# The ratio of the gravitational force between electron and proton

Richard Ros

## Homework Statement

Some of the earliest atomic models held that the orbital velocity of an electron in an atom could be correlated with the radius of the atom. If the radius of the hydrogen atom is 10^−10 m and the electrostatic force is responsible for the circular motion of the electron, what is the ratio of the gravitational force between electron and proton to the electrostatic force? How does this ratio change if the radius of the atom is doubled? Explain {Answer: Fg/Fe = 4.39 x 10-40}.

## Homework Equations

fe = (1/4πε0)*(q^2/r^2)
fg = G m^2/r^2

## The Attempt at a Solution

The answer says Fg/Fe, so I divided fg/fe to get (Gm^2)/((9*10^9)q^2). I tried every different way possible but cannot manage to get the correct answer. Can anyone help me solve this problem, I've been stuck for a long time. I preferred you show me how to do it and how you got to the final answer.

## Answers and Replies

Ampere
What are you using as the masses? One of them would be the mass of a proton; the other would be the mass of an electron.

Richard Ros
Maybe my formula is wrong . Do you think this formula would be correct? G*me*mp/(9*10^9 n m^2/c^2)*q1*q2?

Richard Ros
Oh never mind. I got the answer. How does the ratio change if radius if atom is doubled?

Ampere
What do you think - does it look like the formula depends on the radius?

Richard Ros
Since the radius isn't included in the formula. I'm assuming it doesn't matter?

Ampere
Yep.