What is the gravitational force between the proton (1.67 ✕ 10-27 kg) and the electron (9.11 ✕ 10-31 kg) in a hydrogen atom if they are 3.00 ✕ 10-10 m apart?

Question

*Notice how small the answer is. This is why the gravitational force is normally ignored when thinking about forces at the atomic level. The force of gravity is incredibly small compared to the electrostatic force and other forces.

Answer 1

To find the force of gravitational attraction between these two particles, we treat them the same way that we would planets:

Force = G x M1 x M2 / r^2

G is the Universal Gravitation Constant

M1 is the mass of the proton (1.67 x 10^-27 kg)

M2 is the mass of the electron (9.11 x 10^-31 kg)

r is the distance between the two particles (3.00 x 10^-10 m)

The only thing we aren't provided is the Universal Gravitation Constant, which we look up and find is 6.67 x 10^-11 m^3 kg^-1 s^-2.

Plugging into the above equation, we get:

Force = [6.67 x 10^-11 m^3 kg^-1 s^-2] x [1.67 x 10^-27 kg] x [9.11 x 10^-31 kg] / [3.00 x 10^-10 m]^2

= 1.13 x 10^-48 Newtons