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

Here, electrostiac force = gravitonal force
`(k(e + Delta e)^(2))/(d^(2)) = (G m_(h) m_(h))/(d^(2))`
`(e + Delta e)^(2) = (G m_(h) m_(h))/(k)`
`= (6.7xx10^(-11)(1.67xx10^(-27))^(2))/(9xx10^(9))`
`(6.7xx1.67xx1.67)/(9) xx10^(-74)`
`e + Delta e = (2.076xx10^(-74))^(1//2) = 1.44xx10^(-37)`
Hence `Delta e` is of the order of `10^(-37) C`