The ratio of electric and gravitational force between two protons. Charge of each proton is $1.6\times {10}^{-19}\mathrm{C}$, mass is $1.67\times {10}^{-27}\mathrm{Kg}$ and $\mathrm{G} = 6.67 \times {10}^{–11}{\mathrm{Nm}}^2{\mathrm{Kg}}^{–2}$.

Given Data: Determine the ratio of electric and gravitational force between two protons.

Formula Used:  $\frac{G{\left(m_p\right)}^2}{r^2},=\frac{K\left(e\right)\left(e\right)}{r^2}$

Detailed Solution:

Gravitational force $=\frac{\mathrm{G}{\left({\mathrm{m}}_{\mathrm{p}}\right)}^2}{{\mathrm{r}}^2}$

Electric force $=\frac{\mathrm{K}\left(\mathrm{e}\right)\left(\mathrm{e}\right)}{{\mathrm{r}}^2}$

Ratio $=\frac{\mathrm{K}{\left(1.6\times {10}^{-19}\right)}^2}{{\mathrm{r}}^2}\times \frac{{\mathrm{r}}^2}{\mathrm{G}\times {\left(1.67\times {10}^{-27}\right)}^2}$

$=\frac{\left(9\times {10}^9\right)\times {\left(1.6\times {10}^{-19}\right)}^2}{\left(6.67\times {10}^{-11}\right){\left(1.67\times {10}^{-27}\right)}^2}$

$=1.23\times {10}^{20}\times {10}^{16}=1.23\times {10}^{36}$