The ratio of coulomb's electrostatic force to the gravitational...

The ratio of coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is

2.4 \times 10^{39}

. The ratio of the proportionality constant,

\mathrm{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 \times 10^{-19} \mathrm{C}

, the mass of the electron

=9.11 \times 10^{-31} \mathrm{~kg}

, the mass of the proton =

\left.1.67 \times 10^{-27} \mathrm{~kg}\right)

Options

A. $10^{20}$

A.T.Q, we have,

\begin{aligned} \frac{\mathrm{F}_e}{\mathrm{~F}_{\mathrm{G}}} & =\frac{\frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{r^2}}{\frac{\mathrm{G} m_1 m_2}{r^2}} \\ 2.4 \times 10^{39} & =\frac{\mathrm{K}}{\mathrm{G}} \times \frac{\left(1.6 \times 10^{-19}\right)^2}{\left(9.1 \times 10^{-31} \times 1.67 \times 10^{-22}\right)} \\ & {\left[\because \mathrm{K}=\frac{1}{4 \pi \varepsilon_0}\right] } \end{aligned}

Hence,

\begin{aligned} \frac{\mathrm{K}}{\mathrm{G}} & =\frac{2.4 \times 10^{39} \times 9.1 \times 10^{-31} \times 1.67 \times 10^{-27}}{1.6 \times 10^{-19} \times 1.6 \times 10^{-19}} \\ & =14.247 \times 10^{19} \\ & =1.4247 \times 10^{20} \approx 10^{20} \end{aligned}