Question

The electron and proton of a hydrogen atom are separated (on the average) by a distance of approximately 5.3x10^-11 m. Find the magnitude of the electric force and the gravitational force between the two particles

Answer 1

Given:

$r=5.3*10^{-11}\:\rm m$

$e=1.6*10^{-19}\:\rm C$

$m_e=9.1*10^{-31}\:\rm kg$

$m_p=1.67*10^{-27}\;\rm kg$

The magnitude of the electric force

$$F_e=k\frac{q_1q_2}{r^2}=k\frac{e^2}{r^2}\\ =\rm 9*10^9*\frac{(1.6*10^{-19})^2}{(5.3*10^{-11})^2}=8.2*10^{-8}\:N$$

The magnitude of the gravitational force

$$F_g=G\frac{m_1m_2}{r^2}\\ =\rm 6.67*10^{-11}*\frac{1.67*10^{-27}*9.1*10^{-31}}{(5.3*10^{-11})^2}=3.6*10^{-47}\:N$$