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According to Coulomb's law, the force of repulsion between the two positive ions each of charge \(q\) separated by a distance \(d\) is given by

\(F =\frac{1}{4 \pi \varepsilon_{0}} \frac{(q)(q)}{d^{2}} \)

\(F =\frac{q^{2}}{4 \pi \varepsilon_{0} d^{2}}\)

\(q^{2} =4 \pi \varepsilon_{0} F d^{2} \)

\(q =\sqrt{4 \pi \varepsilon_{0} F d^{2}}..........(i)\)

Since, \(q=ne\)

where,

\(n=\) number of electrons missing from each ion

\(e=\) magnitude of charge on electron

\(\therefore n = \frac{q}{e}\)

\(n = \frac{{\sqrt {4\pi {\varepsilon _0}F{d^2}} }}{e}\)      (Using \((i)\))

\(=\sqrt{\frac{4 \pi \varepsilon_{0} F d^{2}}{e^{2}}}\)