Question

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)

• A. $\frac{4\pi {ϵ}_{0}F{d}^2}{e^2}$
• B. $\sqrt{\frac{4\pi {ϵ}_{0}F{e}^2}{d^2}}$
• C. $\sqrt{\frac{4\pi {ϵ}_{0}F{d}^2}{e^2}}$
• D. $\frac{4\pi {ϵ}_{0}F{d}^2}{q^2}$

Answer 1

The correct option is C $\sqrt{\frac{4\pi {ϵ}_{0}F{d}^2}{e^2}}$

Let the number of $e$ missing in ion be $n$.

So, charge on each ion, $\left(q\right)=ne$

Electrostatic force of repulsion between ions is given by,

$F=\frac{k{q}_1{q}_2}{r^2}$

$(\because q_1=q_2=ne\text{and}r=d)$

$\Rightarrow F=\frac{k\left(ne\right)\left(ne\right)}{d^2}$

$\Rightarrow F=\frac{n^2{e}^2}{4\pi {ϵ}_0{d}^2}$

$\Rightarrow n=\sqrt{\frac{4\pi {ϵ}_{0}F{d}^2}{e^2}}$

Hence, option $\left(c\right)$ is the correct answer.

$\begin{array}{c}\text{Why this question ?}\\ \text{According to the quantization of charge}\\ \text{the charge q can always be represented}\\ \text{as an integral multiple of charge of}\\ \text{an electron}\end{array}$