Question

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of:

• A. 1039
• B. 1019
• C. 1029
• D. 1036

Answer 1

Answer: (A)

1039

Answer 2

The coulombian force ($F_c$) is given by:

$F_c = \frac{k Q_1 Q_2}{r^2} = \frac{9 \times 10^9 \times 1.6 \times 10^{-19} \times 1.6 \times 10^{-19}}{r^2}$

The gravitational force ($F_g$) is given by:

$F_g = \frac{G m_1 m_2}{r^2} = \frac{6.67 \times 10^{-11} \times 9.1 \times 10^{-31} \times 1.6 \times 10^{-27}}{r^2}$

The ratio of the forces is:

$\frac{F_c}{F_g} \approx 0.23 \times 10^{40} \approx 2.3 \times 10^{39}$

Therefore, the answer is approximately $10^{39}$.