The ratio of electrostatic and gravitational forces acting between electron and proton separated by a distance $5 \times 10^{-11} \, m,$ will be (Charge on electron = 1.6 × × 10 –19 C, mass of electron = 9.1 × × 10 –31 kg, mass of proton = $1.6 \times 10^{-27} \text{ kg},$ $G = 6.7 \times 10^{-11} \text{ Nm}^2 / \text{kg}^2$
Text Solution
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Gravitational force $F_{G} = \frac{G m_{e} m_{p}}{r^{2}}$
$F_{G} = \frac{6.7 \times 10^{-11} \times 9.1 \times 10^{-31} \times 1.6 \times 10^{-27}}{(5 \times 10^{-11})^{2}}$
= 3.9 × × 10 –47 N
Electrostatic force $F_{e} = \frac{1}{4 \pi \epsilon_0} \frac{e^2}{r^2}$
$F_{e} = \frac{9 \times 10^{9} \times 1.6 \times 10^{-19} \times 1.6 \times 10^{-19}}{\left(5 \times 10^{-11}\right)^{2}}$
= 9.22 × × 10 –8 N
So, $\frac{F_{e}}{F_{G}} = \frac{9.22 \times 10^{-8}}{3.9 \times 10^{-47}} = 2.36 \times 10^{39}$
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