Suppose the charge of a proton and an electron differ slightly. One of them is e, and the other is (e + Δe). If the net electrostatic and gravitational force between two hydrogen atoms at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of (mass of hydrogen mₕ = 1.67 × 10⁻²⁷ kg):
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Question

Suppose the charge of a proton and an electron differ slightly. One of them is e, and the other is (e + Δe). If the net electrostatic and gravitational force between two hydrogen atoms at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of (mass of hydrogen mₕ = 1.67 × 10⁻²⁷ kg):

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G1 Physics · Accepted Answer

Step 1: Each hydrogen atom has residual charge Δe. Step 2: Set k(Δe)²/d² = Gmₕ²/d². Step 3: Δe = mₕ√(G/k) = 1.67 × 10⁻²⁷√(6.67 × 10⁻¹¹/(9 × 10⁹)) ≈ 1.44 × 10⁻³⁷ C.