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

The Correct Option is A

The coulombian force (\(F_c\)) is calculated as:

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

The gravitational force (\(F_g\)) is calculated as:

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

The ratio of these forces is:

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

The result is approximately \(10^{39}\).