Question

The hydrogen atom consists of one electron orbiting one proton in a circular orbit. (a) Using...

The hydrogen atom consists of one electron orbiting one proton in a circular orbit.

(a) Using Coulomb's Law and concepts of centripetal acceleration/force, show that the radius r of the orbit is given by

where K is the kinetic energy of the electron, k is the Coulomb's Law constant, +e is the charge of the proton, and -e is the charge of the electron.

(b) Calculate r when the kinetic energy of the electron is 13.6 eV.

(c) What percentage of the speed of light (2.998 x 108 m/s) is the speed of the electron when its kinetic energy is 13.6 eV?

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