Question

In the simple Bohr model of the ground state of the hydrogen atom, the electron travels in a circular orbit around a fixed proton. The radius of the orbit is 5.28×10−11m, and the speed of the electron is 2.18×10^6m/s. The mass of an electron is 9.11×10−31kg. What is the force on the electron?

a) 8.99 x 10^9 N
b) 6.67 x 10^-11 N
c) 2.56 x 10^-22 N
d) 1.12 x 10^-18 N

Answer 1

The force on the electron in the Bohr model of the hydrogen atom, given the radius, mass, and speed, is calculated using the centripetal force formula. None of the provided options accurately represent the calculated force of 8.19 × 10-8 N, but option (c) is closest if typos are assumed.

Step-by-step explanation:

In the Bohr model of the hydrogen atom, an electron moves in a circular orbit around a proton.

Given the radius of the orbit (5.28 × 10-11 m), the speed of the electron (2.18 × 106 m/s), and the mass of the electron (9.11 × 10-31 kg), we can calculate the force acting on the electron using centripetal force formula:

F = m×v2/r.

Substituting the given values leads to the calculation of the force as F = (9.11 × 10-31 kg) × (2.18 × 106 m/s)2 / (5.28 × 10-11 m), which results in F = 8.19 × 10-8 N.

Considering the choices given, none of them are correct, but option (c) 2.56 x 10-22 N is closer to the actual computed force if we assume typos in the options provided.