Answer to Question #157712 in Physics for Andu

Question

Calculate the force of gravitational pull between the electron and the proton on the hydrogen atom. It is known that the radius of the electron orbit is R = 0.5 × 10 ‐ ¹⁰m, the mass of the electron m1 = 9.1 × 10 ‐ ³¹ kg and the mass of the proton m2 = 1.67 × 10 ‐ ²⁷ kg. Compare the conclusion you will find with the value of the electric gravitational force, which is Fel = 9 × 10 ‐⁸ N. What conclusion can you formulate?

Answer 1

By the Newton's Universal Gravitation Law, we have:

$$F_g=\dfrac{Gm_em_p}{R^2},$$

$F_g=\dfrac{6.67\cdot10^{-11}\ \dfrac{Nm^2}{kg^2}\cdot9.1\cdot10^{-31}\ kg\cdot1.67\cdot10^{-27}\ kg}{(0.5\cdot10^{-10}\ m)^2}=4.05\cdot10^{-47}\ N.$

Let's calculate the ratio of the electrostatic force and fravitational force between the electron and the proton:

$$\dfrac{F_e}{F_g}=\dfrac{9.0\cdot10^{-8}\ N}{4.05\cdot10^{-47}\ N}=2.2\cdot10^{39}.$$

Therefore, the electric force between electron and proton is $2.2\cdot10^{39}$ times bigger than the gravitational force.