How are principal quantum numbers, nodes, and orbitals related?
(a) The number of nodes is always 1 less than the principal quantum number (e.g., when n=2, there is 1 node in the orbital as shown in Figure 4.36). The 3s orbital will be similar to the 2s orbital shown in 4.36 except that it will have an added concentric ring (so, the orbital is larger and has 2 nodes). (b) There is lots of evidence for d orbitals in the various periodic tables. Perhaps the most important is that there are 10 elements in the transition metal block (headed by Sc through Zn). There must be 5 equivalent orbitals that are being filled with e-, and these are the d orbitals. (c) When n =1, there is 1 type of orbital (s orbital). When n=2, there are 2 types of orbitals (s and p) and a total of four orbitals (one s and three p). When n=3, there are 3 types of orbitals (s, p, d) and a total of nine orbitals (one s, three p, and five d). The relationship is number of orbitals = n2. So, for n=4, the number of orbitals should be n4 = 16. These would be one s, three p, five d, an
