Determine how many times the electrostatic force acting between a proton and an electron is greater

| May 28, 2021 | education

Determine how many times the electrostatic force acting between a proton and an electron is greater than the gravitational one?

mpr = 1.67 * 10 ^ -27 kg.
mel = 9.1 * 10 ^ -31 kg.
qpr = 1.6 * 10 ^ -19 Cl.
qel = 1.6 * 10 ^ -19 Cl.
k = 8.98 * 10 ^ 9 N * m ^ 2 / Kl ^ 2.
G = 6.67 * 10 ^ -11 N * m ^ 2 / kg ^ 2.
Fe / Fgr -?
According to Coulomb’s law, the electrostatic force of interaction between a proton and an electron is determined by the formula: Fe = k * qpr * qel / r ^ 2.
According to the law of universal gravitation, the gravitational force of interaction between a proton and an electron is determined by the formula: Fgr = G * mpr * mel / r ^ 2.
Where qпр, qel is the charge of a proton and an electron, mпр, mel is the mass of a proton and an electron, k is a coefficient of proportionality, G is a gravitational constant, r is the distance between a proton and an electron.
Fe / Fgr = k * qpr * qel / r ^ 2: G * mpr * mel / r ^ 2 = k * qpr * qel / G * mpr * mel.
Fe / Fgr = 8.98 * 10 ^ 9 N * m ^ 2 / Cl ^ 2 * 1.6 * 10 ^ -19 Cl * 1.6 * 10 ^ -19 Cl / 6.67 * 10 ^ -11 N * m ^ 2 / kg ^ 2 * 1.67 * 10 ^ -27 kg * 9.1 * 10 ^ -31 kg = 227 * 10 ^ -31 = 226.71 * 10 ^ 37.
Answer: the electrostatic force of interaction is 226.71 * 10 ^ 37 times greater than the gravitational force.



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