An electron and a proton are separated by a distance of 1.6×10−10m (roughly the diameter of a single atom). The masses of the electron and proton are mp=1.673×10−27kg
and me=9.11×10−31kg,
respectively. The elementary charge e=1.602×10−19C.
The universal gravitational constant G=6.67×10−11N⋅m2/kg2
and the coulomb constant k=8.988×109N⋅m2/C2
What is the magnitude Fe of the electric force between the electron and the proton? Fe= 7.11×10−9N
What is the magnitude Fg
of the gravitational force between the electron and the proton?
Fg= 31.37×10−49N
In this scenario, how many times stronger is the electric force than the gravitational force?

Fe = 9 x 10⁻⁹ N

Fg = 3.97 x 10⁻⁴⁶ N

Fe = 2.26 x 10³⁷ Fg

Explanation:

First we find electric force by Coulomb's Law as follows:

Fe = kq₁q₂/r²

where,

Fe = electric force = ?

k = Coulomb's Constant = 9 x 10⁹ N.m²/C²

q₁ = q₂ = charges on electron and proton = 1.6 x 10⁻¹⁹ C

r = distance between electron and proton = 1.6 x 10⁻¹⁰ m

Therefore,

Fe = (9 x 10⁹ N.m²/C²)(1.6 x 10⁻¹⁹ C)(1.6 x 10⁻¹⁹ C)/(1.6 x 10⁻¹⁰ m)²

Fe = 9 x 10⁻⁹ N

Now we find gravitational force by Newton's Law of Gravitation as follows:

Fg = Gm₁m₂/r²

where,

Fg = gravitational force = ?

G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²

m₁ = mass of electron = 9.11 x 10⁻³¹ kg

m₂ = mass of proton = 1.673 x 10⁻²⁷ kg

r = distance between electron and proton = 1.6 x 10⁻¹⁰ m

Therefore,

Fg = (6.67 x 10⁻¹¹ N.m²/kg²)(9.11 x 10⁻³¹ kg)(1.673 x 10⁻²⁷ kg)/(1.6 x 10⁻¹⁰ m)²

Fg = 3.97 x 10⁻⁴⁶ N

Dividing both forces:

Fe/Fg = (9 x 10⁻⁹ N)/(3.97 x 10⁻⁴⁶ N)

Fe = 2.26 x 10³⁷ Fg