Correct Answer - Option 3 :
\(\sqrt {\frac{{4\pi {\varepsilon _0}F{d^2}}}{{{e^2}}}} \)
Concept:
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:
\(F = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{\left( q \right)\left( q \right)}}{{{d^2}}}\)
\(F = \frac{{{q^2}}}{{4\pi {\varepsilon _0}{d^2}}}\) ---(1)
q = ne
n = number of electrons missing from each ion
e = magnitude of charge on electron
Analysis:
Rearranging Equation (1), we get:
\({q^2} = 4\pi {\varepsilon _0}F{d^2}\)
\(q = \sqrt {4\pi {\varepsilon _0}F{d^2}} \)
With q = ne
\( n = \frac{q}{e} = \sqrt {\frac{{4\pi {\varepsilon _0}F{d^2}}}{{{e^2}}}} \)