Using Thomson's model of the atom, consider an atom consisting of two electrons, each of charge `-e`, embedded in a sphere ofcharge + 2e and radius R. In equilibrium each electron is at distanced from the centre of the atom. What is equilibrium separation between electrons ?

Options

A. R
B. R/2
C. R/3
D. R/4

Answer

B

Explanation

Field due to +2e charge sphere at distance d from the centre is
`E=(K(2e)d)/R^3` Force due to charge +2e on -e
`F_1=€ E=(2 ke^2d)/R^3` Electric force between two charges
`F_2(ke^2)/(4d^2)` For equilibriu, we have `F_1=F_2`
`(2 Ke^2 d)/R^3=(Ke^2)/(4d^2) implies R^3=8d^3 implies R=2d`