The permitted energy levels of hydrogenic atoms

Hydrogenic atoms provide the starting point for the discussion of many-eiectron atoms and hence of the properties of aii atoms and their abiiities to form bonds and hence aggregate into moiecuies. 

With a lot of work, the Schrodinger equation with this potential energy and these boundary conditions can be solved, and we shall summarize the results. As usual, the need to satisfy boundary conditions leads to the conclusion that the electron can have only certain energies. Schrodinger himself found that for a hydrogenic atom of atomic number Z with a nucleus of mass m, the allowed energy levels are given by the expression 

The quantum number n is called the principal quantum number. It gives the energy of the electron in the atom by substituting its value into eqn 9.31. 

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