Theoretical Basis for the Periodic Table

The fact that the one electron approximation preserves the angular part of the hydrogen wavefimction along with the m, I, and n quantum numbers allows us to use these quantum numbers with the Pauli exclusion principle to construct the periodic table and to use the 

Now the periodic table has a solid theoretical basis. Since the Pauli exclusion principle allows only 1 fermion (electron) per quantum state, and since fermions have spin s = 1 /2, the possible states are shown in Table 2.3. 

As shown in Table 2.4, the N-shell (n = 4) starts with potassium, which has the configuration of Ar+ 4s. The 10 3d electrons start filling with scandium and end with krypton, which has the configuration Ar + 3d °4s 4p . 

As may be seen in Table 2.4, the s-electrons of the next highest n number fall below the d-electrons from n = 4 to n = 6, the higher n rows are omitted in the table. This causes the n = 5 or 0-shell to terminate with 4d ° plus 5s 5p and accounts for the first two rows of 18 elements which contain the transition metals. The = 6 or P-shell starts off like the N- and 0-shells with cesium, which is Xe + 6s, but after lanthanum, which is Xe + 5d 6s, the if electrons start to fill before fhe 5d electrons. To preserve the similarity of properties of the n = 6 series with their n = i and 5 coimterparts, the next 14 elements are split off into a separate group called the lanthanide series so that hafnium, which is configured 

Atomic Configuration of the Elements (Lanthanides and Actinides Omitted) 

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