Compare the forces of gravitational and electrical interactions between an electron and a proton. Find the ratio

| July 2, 2021 | education

Compare the forces of gravitational and electrical interactions between an electron and a proton. Find the ratio of the Coulomb forces to the forces of gravity. I get 2.2 * 10 ^ 21 Answers 2.27 * 10 ^ 39 Write your detailed calculations.

Proton mass: mp = 1.67 10 ^ -27 kg.
Electron mass: 9.11 10 ^ -31 kg.
Gravitational constant: G = 6.674 * 10 ^ -11 m3 kg-1 s-2.
Let’s take the distance r = 1 m.

Fg = (Gmpme) / r2 =
(6.674 * 10 ^ -11 m3 / (kg * s ^ 2) * 1.67 10 ^ -27 kg * 9.11 10 ^ -31 kg) / (1 m2) = (6.674 * 1.67 * 9.11 * 10 ^ (- 11 – 27 – 31)) (m * kg) / s2 =
= 101.54 * 10 ^ -69 N.

The absolute values of the charges of the electron and proton:
q = 1.602 × 10 ^ -19 Cl.
Coefficient: k = 9 * 10 ^ 9 (N * m2) / Cl2.

Fe = (kq ^ 2) / r ^ 2 =
= (9 * 10 ^ 9 (N * m2) / Kl ^ 2 * (1.602 * 10 ^ -19 Kl) ^ 2) / (1 m2) =
= (9 * 10 ^ 9 * 1.602 * 10 ^ -19 * 1.602 * 10 ^ -19) H =
= 9 * 1.602 * 1.602 * 10 ^ (9 – 19 – 19) H =
= 23.04 * 10 ^ -29 N.

Fe / Fg ratio:

Fe / Fg = (23.097 * 10 ^ -29 N) / (101.54 * 10 ^ -69 N) =
= 0.227 * 10 ^ (- 29 – (-69)) =
= 0.227 * 10 ^ 40 = 2.27 * 10 ^ 39.

Answer: 2.27 * 10 ^ 39.



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