Answer to Question #187194 in Electricity and Magnetism for Masoom

Question

. Using a hydrogen atom as an example, compare the gravitational 

and the electrostatic forces between a proton and an electron

Answer 1

Using Coulomb’s Law

$F = \dfrac{k q_1 q_2}{ r^2}$

We have, $q_1 = q_2 = 1.6 \times 10^-{19} C$

$r = 0.05nm$ (in the case of Hydrogen atom)

Hence,

$F = \dfrac{9 \times 10^9 \times 1.6 \times 10^{-19} \times 1.6 \times 10^{-19}}{(0.05\times 10^{-9})^2}$

$F = 9.216 \times 10^{-8}N$

Using Newton’s Universal Gravitational Law,

$F =\dfrac{ G m_1 m_2 }{ r^2}$

We can determine the strength of the gravitational force between the proton and electron.

Mass of electron $= m_1 = 9.1 \times 10^{-31}kg$

Mass of proton $= m_2 = 1.67 \times 10^{-27}kg$

Hence,

$F = \dfrac{6.67 \times10^{-11} \times 9.1 \times 10^{-31} \times 1.67 \times 10^{-27}}{(0.05 \times 10^{-9})^2}$

$F = 40.544 \times 10^{-45}N$

Hence, we can compare the gravitational and the electrostatic forces between a Proton and an Electron.