Bohr's Model of the Hydrogen Atom
Bohr made the major innovation of hypothesising the quantization of angular momentum in units ofwhereThis means we can write
We can use the ordinary rules of classical Newtonian mechanics to derive the equation giving the differences in the energy levels of the electrons in the Hydrogen atom.
We can equate the Coulomb force to the force required to keep the electron in orbit around the nucleus.
From this we can obtain
The total energy of the electron in it's orbit is the sum of the kinetic and potential energies: Use of (2) gives
This means an energy change ofwhereis the frequency andis the wavelength of the associated emitted or absorbed photon. Substitute (1) to give
Use this and divide byto get
is called the Rydberg constant and is given the symbolIt has the value