Electric field inside hydrogen atom.

[onyx390]

Homework Statement

A hydrogen atom can be considered as having a central point-like proton of positive charge +e and an electron of negative charge -e that is distributed about the proton according to the volume charge density rho=A*exp(-2r/a_1). Here A is a constant, a_1 = .53x10^(-10)m is the Bohr radius, and r is the distance from the center of the atom. a) Using the fact that hydrogen is electrically neutral, find A. b) Then find the electric field produced by the atom at the Bohr radius.

Homework Equations

The Attempt at a Solution

I've been struggling at part a. Once I find A, I can just integrate and solve for the electric field. However, although I know that hydrogen being electrically neutral is what will help me solve this, I don't know what this implies. My main guess is that I set r equal to a_1. However, that still leaves the unknown of q. Can someone explain to me how hydrogen's neutrality is relevant? Once I figure that out, I'm sure that the problem will become much simpler for me. Thank you in advance.

 

[Mr.Amin]

The term "A" is probably going to be composed of two parts that add together.
Try thinking about how to use a combination of step functions (or delta functions) to represent the electron and proton. Arfken has a little bit of material on this.

If you have not had delta or step functions, I will try to think of other means. But I think most hydrogen solutions will have "A" as two terms.

 

[LuisVela]

hi, i would suggest to try to find the total charge of the whole atom with an integral of the density function over the region, then equal this to 0 (q=0,neutral atom) and probably you will come out with a condition (answer) for your constant A.