# What is the distance an electron is from a proton?

##### 1 Answer

*It varies from atom to atom. Often it is hard to predict, and it is a much better idea to focus on hydrogen-like atoms when learning about it. We have to use a most probable distance.*

In **hydrogen atom**, it is relatively straightforward; the *most probable electron-nucleus distance* is "1 bohr radius".

I am unsure as to how these electron-nucleus separations compare to other hydrogen-like atoms (

In atoms that contain **more than one** electron, there exists *electron-electron correlation* that complicates the location of each electron in space.

- For
helium, we have electron-electron correlation, which isinstantaneous short-range repulsions(dynamical correlation), as well as some set ofdegenerate electron configurations(nondynamical correlation, though not significant).

We

canapproximate the probability density by assuming aone-electron approximation, wherein we take anaverageelectron density and ignore electron-electron repulsions.

Then, we make

special correctionsto account for such repulsions, such as the variational theorem or nth-order perturbation theory.Therefore, we only get an

approximateground-state energy for helium, from which we can acquire an inexact, most-probable electron-nucleus distance.

- For atoms with more than two electrons (
#"Li"# ,#"Be"# , etc), it gets harder and harder to make good approximations, and we computational chemists are trying to determine better and better ways to make special approximations and "corrections" to get more and more exact ground-state energies.