An early model for an atom considered it to have a positively charged point nucleus of charge Z e , surrounded by a uniform density of negative charge upto a radius R . The atom as a whole is neutral. The electric field at a distance r from the nucleus is (r

Step-by-step solution

Charge on nucleus =+Z e Total negative charge =- Ze ( atom is electrically neutral) Negative charge density, = charge volume = -Z e 4 3 R^3 Consider a Gaussian surface with radius r . By Gauss's theorem, Charge enclosed by Gaussian surface, q=Z e+ 4 r^3 3 =Z e-Z e r^3 R^3 (Using (i)) From (ii), E(r)= q 4 ₀ r^2 = Z e- Z e r^3 R^3 4 ₀ r^2 = Z e 4 ₀ [ 1 r^2 - r R^3 ]