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 of an electron) ?

 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 of an electron) ?

(a) \( \dfrac{4\pi \varepsilon_0 F d^2}{e^2} \)

(b) \( \sqrt{\dfrac{4\pi \varepsilon_0 F e^2}{d^2}} \)

(c) \( \sqrt{\dfrac{4\pi \varepsilon_0 F d^2}{e^2}} \)

(d) \( \dfrac{4\pi \varepsilon_0 F d^2}{q^2} \)

Answer : (c) \( \sqrt{\dfrac{4\pi \varepsilon_0 F d^2}{e^2}} \)

Concept: As we remove N no. of electrons from an atom, it acquires a positive charge of Ne. (Small n we use for no. density so capital N used here.)

Coulomb's Law : \( F = \dfrac{1}{4\pi\varepsilon_0} \cdot \dfrac{q_1 q_2}{r^2} \)

\( F = \dfrac{1}{4 \pi \varepsilon_0} \cdot \dfrac{(N e)(N e)}{d^2} \)

\( N^2 = \dfrac{F \cdot 4 \pi \varepsilon_0 \cdot d^2}{e^2} \)

\( N = \sqrt{\dfrac{ 4 \pi \varepsilon_0 F d^2}{e^2}} \)