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

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

(a) \( 10^{-23} \, \text{C} \)

(b) \( 10^{-37} \, \text{C} \)

(c) \( 10^{-47} \, \text{C} \)

(d) \( 10^{-20} \, \text{C} \)

Answer :  (b) \( 10^{-37} \, \text{C} \)

\( F_g = F_E \)

\( \frac{G \, m_1 m_2}{d^2} = \frac{k \, q_1 q_2}{d^2} \)

\( +5c - 2c = 3c \)

\( 6.67 \times 10^{-11} \times (1.67 \times 10^{-27})^2 = 9 \times 10^9 (\Delta e)^2 \)

\( 6.67 \times (1.67)^2 \times 10^{-11 - 54 - 9} = (\Delta e)^2 \)

\( i \times 10^{-74} = (\Delta e)^2 \)