# Stealing an electron

by Meson080
Tags: electron, stealing
P: 100
 Quote by Wikipedia-Atomic orbital:shapes of orbitals Simple pictures showing orbital shapes are intended to describe the angular forms of regions in space where the electrons occupying the orbital are likely to be found. The diagrams cannot, however, show the entire region where an electron can be found, since according to quantum mechanics there is a non-zero probability of finding the electron (almost) anywhere in space.
Is the statement by wikipedia correct?

Since, there is a probability of finding electron at any distance from the nucleus, when the electron comes far from the nucleus, I will block it, so that it won't return to its parent atom. Am I not stealing the electron? I can steal even the electron of your body being in India, be careful!

That's what we layman think from those statements. What's the actual meaning of the wikipedia statement?
 Mentor P: 12,005 It means that if we perform a measurement to find out where the electron is, its location could technically be almost anywhere, including in India. But the probability of finding the electron further than about a nano-meter from the nucleus is so low that you could perform this measurement every second for a billion years and not find it there.
P: 100
 Quote by Drakkith It means that if we perform a measurement to find out where the electron is, its location could technically be almost anywhere, including in India.
Then I do have the chance of stealing your body's electron. Is that what you mean?

 But the probability of finding the electron further than about a nano-meter from the nucleus is so low that you could perform this measurement every second for a billion years and not find it there.
Can I have the source for this?

 Mentor P: 12,005 Stealing an electron Have you checked the list of references at the bottom of the wikipedia article you quoted from?
P: 100
 Quote by Drakkith Have you checked the list of references at the bottom of the wikipedia article you quoted from?
It will be helpful, if you can point the source among that bunch of reference links.
 P: 100 The same question is also posted in Physics Stack Exchange. Interested folks can read this page: Can I steal your electron? The page might help to have better discussion.
 Mentor P: 12,005 I don't have a specific source, it's just general knowledge how atomic orbitals work. My response wasn't meant to be taken literally, as I haven't done the math. I just know that the probability of an electron being found a few thousand miles away from its atom is exceedingly low. So low that we never worry about objects falling apart because they lose their electrons in this manner.
Mentor
P: 17,535
 Quote by Meson080 It will be helpful, if you can point the source among that bunch of reference links.
See
http://en.m.wikipedia.org/wiki/Hydro...m#Wavefunction

For the ground state electron this simplifies to a probability density of:
$$|\Psi(r)|^2 = \frac{1}{a_0^3 \pi} e^{-2r/a_0}$$

Since ##a_0=5.29 \; 10^{-11} \; m## if you want to steal an electron in a 1 m cubic box located even just 10 m away, the probability is so small that it cannot be distinguished from 0 with even a million digits of precision, and the probability of finding it anywhere in the universe further than 1 m distance away is less than 1.6E-16419451091
 P: 901 Meson, you have a very, very, very small chance. This chance is really too small to worry about in any context.
P: 100
 Quote by Drakkith I don't have a specific source, it's just general knowledge how atomic orbitals work. My response wasn't meant to be taken literally, as I haven't done the math. I just know that the probability of an electron being found a few thousand miles away from its atom is exceedingly low. So low that we never worry about objects falling apart because they lose their electrons in this manner.
So, once electron comes far from its parent atom, it won't return to it? Did you mean this?
 Mentor P: 12,005 I believe that's how it works.
P: 100
 Quote by Meson080 So, once electron comes far from its parent atom, it won't return to it? Did you mean this?
 Quote by Drakkith I believe that's how it works.
The question is, what provides energy to the electron to go any far distance from the nucleus?

As there is the force which is holding the electron, it should not have any "probability" of going far from the nucleus, isn't it? How does QM tackle this discrepancy?
Mentor
P: 3,942
 Quote by Meson080 The question is, what provides energy to the electron to go any far distance from the nucleus?
To measure the position of the electron you have to interact with it, and that interaction supplies any necessary energy. The total energy of the system (nucleus, electron, and measuring device) is conserved.

Understand also that the electron isn't anywhere until you interact with it. The function that DaleSpam posted does not give you the probability that the electron is at a given location, it gives you the probability that the electron will be found at that location if you make a measurement. Thus, there's no question about how the electron moved far away from the nucleus before you looked and found it out there - until you measured its position it didn't have a position, it wasn't far away from the nucleus, or near it, or anywhere else.

That's how quantum mechanics works. If you don't like it, you're in good company - but like it or not, them's the rules.
 Mentor P: 12,005 I believe energy conservation in QM is a bit more complicated than it is in classical physics, but you'd need to ask in the QM forum if you want to know about that.
P: 100
 Quote by Nugatory Understand also that the electron isn't anywhere until you interact with it. The function that DaleSpam posted does not give you the probability that the electron is at a given location, it gives you the probability that the electron will be found at that location if you make a measurement. Thus, there's no question about how the electron moved far away from the nucleus before you looked and found it out there - until you measured its position it didn't have a position, it wasn't far away from the nucleus, or near it, or anywhere else.
I felt this as the misconception of Heisenberg's Uncertainity principle. Isn't this?

 That's how quantum mechanics works. If you don't like it, you're in good company - but like it or not, them's the rules.
If it works that way, I need to learn more to unlearn as Feynman always says.
PF Gold
P: 6,498
 Quote by Meson080
No, they have nothing do do with each other. That article is about the false presentation of the HUP as a measurement problem. It is not and never has been a measurement problem, it is a fundamental fact of nature. That presentation was a dumbed-down common language presentation that does not represent the math.

 If it works that way, I need to learn more to unlearn as Feynman always says.
As did we all when we first got into this stuff.

EDIT: just to be sure I'm clear, when I say "they have nothing to do with each other", I'm saying that the fact that an electron has a probability distribution that gives a non-zero (but incredibly tiny) result for positions far away from its atom has nothing to do with the HUP.
Mentor
P: 17,535
 Quote by Meson080 The question is, what provides energy to the electron to go any far distance from the nucleus?
The formula I provided is for the ground state, meaning that it has the minimal amount of energy and is not excited. No energy is required for the electron to be measured in different locations in the ground state. Energy is only required to raise it to a different state.
Mentor
P: 3,942
 Quote by DaleSpam The formula I provided is for the ground state, meaning that it has the minimal amount of energy and is not excited. No energy is required for the electron to be measured in different locations in the ground state. Energy is only required to raise it to a different state.
OP is capturing the electron ("stealing" in the thread title). The state in which the electron has been localized at some distance from the nucleus isn't an energy eigenstate.

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