Answer to Question #99898 in Physics for Fahad

Question

show that the electrical force between the electron and proton in the hydrogen atom is approximately 2.2e39 times stronger than the gravitational force between them.
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Answer 1

The absolute value of electric force between proton and electron in the hydrogen atom is $F_E = \frac{k e^2}{R^2}$, where $k = 9 \cdot 10^9 N m^2 C^{-2}$ is Coulomb constant, $e = 1.6 \cdot 10^{-19} C$ is the charge of the electron, $R$ is the radius of the hydrogen atom.

The absolute value of the gravitational force between proton and electron in the hydrogen atom is $F_G = \frac{G m_e m_p}{R^2}$, where $G = 6.67 \cdot 10^{-11} m^3 kg^{-1}s^{-2}$ is the gravitational constant, $m_e = 9.11 \cdot 10^{-31} kg$ is the mass of the electron, $m_p = 1.67 \cdot 10^{-27} kg$ is the mass of the proton.

The ratio of $F_E$ to $F_G$ is $\frac{k e^2}{R^2} \frac{R^2}{G m_e m_p} = \frac{k e^2}{G m_e m_p}$.

Calculating with the values above, obtain $\frac{F_E}{F_G} \approx 2.2 \cdot 10^{39}$.