Using thomson’s model of the atom, consider an atom consisting of two electrons, each of charge –e, embeded in a sphere of charge + 2e and radius R. In equilibrium each electron is at distance d from the centre of the atom. What is equilibrium separation between electrons?

Engineering

Physics

Equilibrium

Charge and Coulombs Law

Electric Flux and Gauss Law and its Applications

Question

Using thomson’s model of the atom, consider an atom consisting of two electrons, each of charge –e, embeded in a sphere of charge + 2e and radius R. In equilibrium each electron is at distance d from the centre of the atom. What is equilibrium separation between electrons?

R/3

R/4

R/2

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Field due to +2e charge sphere at distance d from the centre    E = $\frac{2 ked}{R^{3}}$
Force on electron    F = eE = $\frac{2 {ke}^{2} d}{R^{3}}$
F_c = $\frac{{ke}^{2}}{4 d^{2}}$
$\frac{2 {ke}^{2} d}{R^{3}} = \frac{{ke}^{2}}{4 d^{2}} \Rightarrow$ R³ = 8d³   ⇒   R = 2d