# About the position of electrons (uncertainty)

• I
• pokespriter
In summary, the teacher told me that if the atom was right on my table, the electron could possibly be anywhere, including:- one centimeter away from the atom- in the sun- in Obama's forehead- in the salad my mom is preparing currently.f

#### pokespriter

TL;DR Summary
Where can I find an electron within an atom? Is it truly everywhere?
Hello guys, I don't know if this is the right place to ask, so please be kind :/
I have a question regarding the location of an electron that belongs to an atom. A teacher told me that the probability of an electron to be found within its orbital is around 99%.

When I asked about the remaining percentage, the teacher told me that if the atom was right on my table, the electron could possibly be anywhere, including:
- one centimeter away from the atom
- in the sun
- in Obama's forehead
- in the salad my mom is preparing currently

He said that the percentage of the electron to be literally anywhere else is never zero, because of how electrons move as a quantum object. They could be literally anywhere in the universe and still be part of that atom. They could even be within the nucleus.
Is that true? I mean quantum physics is weird, so why not, but I just want to be certain that this is correct.

Because usually I'd assume there are places where electrons are not allowed to be, for example the nucleus. Also if they where in another atom wouldn't they disturb that atoms structure?

I hope you can help me with this, thanks :D

Summary: Where can I find an electron within an atom? Is it truly everywhere?
”Everywhere” is not exactly wrong - but so is “nowhere”. They’re both about equally (and not very) good explanations of what the math is telling us. It’s better to say that quantum mechanics has nothing to say about the position unless and until we measure it and then it only tells us where the particle was at the moment of measurement.
Because usually I'd assume there are places where electrons are not allowed to be, for example the nucleus.
Nothing prevents the electron being found within the nucleus - Google for “electron capture”. More generally, there are areas where it is very unlikely, for all practical purposes impossible, for the electron to be detected. But that’s “for all practical purposes” - no experiment can distinguish between the propositions “There is zero probability of the electron being found here” and “The probability of finding the electron here is ##10^{-500}##”.
Also if they where in another atom wouldn't they disturb that atoms structure?
With a great deal of handwaving and oversimplification that’s how molecular bonds work

mattt, dextercioby, topsquark and 3 others
If the hydrogen atom is in the 1s ground state, then the value of the wavefunction becomes 2 times smaller every time the distance from nucleus increases by about 36.7 picometers. So finding the electron even 1 meter away from the nucleus just by chance is so unlikely that no one in the universe probably has ever measured that to happen. You can compare this to an exponential growth equivalent, the "Wheat and chessboard problem".

Note that in this it is assumed that the hydrogen atom really is in the ground state and not disturbed in any way. The chance of a stray high-energy particle knocking the electron off the atom and to 1 meter distance from the nucleus is much larger, but still negligible for any given H atom.

I don't know enough quantum field theory to tell what happens if a hydrogen atom is created from other particles at some location right now and then someone tries to find the electron 1 light year away after a few seconds. It shouldn't be able to end up somewhere faster than light even with a theoretical chance, but every electron and proton being indistinguishable can possibly make this thought experiment impossible.

topsquark and vanhees71
”Everywhere” is not exactly wrong - but so is “nowhere”. They’re both about equally (and not very) good explanations of what the math is telling us. It’s better to say that quantum mechanics has nothing to say about the position unless and until we measure it and then it only tells us where the particle was at the moment of measurement.

Nothing prevents the electron being found within the nucleus - Google for “electron capture”. More generally, there are areas where it is very unlikely, for all practical purposes impossible, for the electron to be detected. But that’s “for all practical purposes” - no experiment can distinguish between the propositions “There is zero probability of the electron being found here” and “The probability of finding the electron here is ##10^{-500}##”.

With a great deal of handwaving and oversimplification that’s how molecular bonds work
Quantum theory tells you the probability distribution of the electron's position around the nucleus, given it's energy eigenstate.

topsquark
Summary: Where can I find an electron within an atom? Is it truly everywhere?

Hello guys, I don't know if this is the right place to ask, so please be kind :/
I have a question regarding the location of an electron that belongs to an atom. A teacher told me that the probability of an electron to be found within its orbital is around 99%.

When I asked about the remaining percentage, the teacher told me that if the atom was right on my table, the electron could possibly be anywhere, including:
- one centimeter away from the atom
- in the sun
- in Obama's forehead
- in the salad my mom is preparing currently
I think this sort of nonsense isn't what QM is all about. Electrons are indistinguishable, so I'm not sure how you'd know that the one in your salad was the one from your hydrogen atom.

The important point is the the electron in an atom does not have a well-defined classical trajectory about the nucleus. Instead, it is in a bound energy state. That is what QM is all about.

mattt, DrClaude, vanhees71 and 2 others
In an energy eigenstate nothing moves at all since the energy eigenstates are the stationary states of the system.

topsquark
TL;DR Summary: Where can I find an electron within an atom? Is it truly everywhere?

Hello guys, I don't know if this is the right place to ask, so please be kind :/
I have a question regarding the location of an electron that belongs to an atom. A teacher told me that the probability of an electron to be found within its orbital is around 99%.

When I asked about the remaining percentage, the teacher told me that if the atom was right on my table, the electron could possibly be anywhere, including:
- one centimeter away from the atom
- in the sun
- in Obama's forehead
- in the salad my mom is preparing currently

He said that the percentage of the electron to be literally anywhere else is never zero, because of how electrons move as a quantum object. They could be literally anywhere in the universe and still be part of that atom. They could even be within the nucleus.
Is that true? I mean quantum physics is weird, so why not, but I just want to be certain that this is correct.

Because usually I'd assume there are places where electrons are not allowed to be, for example the nucleus. Also if they where in another atom wouldn't they disturb that atoms structure?

I hope you can help me with this, thanks :D
First of all the electron isnt a classical particle in case you are imagining a blue ball doing who knows what abandon that picture its completely wrong.

The electron is a Quantum Object and thus can take on multiple positions at once due to its quantum nature so until we measure it and change its state by doing so its in a wavy superposition of all the possible places it could be.

When I asked about the remaining percentage, the teacher told me that if the atom was right on my table, the electron could possibly be anywhere, including:
- one centimeter away from the atom
- in the sun
- in Obama's forehead
- in the salad my mom is preparing currently

This isnt accurate as it assumes a false underlying classical picture where the electron is a blue ball doing who knows what until we measure. In reality it doesnt have a defined position but has a nonzero probability of being there but we have to measure it first to localize it. Until we do so its delocalized across all possible positions in a fuzzy cloud state.

Also if they where in another atom wouldn't they disturb that atoms structure?
They do disturb the structure due to electron repulsion its one of the fundamental obstacles to applying QM to multielectron Atoms. The repulsion causes significant change in the electronic structure but isnt so strong it ionizes the atom. So electrons do indeed disturb the Atom’s structure.

You also say it isnt allowed to be in the nucleus. Actually thats not true the electron indeed has a nonzero probability of being in the nucleus in fact the ground state is peaked on the nucleus. Dont forget electron capture