Answer:
Electric force is 1.23 x 10³⁶ times stronger than gravitational force.
Explanation:
First, we will calculate the gravitational force using Newton's Law:
[tex]F_G = \frac{Gm^2}{r^2}\\\\[/tex]
where,
F_G = Gravitational Force = ?
G = Gravitational Constant = 6.67 x 10⁻¹¹ Nm²/kg²
m = mass of proton = 1.67 x 10⁻²⁷ kg
r = distance between protons
Therefore,
[tex]F_G = \frac{(6.67\ x\ 10^{-11}\ Nm^2/kg^2)(1.67\ x\ 10^{-27}\ kg)^2}{r^2}\\\\F_G = \frac{1.86\ x\ 10^{-64}\ Nm^2}{r^2}\\\\[/tex]
Now, we will calculate the electrostatic force using Colomb's Law:
[tex]F_E = \frac{kq^2}{r^2}\\\\[/tex]
where,
F_E = Electrostatic Force = ?
k = Colomb's Constant = 9 x 10⁹ Nm²/C²
q = charge of proton = 1.6 x 10⁻¹⁹ C
r = distance between protons
Therefore,
[tex]F_E = \frac{(9\ x\ 10^{9}\ Nm^2/kg^2)(1.6\ x\ 10^{-19}\ C)^2}{r^2}\\\\F_E = \frac{2.3\ x\ 10^{-28}\ Nm^2}{r^2}\\\\[/tex]
Dividing both forces:
[tex]\frac{F_E}{F_G} = \frac{2.3\ x\ 10^{-28}}{1.86\ x\ 10^{-64}}[/tex]
F_E = 1.23 x 10³⁶ F_G
Therefore, electric force is 1.23 x 10³⁶ times stronger than gravitational force.
