Orbitals and Quantum Numbers
        • Orbitals are the 3-dimensional representation of where electrons are 
          allowed to be.
            • Conventional atomic orbitals are created from the one-electron Hydrogen 
              atom wave functions.
               • These are the beginning of any description of atomic structure and bonding.
               • Hybrid bonding orbitals are created by wave function mixing.
            • Each Hydrogen atom orbital wave function can be described by three 
              quantum numbers: n, l, ml.
        • The pattern of these numbers is described in rules based on the 
          behavior of waves.  (We will get to these in practice.)
            • n is a counting number.
            • l is from 0 to (n-1)
            • ml from +l to –l by 1. 
                                                                                           2
              Flattening the 3-Dimensional
         • The pattern described by the quantum numbers is both beautiful and 
           difficult to see from these rules.
         • The quantum numbers, n, l and m are all integers.
                                                     l
         • Taking the shape out of the orbitals allows the pattern of the 
           quantum numbers to be seen more clearly.  
         • Flattening the shapes to a uniform cube allows stacking.
             • The pattern reveals itself in the stacking.
             • Revealing the now visible pattern to the students, either as an introduction or 
               recapitulation, teaches both the concept and reveals the underlying beauty of 
               the pattern.
                                                                                                  3
                         Atomic Orbitals
       Counting up Orbitals: In subshells
         Number of orbitals 
              in a subshell
          Seven f-orbitals                           Color adds 
            Five d-orbitals
         Three p-orbitals                           a dimension
             One s-orbital
                                                                          4
           Counting up Orbitals: in shells
       Number of orbitals                            Number of orbitals
            in a subshell                                   in a shell
        Seven f-orbitals +                            n = 4, 16 orbitals
          Five d-orbitals +                           n = 3, 9 orbitals
        Three p-orbitals +                            n = 2, 4 orbitals 
            One s-orbital                             n =1, 1 orbital
                                           2
                                     1= 1  
                                               2
                                     1+3 = 2
                                                  2
                                     1+3+5 = 3  
                                     1+3+5+7 = 42 
                                                                            5
               Orbitals in shells: Stacking them up
                                       One s-orbital
                                       Three p-orbitals
                                                                                    2
   n = 4                               Five d-orbitals        16      1+3+5+7 = 4  
                                        Seven f-orbitals
                                   One s-orbital
                                                                             2
   n = 3                           Three p-orbitals       9       1+3+5 = 3  
                                   Five d-orbitals
                            One s-orbital
   n = 2                                            4       1+3 = 22
                             Three p-orbitals
                                                                2
   n = 1                One s-orbital          1          1 = 1  
                                                                                         6