Q: 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 m_{h} = 1.67 × 10^{-27} kg]

(a) 10^{-23} C

(b) 10^{-37} C

(c) 10^{-47} C

(d) 10^{-20} C

Ans: (b)

Sol: $F_g = F_e $

$ \frac{G m^2}{r^2} = \frac{1}{4\pi \epsilon_0}\frac{(\Delta e)^2}{r^2} $

$ \Delta e = \sqrt{G m^2 4 \pi \epsilon_0}$

$ = \sqrt{6.67 \times 10^{-11} \times (1.67 \times 10^{-27})^2 \times \frac{1}{9 \times 10^9} } $

= 10^{-37} C