Physicists first attempted to understand the hydrogen atom by applying the laws of classical physics. Consider an electron of mass m and charge -e in a circular orbit of radius r around a proton of charge +e.
a. Use Newtonian physics to show that the total energy of the atom is E = -e²/8πє₀r.
b. Show that the potential energy is -2 times the electron’s kinetic energy. This result is called the virial theorem.
c. The minimum energy needed to ionize a hydrogen atom (i.e., to remove the electron) is found experimentally to be 13.6 eV. From this information, what are the electron’s speed and the radius of its orbit?