Learning Goal: To understand the Bohrmodel of the hydrogen atom. Learning Goal:

Question

Learning Goal: To understand the Bohrmodel of the hydrogen atom.

Learning Goal: To understand the Bohrmodel of the hydrogen atom. 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 hydrogennucleus (a single proton) with charge +e. In the classical model, the electronorbits around the nucleus, being held in orbit by theelectromagnetic interaction between itself and the protons in thenucleus, much like planets orbit around the sun, being held inorbit by their gravitational interaction. When the electron is in acircular orbit, 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 of e, m, r, and epsilon_0, the permittivity offree space.

Explanation / Answer

F= [1/(4_0)]*[(q1q2)/r^2] v== (e^2) / (4_0rm)

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