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The ratio of Coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is $2.4\times10^{39}$. The ratio of the proportionality constant, $K=\frac{1}{4\pi\varepsilon_0}$ to the Gravitational constant G is nearly (Given that the charge of the proton and electron each $=1.6\times10^{-19}$ C, the mass of the electron $=9.11\times10^{-31}$ kg, the mass of the proton $=1.67\times10^{-27}$ kg):
Detailed Solution
$\frac{F_E}{F_G}=\frac{kq_1q_2/r^2}{Gm_1m_2/r^2}=\frac{k}{G}\cdot\frac{(1.6\times10^{-19})^2}{(1.67\times9.11)\times10^{-58}}$. So $2.4\times10^{39}=\frac{k}{G}\cdot\frac{2.56\times10^{-38}}{15.2\times10^{-58}}$, giving $\frac{k}{G}\approx10^{20}$.