Energy Levels

Let's calculate the energy corresponding to a given orbit in the hydrogen atom according to the Bohr model. The kinetic energy is

KE = mv2 = ke2/(2rn)

The potential energy from the Coulomb interaction is

PE = -eV = -ke2/rn

The total energy then becomes

En = ke2/(2rn) - ke2/rn = - ke2/(2rn)

Putting in our quantized radii we get

where Eo = 2.210-18 J = 13.6 eV.

The negative sign in the equation for the En means that the system has less energy than a free electron and proton or that the electron is bound to the proton, and it takes 13.6 eV of energy to remove the electron from the atom.

MultiMedia Physics 2000