Quantum number periodic table arrangement

Pauli justified the identification of four quantum numbers with each electron with the following apparently clever argument. He supposed that if a strong magnetic field is applied, the electrons are decoupled and so do not interact, and can be said to be in individual stationary states. Of course, the periodic table arrangement must also apply in the absence of a magnetic field. 

Armed with these conditions, we can correlate the rows and columns of the periodic table with values of the quantum numbers it and /. This correlation appears in the periodic table shown in Figure 8. Remember that the elements are arranged so that Z increases one unit at a time from left to right across a row. At the end of each row, we move down one row, to the next higher value of It, and return to the left side to the next higher Z value. Inspection of Figure reveals that the ribbon of elements is cut after elements 2, 10, 18, 36, 54, and 86. 

It is possible to distinguish atoms by writing sets of quantum numbers for each of their electrons. However, writing quantum numbers for an atom such as uranium, which has 92 electrons, would be mind-bogglingly tedious. Fortunately, chemists have developed a shortcut to represent the number and orbital arrangements of electrons in each atom. As you will see shortly, these electron configurations, as they are called, are intimately connected to the structure and logic of the periodic table. 

The arrangement of elements in the periodic table is a direct consequence of the allowed values for the four quantum numbers. If the laws of physics allowed these numbers to have different values, the appearance of the periodic table would change. In this activity, you will examine the effect on the periodic arrangement of the elements when one of the quantum numbers has a different set of allowed values. 

For our purposes the main significance of the electron spin quantum number is connected with the postulate of Austrian physicist Wolfgang Pauli (1900-1958), which is often stated as follows In a given atom no two electrons can have the same set of four quantum numbers (n, , me, and ms). This is called the Pauli exclusion principle. Since electrons in the same orbital have the same values of n, i, and mc, this postulate requires that they have different values of ms. Since only two values of ms are allowed, we might paraphrase the Pauli principle as follows An orbital can hold only two electrons, and they must have opposite spins. This principle will have important consequences when we use the atomic model to relate the electron arrangement of an atom to its position in the periodic table. 

The results considered in this section are very important. We have seen that the wave mechanical model can be used to explain the arrangement of elements in the periodic table. This model allows us to understand that the similar chemistry exhibited by the members of a given group arises from the fact that they all have the same valence electron configuration. Only the principal quantum number of the occupied orbitals changes in going down a particular group. 

The periodic law is not of the physical but the chemical kind, although not often properly realized. It resides in the fact of attributing four quantum numbers (principal, orbital, magnetic, and spin) to each electron in arranging them in the so-called configuration by the aujbau principle according which the Periodic Table is constructed. Certainly, such quantum labeling... 

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