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Two positives ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)

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$\frac{4 {πε}_{0} {Fd}^{2}}{e^{2}}$

$\sqrt{\frac{4 {πε}_{0} {Fe}^{2}}{d^{2}}}$

$\sqrt{\frac{4 {πε}_{0} {Fd}^{2}}{e^{2}}}$

$\frac{4 {πε}_{0} {Fd}^{2}}{q^{2}}$

answer is C.

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Detailed Solution

$\begin{aligned} F = \frac{1}{4 π ε_{0}} \frac{(ne) (ne)}{d^{2}}; F = \frac{n^{2} e^{2}}{4 π ε_{0} d^{2}} \\ \Rightarrow n^{2} = \frac{4 π ε_{0} {Fd}^{2}}{e^{2}} \Rightarrow n = \sqrt{\frac{4 π ε_{0} {Fd}^{2}}{e^{2}}} \end{aligned}$

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