# Can an electron be found outside the atom it belongs to?

What is the probability of an electron being found outside the atom it belongs to? Is it zero or nonzero?

## Answers and Replies

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Nugatory
Mentor
How are you defining "outside" and "inside"? That is, how far away must the detection be before it counts as outside instead of inside?

How are you defining "belongs to"? That is, how do you decide which atom any given electron belongs to if there are multiple atoms involved?

mitrasoumya and Buzz Bloom
TeethWhitener
Science Advisor
Gold Member
There isn’t really a good definition of “inside” and “outside” an atom in this context. It is possible to calculate the probability that the electron is within a certain radius from the nucleus, but the choice of radius is varying degrees of arbitrary.

In general, the probability of finding an electron subjected to a nuclear potential in a finite volume is nonzero everywhere. There are, however, certain (non-3D) regions where the probability density of the electron wavefunction is zero.

Edit: ninja’d by @Nugatory !

There isn’t really a good definition of “inside” and “outside” an atom
Does that imply that an atom is not bound by a "shape" or "closed" surface and is in a way "open" for sharing its contents with other atoms?

TeethWhitener
Science Advisor
Gold Member
Kind of. According to quantum mechanics, the electron has a nonzero (but very very small) probability of being arbitrarily far away from the nucleus.

The “atomic radius” that is referred to in chemistry, and is generally regarded as the “size” of an atom, can refer to several different concepts. Covalent radius is just half the average covalent bond for an atom. So for example, to get hydrogen’s covalent radius, you would look at several different representative covalent compounds of hydrogen, measure their bond lengths, and average them. Similar procedures apply for measuring ionic radius, as well as other flavors of atomic radius.

As for atoms sharing electrons with one another, this is what chemists mean when they talk about covalent bonding. In these systems, each electron interacts with multiple nuclei, so it’s impossible to assign a given electron unambiguously to a single nucleus (indeed, the electrons themselves are indistinguishable, by the Pauli principle). This happens in all polyatomic systems regardless of the nature of the nuclei (that is, even ionic compounds like NaCl will show some small degree of covalency), but we usually only assign the moniker “covalent bond” to situations where this electron sharing effect is particularly strong.

(NB—there are ways to make this language more precise, but I’m not sure if it goes beyond an I level thread, and I’m trying to gear it toward what I ascertain to be your level of expertise.)

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mitrasoumya
Thank you.

According to tunneling effect, there is a certain probability of stationary state electron appear in whole space, even they are in bound state. When the eletron reach the space where Coulomb potential is greater than its stationary state energy, the probability decline exponentially.