Estimate the ratio of electric force and gravitational force between electron and proton in a hydrogen atom.
`m_(e) = 9 xx 10^(-31)` kg `m_(p) = 1.6 xx 10^(-27)` kg e = `1.6 xx 10^(-19)` C
Distance between electron and proton = `0.5 xx 10^(-80)` m
`G = 6.6 xx 10^(-11) N -m^(2) // kg^(2)`

Explanation

Charge on electron , `q_(1) = 1.6 xx 10^(-19) C`
Charge on proton , `q_(2) = 1 . 6 xx 10^(-19) C`
Distance between them , `r = 0.5 xx 10^(-80)` m
Mass of electron , `m_(e) = 9 xx 10^(-31)` kg
Mass of proton , `m_(p) = 1.6 xx 10^(-27)` kg
Now , electric force , `F_(e) = (kq_(1) q_(2))/(r^(2))`
= `(1)/(4 pi epsi_(0)) ((1.6 xx 10^(-19)) (1.6 xx 10^(-19)))/((0.5 xx 10^(-80))^(2))`
`= (9 xx 10^(9) xx (1.6 xx 10^(-19))^(2))/((0.5 xx 10^(-80))^(2))`
Gravitational force , `F_(G) = (G m_(e) m_(p))/(r^(2))`
= `((6.6 xx 10^(-11)) xx (9 xx 10^(-31)) xx (1 .6 xx 10^(-27)))/((0.5 xx 10^(-80))^(2))`
`(F_(e))/(F_(G)) = ((9 xx 10^(9)) xx (16 xx 10^(-19))^(2))/((6.6 xx 10^(-11)) xx (9 xx 10^(-31)) xx (1.6 xx 10^(-27)))`
`(F_(e))/(F_(G)) = 2.3 xx 10^(39)`