devarshi-dt-logo

Question:

Suppose the charge of a proton and an electron differ slightly. One of them is -e, the other is (e+Δe). 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 Δe is of the order of [Given mass of hydrogen mh=1.67×10⁻²⁷Kg]

10⁻²⁰C

10⁻²³C

10⁻³⁷C

10⁻⁴⁰C

Solution:

Given : mh=1.67×10⁻²⁷ kg
Net charge on hydrogen atom q=(e+Δe)-e=Δe
Let the distance between them be d.
Equating gravitational force and the electrostatic force, we get
Gm²hd²=k(Δe)²/d²
Or (6.67×10⁻¹¹)(1.67×10⁻²⁷)²/d²=(9×10⁹)(Δe)²/d²
⇒ Δe=2.06×10⁻⁴⁰ C
The correct answer is option D.