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Suppose the charge of a proton and an electron differ slightly. One of them is −e, the other is (e + Δe). If the net 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 × 10⁻²⁷ kg]:

1. 10⁻²³ C
2. 10⁻³⁷ C
3. 10⁻⁴⁷ C
4. 10⁻²⁰ C

Correct answer: 10⁻⁴⁷ C

Solution

For the net force to be zero, the electrostatic force must balance the gravitational force. Using Coulomb's law and Newton's law of gravitation, we equate k(Δe)^2/d^2 = G(mₕ)^2/d^2. Simplifying, Δe = √(G * (mₕ)^2 / k). Substituting values, Δe ≈ 10⁻⁴⁷ C.

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