Answer:
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
<u>Fe = 9 x 10⁻⁹ N </u>
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
<u>Fg = 3.97 x 10⁻⁴⁶ N</u>
Dividing both forces:
Fe/Fg = (9 x 10⁻⁹ N)/(3.97 x 10⁻⁴⁶ N)
<u>Fe = 2.26 x 10³⁷ Fg</u>
