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. If equilibrium separation between electrons is R/n then write n.

Engineering

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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. If equilibrium separation between electrons is R/n then write n.

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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