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
$\frac{4 {πε}_{o} F d^{2}}{e^{2}}$
B
$\sqrt{\frac{4 {πε}_{o} F e^{2}}{d^{2}}}$
C
$\sqrt{\frac{4 {πε}_{o} F d^{2}}{e^{2}}}$
D
$\frac{4 {πε}_{o} F d^{2}}{q^{2}}$

Solution:

Let n be the number of electrons missing.

$F = \frac{1}{4 {πε}_{o}} \cdot \frac{q^{2}}{d^{2}} \Rightarrow q = \sqrt{4 {πε}_{o} d^{2} F} = n e ∴ n = \sqrt{\frac{4 {πε}_{o} F d^{2}}{e^{2}}}$

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