Suppose the charge of a proton and an electron differ slightely. One of them is `-e`, the other is `(e+Deltae)`. If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance `d` (much greater than atomic size) apart is zero. Then `Deltae` is of the order of [Given mass of hydrogen `m_(h)=1.67xx10^(-27)kg`]

Options

A. `10^(-20)C`
B. `10^(-23)C`
C. `10^(-37)C`
D. `10^(-47)C`

Answer

C

Explanation

Net charge on one H - atom = `-e + (e + Deltae) = Deltae`
Net electrostatic force between two H atoms
`= (k(Deltae)(Deltae))/(d^2)` repulsive
Net gravitational force between two H atoms `=(G(m)(m))/d^2`
For equilibrium : `(k(Deltae)^2)/(d^2)=(Gm^2)/(d^2)`
`Deltae^2 =(Gm^2)/(k)=((6.67 xx10^(-11))xx(1.67 xx10^(-27))^(2))/((9xx10^9))`
`Deltae^2` is of the order of `10^(-74)`
`Deltae` is of the order of `10^(-37)` C