Respuesta :
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,
[tex]F_g = G\frac{m_pm_e}{d^2}[/tex]
Here,
G = Gravitational Universal Constant
[tex]m_p[/tex] = Mass of Proton
[tex]m_e[/tex] = Mass of Electron
d = Distance between them.
[tex]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})[/tex]
[tex]F_g = 3.631*10^{-47}N[/tex]
In the case of the Electric Force we have,
[tex]F_e = k\frac{q_pq_e}{d^2}[/tex]
k = Coulomb's constant
[tex]q_p[/tex] = Charge of proton
[tex]q_e[/tex] = Charge of electron
d = Distance between them
[tex]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})[/tex]
[tex]F_e = 82.446*10^{-9}N[/tex]
Therefore
[tex]\frac{F_e}{F_g} = 2.270*10^{39}[/tex]
We can here prove that the statement is True
It has been proved in below calculation that the gravitational force exerted by a proton on an electron is [tex]2\times10^{39}[/tex]times weaker than the electric force that the proton exerts on an electron
What is gravitational force?
Gravitational force is the universal force of attraction acting between two bodies.
It is given by,
[tex]Fg=G\times\dfrac{m_1 \times m_2}{x^2}[/tex]
Here [tex]G[/tex] is gravitational constant [tex]m[/tex] is the mass of the bodies and [tex]x[/tex] is the distance between bodies.
What is electric force?
Electric force is the force of attraction or repulsion acting between two charged bodies,
[tex]F_E=k\times\dfrac{q_1 \times q_2}{x^2}[/tex]
Here, [tex]k[/tex] is Coulomb's constant [tex]q[/tex] is the charge and [tex]x[/tex] is the distance between bodies.
The gravitational force exerted by a proton on an electron is,
[tex]Fg=6.673\times{10^{-11}}\times\dfrac{1.673\times10^{-27}\times9.1094\times10^{-31}}{x^2}[/tex]
The electric force exerted by a proton on an electron is,
[tex]F_E=9\times{10^{9}}\times\dfrac{1.602\times10^{-19}\times1.602\times10^{-19}}{x^2}[/tex]
Compare both,
[tex]\dfrac{F_g}{F_e} =\dfrac{6.673\times{10^{-11}}\times\dfrac{1.673\times10^{-27}\times9.1094\times10^{-31}}{x^2}}{9\times{10^{9}}\times\dfrac{1.602\times10^{-19}\times1.602\times10^{-19}}{x^2}}\\\dfrac{F_g}{F_e} =\dfrac{1}{2\times10^{39}}[/tex]
Thus, It has been proved in below calculation that the gravitational force exerted by a proton on an electron is [tex]2\times10^{39}[/tex]times weaker than the electric force that the proton exerts on an electron.
Learn more about the gravitational force electric force here;
https://brainly.com/question/1076352
