I The atomic Coulomb potential extends to infinity?

[aaronll]

I'm studying nuclear physics in a text, but at one point that is said: "Both the Coulomb potential that binds the atom and the resulting electronic charge distribution extends to infinity" , I don't understand what is that "resulting electronic charge distribution extends to infinity" what they mean? ( maybe I misunderstand the phrase but i don't know)
thanks

 

[PeroK]

I'm studying nuclear physics in a text, but at one point that is said: "Both the Coulomb potential that binds the atom and the resulting electronic charge distribution extends to infinity" , I don't understand what is that "resulting electronic charge distribution extends to infinity" what they mean? ( maybe I misunderstand the phrase but i don't know)
thanks

I assume by "charge distribution" it means the wave-function for the electron. And, theoretically the spatial wave-function for the electron is non-zero everywhere. I.e. no matter how far the distance from the nucleus, there is still a non-zero probability of detecting the electron there.

In practical terms, of course, the electron probability distribution drops off to nearly zero very quickly - of the order of magnitude of a few times the Bohr radius.

 

[aaronll]

I assume by "charge distribution" it means the wave-function for the electron. And, theoretically the spatial wave-function for the electron is non-zero everywhere. I.e. no matter how far the distance from the nucleus, there is still a non-zero probability of detecting the electron there.

In practical terms, of course, the electron probability distribution drops off to nearly zero very quickly - of the order of magnitude of a few times the Bohr radius.

Thank you

 

[vanhees71]

Which text is this? I guess, I'll like to avoid its use ;-)).

 

[aaronll]

Which text is this? I guess, I'll like to avoid its use ;-)).

Is the "Introduction to Nuclear Physics" written by Kennet S. Krane, I believe is a good book

 

[vanhees71]

Yes, I like it too, but are there really such statements as that the long-ranged nature of the Coulomb potential of the nucleus in an atom were "resulting electronic charge distribution extends to infinity"? That doesn't make sense or at least hints at an pretty unusual interpretation of the (energy-eigen) wave functions of the electron(s) in atoms. It sounds something like Schrödinger's very first interpretation of his $\psi(t,\vec{x})$ before Born's probabilistic interpretation. Even then it's strange since as the hydrogen wave functions show, the bound states all fall exponentially for $r \rightarrow \infty$, and from that the typical atomic length scales are determined by the Born radius of about $0.5 \mathring{\text{A}}$.