Question

The distance between the electron and proton in hydrogen atom is $5.3\times {10}^{-11}m$. Determine the magnitude of the ratio of electrostatic and gravitational force between them.
Given me $=9.1\times {10}^{-31}kg,mp=1.67\times {10}^{-27}kg,e=1.6\times {10}^{-19}C$ and $G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$

Answer 1

$F_e=\frac{k{q}_1{q}_2}{r^2}=\frac{k{e}^2}{r^2}$
$F_g=\frac{G{m}_e{m}_p}{r^2}$
$\frac{F_e}{F_g}=\frac{k{e}^2}{r^2}\times \frac{r^2}{G{m}_e{m}_e}$
$=\frac{k{e}^2}{G{m}_e{m}_p}$
$=\frac{9\times {10}^9\times (1.6\times {10}^{-19}{)}^2}{6.67\times {10}^{-11}\times 9.1\times {10}^{-31}\times 1.67\times {10}^{-27}}$
$=\frac{23.04\times {10}^{-29}}{101.364\times {10}^{-9}}$
$=0.227\times {10}^{40}$
$=2.27\times {10}^{39}$