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Two positive 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)
$\frac{{4\pi {\varepsilon _0}F{d^2}}}{{{e^2}}}$
$\sqrt {\;\frac{{4\pi {\varepsilon _0}F{e^2}}}{{{d^2}}}} $
$\sqrt {\;\frac{{4\pi {\varepsilon _0}F{d^2}}}{{{e^2}}}} $
$\;\frac{{4\pi {\varepsilon _0}F{d^2}}}{{{q^2}}}$
Solution
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 $(i)$)
$=\sqrt{\frac{4 \pi \varepsilon_{0} F d^{2}}{e^{2}}}$
