Determine the ratio of the electrostatic force to the gravitational force between a proton and an electron?

Question

Fe/Fg. note k = 8.99*10^9 N m^2/C^2; G = 6.672 * 10^-11 N m^2/kg^2; me = 9.109 * 10^-31 kg; mp = 1.672 * 10^-27 kg

Answer 1

Let R be the distance between the electron and the proton

According to Newton's law of gravity the magnitude of the gravitational force between them is given by:

Fg = G∙me∙mp/R²

Electron as well as proton carry single elementary charge

|q| = e = 1.602∙10⁻¹⁹C

According to Coulomb's law the magnitude of electrostatic force between them is given by:

Fg = k∙e²/R²

Therefore

Fe/Fg = (k∙e²/R²) / (G∙me∙mp/R²)

= (k∙e²) / (G∙me∙mp)

= (8.99∙10⁹Nm²/C² ∙ (1.602∙10⁻¹⁹C)² ) / ( 6.672∙10⁻¹¹Nm²/kg ∙ 9.109∙10⁻³¹kg ∙ 1.672∙10⁻²⁷kg )

= 2.27∙10³⁹