Question

For a while in the early 20th century one proposed model for the structure of atoms was that a positive point charge (the nucleus) +Ze was at the center of a charged sphere of radius R and charge −Ze. To be clear, the negative charge in the sphere was proposed to be spread through the volume of the sphere, not on its surface. Z is the atomic number.

(a) In terms of the symbols, Z and R, what is the strength of the electric field at the surface of this model of the atom?

(b) Assume that the negative charge is spread uniformly through the volume of the atom. Derive an expression for the electric field strength as a function of distance from the nucleus for r < R.

(c) Look up the values of R and Z for iron (use the most common isotope). Plot your result from 3b to plot the E-field magnitude vs. distance from the nucleus. Be sure to evaluate the values found on the vertical scale of your graph.

(d) Suppose the charge density in the electron cloud is not uniform. Suppose that it is zero at the “surface” of the atom (dubious concept...) and declines linearly from a maximum value at the center of the atom according to the function ρe(r) = ρ0(r/R − 1). Find the expression for the E-field magnitude vs. distance from nucleus inside the atom if this is the case.

Answer 1

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