The Bohr Model of the Hydrogen Atom

Bohr postulated that the electron in the hydrogen atom could only exist stably in orbits that had angular momentum equal to an integer multiple ofwherecalled Planck's constant.

Mathematically, for an assumed circular orbit, the angular momentum(1)

The centripetal force is given by mv^2 over r and this is equal to the electrostatic force between the proton and electron.

Substitute the expression for v from (1) into this and rearrange to obtain

The energy levels are given by the sum pf the kinetic and potential energies.


Substitution of the values ofandinto this expression gives the formula

We can derive the Rydberg formula by considering the difference between two energy levels.

Dividing byand taking thesign inside the brackets gives

which becomes the Rydberg formula by putting