3rd Postulate

3rd Postulate: As a consequence of the restrictions on the angular momentum of an orbit, the energy of an electron in a given orbit is constant. As long as the electron stays in that orbit, it neither absorbs nor radiates energy (hence the orbit is called a stationary state). The total energy, E, of an electron is the sum of its potential energy,

(negative because the electric force between the electron and the nucleus is attractive and its kinetic energy),

(from

Bohr 1st postulate ). Bohr 2nd Postulate Therefore

Thus, the total energy is equal to half the potential energy.

Substituting the expression for r from the above yields

All of the quantities on the right-hand side of this equation are known constants except for the arbitrary integer n. Hence, the possible energies of the electron are determined by the values of n. It should be noted that the negative sign in the energy expression means that the larger the value of n, the higher will be the energy of the electron.