Understanding Orbital Shapes: The Probability of Electron Location

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In summary: It gives you the probability that if you measure the electron at some particular point it will be found at that point.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.
  • #1
Meson080
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Wikipedia-Atomic orbital:shapes of orbitals said:
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!:smile:

That's what we layman think from those statements. What's the actual meaning of the wikipedia statement?
 
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  • #2
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.
 
  • #3
Drakkith said:
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? :biggrin:

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?
 
  • #4
Have you checked the list of references at the bottom of the wikipedia article you quoted from?
 
  • #5
Drakkith said:
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.
 
  • #6
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.
 
  • #7
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.
 
  • #8
Meson080 said:
It will be helpful, if you can point the source among that bunch of reference links.
See
http://en.m.wikipedia.org/wiki/Hydrogen_atom#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
 
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  • #9
Meson, you have a very, very, very small chance. This chance is really too small to worry about in any context.
 
  • #10
Drakkith said:
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?
 
  • #11
I believe that's how it works.
 
  • #12
Meson080 said:
So, once electron comes far from its parent atom, it won't return to it? Did you mean this?

Drakkith said:
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?
 
  • #13
Meson080 said:
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.
 
  • #14
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.
 
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  • #15
Nugatory said:
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? :confused:

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.
 
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  • #16
Meson080 said:

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.
 
  • #17
Meson080 said:
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.
 
  • #18
DaleSpam said:
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.
 
  • #19
Nugatory said:
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.

Can I have any reliable source which supports this idea?
 
  • #20
Meson080 said:
Can I have any reliable source which supports this idea?

Any decent QM textbook will work. To see it in modern terms you'll want one that stresses the statistical interpretation, but the idea that it makes no sense to talk about the value of quantities that haven't been measured goes all the way back to Bohr.
 
  • #21
You can steal a few million of my electrons by brushing your hand across my sweater, it's no big deal. I'll get them back later.
 
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  • #22
Nugatory said:
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.
Correct, after the measurement of its position it is a position eigenstate, by definition.
 
  • #23
Drakkith said:
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.

I have exam tomorrow, I will try to post a new question in QM forum within two days. But, let the discussion go on, so that we can have a well built query in QM forum.
 
  • #24
MrAnchovy said:
You can steal a few million of my electrons by brushing your hand across my sweater, it's no big deal. I'll get them back later.

We are planning to steal electrons sitting far from you. We have missile ideas and not gun ideas like your's!:biggrin:
 
  • #25
Nugatory said:
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.

Just to make sure I understand you better, do you agree this statement: There is a non-zero probability of finding an electron at any distance from the nucleus, even if we don't make a measurement. By "measurement" I mean, using photons to know the address of electron.
 
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  • #26
I don't think it could be outside the light cone of the electron, so "any distance" is too much even if the rest is correct (and I'm not saying it is or isn't, although I THINK that it is).
 
  • #27
Meson080 said:
There is a non-zero probability of finding an electron at any distance from the nucleus, even if we don't make a measurement.
No. If you don't make a measurement then you have exactly 0 probability of finding it anywhere. You cannot find something if you don't look.
 
  • #28
Meson080 said:
Just to make sure I understand you better, do you agree this statement: There is a non-zero probability of finding an electron at any distance from the nucleus, even if we don't make a measurement. By "measurement" I mean, using photons to know the address of electron.

There might be other ways of locating the position of the electron... But if you don't interact with it in some way you have no way of finding it anywhere.
 
  • #29
phinds said:
I don't think it could be outside the light cone of the electron, so "any distance" is too much even if the rest is correct (and I'm not saying it is or isn't, although I THINK that it is).

Where are you putting the apex of that light cone? Basic first-quantization QM is neither relativistic nor local and you can plug arbitrarily large values of r into the spherical harmonics.

QED is relativistic, but it doesn't let you talk about "the" electron at all.
 
  • #30
Nugatory said:
Where are you putting the apex of that light cone? Basic first-quantization QM is neither relativistic nor local and you can plug arbitrarily large values of r into the spherical harmonics.

QED is relativistic, but it doesn't let you talk about "the" electron at all.

OK, I'll take your word for it. Thanks.
 
  • #31
DaleSpam said:
No. If you don't make a measurement then you have exactly 0 probability of finding it anywhere. You cannot find something if you don't look.

So, atom has definite boundary if we don't try to make measurement i.e if we don't try to see the atom. Is this what you mean?
 
  • #32
No, that is not at all what I said. If you don't make a measurement then you have a 0 probability of finding the electron anywhere, including very close to the nucleus. There is no definite boundary whatsoever.

If you want to find the electron anywhere you must measure its location. In a fundamental sense quantum objects do not have any definite value of a property until that property is measured.
 
  • #33
DaleSpam said:
No, that is not at all what I said. If you don't make a measurement then you have a 0 probability of finding the electron anywhere, including very close to the nucleus. There is no definite boundary whatsoever.

Even if we don't make measurement, there will be electron in the atom, I hope this is obvious. This means, there is a probability of finding electron anywhere, at least very close to the nucleus, even if don't make measurement.
 
  • #34
Meson080 said:
Even if we don't make measurement, there will be electron in the atom, I hope this is obvious. This means, there is a probability of finding electron anywhere, at least very close to the nucleus, even if don't make measurement.
You are still trying to hold on to the idea that the electron has a position before it is measured. It doesn't.

The quantum mechanical wave function gives the probability that a measurement will give a particular result, but says nothing about what's going on if no measurement is made. It seems very natural to assume that if a measurement of the electron position would give us a particular position, then the electron must really be in that position whether we look or not... But that's an additional assumption, and one that turns out not to be valid.
 
  • #35
"finding" is "making a measurement". Grasp this, or you will never understand the rest.
 
<h2>1. What are orbital shapes and how are they related to electron location?</h2><p>Orbital shapes refer to the three-dimensional regions where there is a high probability of finding an electron in an atom. These shapes are determined by the quantum numbers of the electron and the energy level it occupies.</p><h2>2. How is the probability of electron location calculated?</h2><p>The probability of electron location is calculated using mathematical equations based on the Schrödinger equation. This equation takes into account the electron's energy, position, and momentum to determine the probability of finding it in a specific region of space.</p><h2>3. What is the significance of orbital shapes in understanding the behavior of atoms?</h2><p>Orbital shapes play a crucial role in understanding the chemical and physical properties of atoms. They determine the electron configuration, which in turn affects the atom's reactivity, bonding, and other properties.</p><h2>4. How many orbital shapes are there and what are their names?</h2><p>There are four main orbital shapes: s, p, d, and f. The s orbital is spherical, the p orbital has a dumbbell shape, the d orbital is clover-shaped, and the f orbital is more complex with multiple lobes.</p><h2>5. Can the exact location of an electron be determined using orbital shapes?</h2><p>No, orbital shapes only give us a probability distribution of where an electron is likely to be found. The Heisenberg uncertainty principle states that it is impossible to know the exact position and momentum of an electron simultaneously.</p>

1. What are orbital shapes and how are they related to electron location?

Orbital shapes refer to the three-dimensional regions where there is a high probability of finding an electron in an atom. These shapes are determined by the quantum numbers of the electron and the energy level it occupies.

2. How is the probability of electron location calculated?

The probability of electron location is calculated using mathematical equations based on the Schrödinger equation. This equation takes into account the electron's energy, position, and momentum to determine the probability of finding it in a specific region of space.

3. What is the significance of orbital shapes in understanding the behavior of atoms?

Orbital shapes play a crucial role in understanding the chemical and physical properties of atoms. They determine the electron configuration, which in turn affects the atom's reactivity, bonding, and other properties.

4. How many orbital shapes are there and what are their names?

There are four main orbital shapes: s, p, d, and f. The s orbital is spherical, the p orbital has a dumbbell shape, the d orbital is clover-shaped, and the f orbital is more complex with multiple lobes.

5. Can the exact location of an electron be determined using orbital shapes?

No, orbital shapes only give us a probability distribution of where an electron is likely to be found. The Heisenberg uncertainty principle states that it is impossible to know the exact position and momentum of an electron simultaneously.

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