Question

The gravitational force exerted by a proton on an electron is 2x1039 times weaker than the electric force that the proton exerts on an electron? True or False? explain.

Answer 1

To solve this problem we will rely on the theorems announced by Newton and Coulomb about the Gravitational Force and the Electrostatic Force respectively.

In the case of the Force of gravity we have to,

$F_g = G\frac{m_pm_e}{d^2}$

Here,

G = Gravitational Universal Constant

$m_p$ = Mass of Proton

$m_e$ = Mass of Electron

d  = Distance between them.

$F_g = (6.673*10^{-11} kg^{-1} \cdot m^3 \cdot s^{-2}) (\frac{(1.672*10^{-27}kg)(9.109*10^{-31})}{(52.9pm)^2})$

$F_g = 3.631*10^{-47}N$

In the case of the Electric Force we have,

$F_e = k\frac{q_pq_e}{d^2}$

k = Coulomb's constant

$q_p$ = Charge of proton

$q_e$ = Charge of electron

d = Distance between them

$F_e = (9*10^9N\cdot m^2 \cdot C^{-2})(\frac{(1.602*10^{-19}C)(1.602*10^{-19}C)}{(52.9pm)^2})$

$F_e = 82.446*10^{-9}N$

Therefore

$\frac{F_e}{F_g} = 2.270*10^{39}$

We can here prove that the statement is True