91Ó°ÊÓ

1. Electrostatic force on either of the proton is equal to the magnitude of the gravitation force on a proton.
2. Mass of the proton,$\mathrm{m}=1.67×{10}^{−27}\mathrm{kg}$
3. Acceleration due to gravity,$\mathrm{g}=9.8\mathrm{m}/{\mathrm{s}}^2$

Using the concept of gravitational force and Force from Coulomb's law, we can get the value of the distance between the two protons.

Formulae:

The magnitude of the electrostatic force between any two protons of charge q,

${\mathrm{F}}_{\mathrm{e}}={\mathrm{kq}}^2/{\mathrm{r}}^2$ (i)

The magnitude of gravitational force, ${\mathrm{F}}_{\mathrm{g}}=\mathrm{mg}$ (ii)

The problem compares the electrostatic force between two protons and the gravitational force by Earth on a proton. Thus, equating equations (i) and (ii) and the given data, we can get the distance between the two protons as follows:

$\begin{array}{c}{\mathrm{kq}}^2/{\mathrm{r}}^2=\mathrm{mg}\\ \mathrm{r}=\mathrm{q}\sqrt{\frac{\mathrm{k}}{\mathrm{mg}}}\\ =(1.60×{10}^{−19}\mathrm{C})\sqrt{\frac{9.00×{10}^9{\mathrm{Nm}}^2/{\mathrm{C}}^2}{(1.67×{10}^{−27}\mathrm{kg})(9.8\mathrm{m}/{\mathrm{s}}^2)}}\\ =0.119\mathrm{m}\end{array}$

Hence, the value of the distance between the protons is $0.119\mathrm{m}.$