Question

What is the magnitude of the electrostatic force between a singly charged sodium ion (${\mathbf{Na}}^{\mathbf{+}}$, of chargerole="math" localid="1661780999867" $\mathbf{+}\mathbf{e}$) and an adjacent singly charged chlorine ion (${\mathbf{Cl}}^{\mathbf{-}}$, of charge$\mathbf{-}\mathbf{e}$) in a salt crystal if their separation is$\mathbf{2.82}\mathbf{}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathbf{\text{\hspace{0.17em}m}}$?

Short answer

The magnitude of the electrostatic force between sodium and chlorine is $2.89\times {10}^{-9}\text{N}$.

Step-by-step solution

Stating the given data

1. Singly charged sodium ion, ${\mathrm{Na}}^{+}$, of charge$+\mathrm{e}$ and a singly charged chlorine ion, ${\mathrm{Cl}}^{-}$, of charge $-\mathrm{e}$.
2. The separation between the ions, $\mathrm{r}=2.82\times {10}^{-10}\text{m}$.

Understanding the concept of Coulomb’s law

Using the formula of Coulomb's law, we can get the magnitude value of the electrostatic force of attraction for oppositely charged bodies.

Formula:

The magnitude of the electrostatic force between any two particles,$\mathrm{F}=\mathrm{k}\frac{\left|{\mathrm{q}}_1\right|\left|{\mathrm{q}}_2\right|}{{\mathrm{r}}^2}$ (i)

Calculation of the magnitude of the electrostatic force

The magnitude of the force using the given data in the equation (i) is

$\begin{array}{c}\mathrm{F}=\mathrm{k}\frac{{\mathrm{e}}^2}{{\mathrm{r}}^2}\\ =9.00\times {10}^9{\text{Nm}}^{\text{2}}{\text{/C}}^{\text{2}}\cdot \frac{{(1.60\times {10}^{-19}\text{C})}^2}{{(2.82\times {10}^{-10}\text{m})}^2}\\ =2.89\times {10}^{-9}\text{N}\end{array}$

Hence, the value of the force is $2.89\times {10}^{-9}\text{N}$.