- #1
ratphysicsfun
- 1
- 0
Homework Statement
The IPA potential-energy function U(r) is the potential energy "felt" by an atomic electron in the average field of the other Z - 1 electrons plus the nucleus. If one knew the average charge distribution rho(r) of the Z - 1 other electrons, it would be a fairly simple matter to find U(r). The calculation of an accurate distribution rho(r) is very hard, but it is easy to make a fairly realistic guess. For example, one might guess that rho(r) is spherically symmetric and given by rho(r)=(rho.naught)exp(-r/R) where R is some sort of mean atomic radius. (a) Given that rho(r) is the average charge distribution of Z - 1 electrons, find rho.naught in terms of Z, e, and R. (b) Use Gauss's law to find the electric field E at a point r due to the nucleus and the charge distribution rho. (c) Verify that as r goes to 0 and r goes to infinity, E bahaves as required by F= Zkexp2/(r^2) for r inside all other electrons, and F=kexp2/(r^2) for r outside all other electrons.
Homework Equations
F=Zke^2/(r^2), F=ke^2/(r^2), U(r)= -ke^2/r for r outside other electrons, U(r)=~-Zke^2/r as r goes to zero (inside other electrons)The Attempt at a Solution
I'm not sure how rho fits into my equations. I know it's related to e, and Z.
Last edited: