According to Coulomb's Law, the electrostatic force of repulsion $F$ between two identical charges $q$ separated by a distance $d$ is given by: $F = \frac{1}{4\pi\varepsilon_0} \frac{q^2}{d^2}$

Rearranging this equation to solve for the charge $q$: $q^2 = 4\pi\varepsilon_0 F d^2$ $q = \sqrt{4\pi\varepsilon_0 F d^2}$

According to the principle of quantization of charge, the charge $q$ on an ion is an integral multiple of the elementary charge $e$ (charge of an electron). If $n$ is the number of electrons missing from the ion, then: $q = ne$

Substituting this into the expression for $q$: $ne = \sqrt{4\pi\varepsilon_0 F d^2}$ $n = \frac{\sqrt{4\pi\varepsilon_0 F d^2}}{e}$ $n = \sqrt{\frac{4\pi\varepsilon_0 F d^2}{e^2}}$