The electrostatic force between two point charges and the gravitational attractive force between two point masses- both are inversely proportional to the square of the distance between the charges and the masses, respectively.
(1)(a) Compare the eletrostatic force `(F_(C))` and the gravitational force `(F_(G))` between an electron and a proton. (b) Compare `F_(C)` and `F_(G)` between two protons.
(ii) Find out the accelerations of an electron and of a proton due to the electrostatic force between them when htey are placed at a distance of `1 Å`

Explanation

(a) An electron and a proton have the same amount of charge e.
`therefore` Electrostatic force, `F_(C) = 1/(4pi epsilon_(0)).e^(2)/r^(2)`
Gravitational force, `F_(G) = G.(m_(e)m_(p))/(r^(2))`
`therefore F_( c)/F_(G) = 1/(4pi epsilon_(0)) e^(2)/r^(2) .r^(2)/(gm_(e)m_(p)) = 1/(4pi epsilon_(0)).e^(2)/(Gm_(e)m_(p))`
`=((9 xx 10^(9)) xx (1.6 xx 10^(-19))^(2))/((6.67 xx 10^(11)) xx (9.1 xx 10^(-31)) xx (1.67 xx 10^(-27))`
`2.27 xx 10^(39)`
(b) Electrostatioc force between two protons,
`F_( C) =1/(4pi epsilon_(0)) .e^(2)/r^(2)`
The gravitational force betweenthem,
`F_(G) = (Gm_(p)^(2))/(r^(2))`
`therefore F_(C)/F_(G) = 1/(4pi epsilon_(0)).e^(2)/(Gm_(p)^(2))`
`=(9 xx 10^(9)) xx ((1.67 xx 10^(-19))^(2))/((6.67 xx 10^(-11)) xx (1.67 xx 10^(-27))^(2))`
`=1.24 xx 10^(36)`
(ii) The electrostatic force between an electron and a proton.
`F_(C) = 1/(4pi epsilon_(0)).e^(2)/r^(2) = (9 xx 10^(9)) xx ((1.6 xx 10^(-19))^(2)/(10^(-10))^(2))` `[therefore r=1 Å = 10^(-10)m]`
`therefore ` Acceleration of the electron,
`a_(e) = F_(C)/m_(e) = (2.3 xx 10^(-8))/(9.1 xx 10^(-31)) = 2.5 xx 10^(22) ms^(-2)`
Acceleration of the proton,
`a_(p) = F_(C)/m_(p) = (2.3 xx 10^(-8))/(1.67 xx 10^(-27)) = 1.4 xx 10^(19) m.s^(-2)`