In 1913 Niels Bohr formulated a method of calculating the differentenergy levels of the hydrogen atom. He did this by combining bothclassical and quantum ideas. In this problem, we go through thesteps needed to understand the Bohr model of the atom.


Consider an electron with charge -e and mass m orbiting in a circle around a hydrogen nucleus(a single proton) with charge +e. In the classical model, the electron orbitsaround the nucleus, being held in orbit by the electromagneticinteraction between itself and the protons in the nucleus, muchlike planets orbit around the sun, being held in orbit by theirgravitational interaction. When the electron is in a circularorbit, it must meet the condition for circular motion: Themagnitude of the net force toward the center, F_c, is equal to mv^2/r. Given these two pieces ofinformation, deduce the velocity v of the electron as it orbits around thenucleus.
Express your answer in terms ofe, m, r, and epsilon_0, the permittivity offree space.