# The point of charge neutrality in the Hydrogen Atom

If we treat the Hydrogen Atom like the Bohr model then we have a proton in the center with an electron orbiting at some radius (the Bohr radius). In this picture you can imagine the electric field between the two objects has a zero where it goes from positive to negative. Like a saddle point. I have seen this referenced to as the point of charge neutrality

My issue is that I know this is an overly simplified picture of what is really going on. We know that the electron is really 'distributed' over some volume with certain probability to appear somewhere within the cloud when measured.

If the latter is so can we still talk about a 'point of charge neutrality' and, if so, how?

My feeling is that it depends where we measure the electron/the radius of the spherical shell we deem it most likely to appear in.

Thanks.

• Between two point charges is a plane of neutrality, not just a point. Small tweak. – Jon Custer Nov 25 '15 at 2:45

## 1 Answer

If you treat the 1s ground state's probability distribution as a classical charge density distribution (not really accurate, but I think the simplest way to interpret the problem), then there isn't one. This state is spherically symmetric, so the electric field is always radial and depends only on the radial coordinate and not on the angular coordinates. So the electric field is only zero when the total expectation value of charge inside a sphere of that radius is zero. But that never happens, since the 1s orbital decays asymptotically and never reaches zero at any finite radius. So now matter how far out you go, the +1 charge of the proton is never quite cancelled out by the expectation value for the total electron charge inside the sphere.