# Gravitational Force and Electric Force

## Homework Statement

A hydrogen atom is composed of a nucleus containing a single proton, about which a single electron orbits. The electric force between the two particles is about 2.3 x 10^39 times greater than the gravitational force. Suppose we could change the distance between the proton and electron, could we adjust the distance between the two particles and find a separation at which the electric and gravitational forces are equal?

a. Yes, we must move the particles farther apart.
b. Yes, we must move the particles closer together.
c. No, at any distance the forces will be different.

## Homework Equations

F_g = (G*m_p*m_e)/r^2 and F_ele = (k*q_p*q_e)/r^2,

where G = 6.67*10^-11 and k = 8.988 *10^9

## The Attempt at a Solution

Is the correct answer choice c. No, at any distance the forces will be different????

I tried solving it mathematically by having the two above equations equal each other, but the r values cancel out. If both are placed on one side:

G*m_p*m*e*r^2 = k*q_e*q_p*r^2

r^2*[(G*m_p*m_e) - (k*q_p*q_e)] = 0

r = 0 m

Thanks.