM potential (that outer lying protons will create) will keep the alpha inside the nucleus. However, there is a small probability of tunneling through this barrier.

If you want, I can give you plenty of material and references for all of this. But I think you know all of this, you are much older than me and you are about to make this theory of everything :-)

Hmmmm,
I did not quite find the answers to my questions. Please re-read my questions and try again.
Thanks!
Vince

Hootenanny
Staff Emeritus
Gold Member
Hmmmm,
I did not quite find the answers to my questions. Please re-read my questions and try again.
Thanks!
Vince
Hmmm, perhaps you didn't find any answers to your question because your question may be based on false premise. Could you start by explaining what you understand by Quantum Tunnelling and we'll take it from there?

malawi_glenn
Homework Helper
Hmmmm,
I did not quite find the answers to my questions. Please re-read my questions and try again.
Thanks!
Vince

The point is that your question was based on wrong understanding of the tunnel effect and how the physics of the atom works and refreashing our defenition of a wave function.

Are you asking how fast the information travels? As in the two-photon state example in bells inequality in the 80's ?

If not, then the underlying physics behind the wave function are the Schrodinger equation and the quantum mechanical poisson bracket. (I don't understand what is the driving force for this process?)

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Hmmm, perhaps you didn't find any answers to your question because your question may be based on false premise. Could you start by explaining what you understand by Quantum Tunnelling and we'll take it from there?

OK. Thanks.

My reading suggests that Quantum Tunneling accounts for (or explains) the ability of the point-charge electron to appear on both sides of the corresponding nucleus for any L>0. Is this true?

I think you mean something similar to https://www.physicsforums.com/showthread.php?t=234989"

I think that you can get a similar situation with certain molecules like NH3 if I remember correctly. The N can tunnel from above the plane formed by te 3 H's to below and that tunnelling rate is elated to the energy diffeenceof the two eigenstates, the eigenstates being the symmetric and anti-symmetric linear combinations of the N being above and below the plane.

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I think you mean something similar to https://www.physicsforums.com/showthread.php?t=234989"

I think that you can get a similar situation with certain molecules like NH3 if I remember correctly. The N can tunnel from above the plane formed by te 3 H's to below and that tunnelling rate is elated to the energy diffeenceof the two eigenstates, the eigenstates being the symmetric and anti-symmetric linear combinations of the N being above and below the plane.

That is a useful comparison, but that inversion can be stopped at low temperatures so it is probably not due to QT.

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malawi_glenn
Homework Helper
OK. Thanks.

My reading suggests that Quantum Tunneling accounts for (or explains) the ability of the point-charge electron to appear on both sides of the corresponding nucleus for any L>0. Is this true?

1) there is no tunneling in the atom, the electron does not tunnel through the nucleus.

see my post #3

"But in the atom, the potential is attractive (the one that the nucleus are generating) so the electron has no potential barrier to overcome, so tunneling is not occuring in the atom. The nucleus can bind the atom, and there exists an (infinite) number of bound states."

2) there is an angular degree of freedom, the electron can move in theta and phi direction aswell. So in order to be located at the total opposite place in the atom, angular translation is also a possibility.

Have you worked out the shrodinger equation for the hydrogen atom yourself? It's quite easy :-)