Quantum Numbers

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					                                             Quantum Numbers

                  Quantum #          name            Related to         Possible values
                      n            principle          Energy             1, 2, 3, 4, ….
                         l         Angular          Orbital shape         0 → (n – 1)
                                  momentum
                       ml          magnetic           Orbital               -l → +l
                                                    orientation
                       ms             spin        Pauli Exclusion           +½ or -½
                                                     principle


                                 Angular momentum quantum number
         l=       Orbital type      Orbital shape   # orbitals # electrons                     Orbital
                                                    per shell   per shell                   designations
          0              s             spherical        1           2                              s
          1              p           Double lobe        3           6                         px py pz
          2              d         Quadruple lobe       5          10                        dxy dxz dyz
                                       (sort of)                                              dx2-y2 dz2
          3              f            ------------      7          14                        ------------


Pauli Exclusion Principle:   Each orbital can be occupied by 2 electrons.
                             The electrons in an orbital must have opposite spins.
                             The first electron in the orbital is assigned a spin value of +½

Hund’s Rule: When orbitals of the same type have the same energy, all orbitals of that type will have
             1 electron before any orbital of that type will be completely filled.



                  Periodic Table                    Main Group Elements




                      s                                                       p
                                             d
                                  Transition Metals                Rare Earth Metals 
                  Fig.
                  7.26
                                                           f