The Complete Atomic Orbitals

We now have all three quantum numbers for defining atomic orbitals the principal quantum number n, the angular momentum quantum number Z and the magnetic quantum number mi. We have also seen how the possible values of the quantum numbers are interrelated. These are summarized in Table A9.3, which also covers the common nomenclature for atomic orbitals. This gives the principal quantum number followed by a letter indicating the angular momentum quantum number, with s, p, d,. .. referring to Z = 0, 1,2,  

For any atomic orbital quoted in this way there may be a level of degeneracy because the Ml quantum number can have 21 + 1 values. Since the radial equation does not contain trii, its value does not generally affect the orbital energy (unless the atom is in a magnetic field). So, orbitals occur in degenerate sets, i.e. all three 2p atomic orbitals have the same orbital energy 2,1- 

The orbital functions are formed as a product of the radial and angular solutions  

As we have seen before, the wavefunction itself is not an experimentally observable quantity, but it is related to the probability of finding an electron in the orbital at a particular point in space. The probability Pe of finding the electron that is occupying a given wavefunction in an infinitesimal volume dr is given by 

The probability depends on the compiete wavefunction with its radial and angular parts combined. For example, if we wish to find the probability that the eiectron is at a distance r from the nucleus then we have to integrate over the angular degrees of freedom  

---