Quantum numbers configurations

MOs around them - rather as we construct atomic orbitals (AOs) around a single bare nucleus. Electrons are then fed into the MOs in pairs (with the electron spin quantum number = 5) in order of increasing energy using the aufbau principle, just as for atoms (Section 7.1.1), to give the ground configuration of the molecule. 

In the case of atoms, deriving states from configurations, in the Russell-Saunders approximation (Section 7.1.2.3), simply involved juggling with the available quantum numbers. In diatomic molecules we have seen already that some symmetry properties must be included, in addition to the available quantum numbers, in a discussion of selection rules. 

Spin quantum number (S) Ion Electronic configuration Typical compounds... 

Given the rules referred to in Section 6.3, it is possible to assign quantum numbers to each electron in an atom. Beyond that, electrons can be assigned to specific principal levels, sub-levels, and orbitals. There are several ways to do this. Perhaps the simplest way to describe the arrangement of electrons in an atom is to give its electron configuration, which shows the number of electrons, indicated by a superscript, in each sublevel For example, a species with the electron configuration... 

There is no more room in the 2s orbital for a fifth electron, which appears when we move on to the boron atom. However, another orbital with principal quantum number 2 is available. A 2p orbital accepts the fifth electron, giving the configuration Is ls-lfi. Continuing this process, we obtain the following configurations ... 

Figure 2. New proposed form of the periodic table based on symmetry of electronic configurations and quantum numbers.

Furthermore, LandS s theory only represents a first-order approximation, and the L and S quantum numbers only behave as good quantum numbers when spin-orbit coupling is neglected. It is interesting to note that the most modem method for establishing the atomic ground state and its configuration is neither chemical nor spectroscopic in the usual sense of the word but makes use of atomic beam techniques (38). 

According to the Stoner scheme the electronic configuration for the element sulphur, for example, is 2, 2, 2t 4, 2, 2, 2. This configuration could account successfully for the various valency states shown by the element, that is 2, 4, 6 as mentioned before. However, this new scheme did nothing to resolve the problem of the violation of quantum numbers as seen in the splitting of spectral lines in a magnetic field. 

Soon after Bohr developed his initial configuration Arnold Sommerfeld in Munich realized the need to characterize the stationary states of the electron in the hydrogen atom by. means of a second quantum number—the so-called angular-momentum quantum number, Bohr immediately applied this discovery to many-electron atoms and in 1922 produced a set of more detailed electronic configurations. In turn, Sommerfeld went on to discover the third or inner, quantum number, thus enabling the British physicist Edmund Stoner to come up with an even more refined set of electronic configurations in 1924. 

This problem clearly did not worry Stoner, who just went ahead and assumed that three quantum numbers could be specified in many-electron atoms. In any case, Stoner s scheme solved certain problems present in Bohr s configurations. For example, Bohr had assigned phosphorus the configuration 2,4,4,41, but this failed to explain the fact that phosphorus shows valencies of three and five. Stoner s configuration for phosphorus was 2,2,2,4,2,2,1, which easily explains the valencies, since it becomes plausible that either the two or the three outermost subshells of electrons form bonds. 

But does the fact that the third shell can contain 18 electrons, for example, which emerges from the relationships among the quantum numbers, also explain why some of the periods in the periodic system contain eighteen places Actually not exactly. If electron shells were filled in a strictly sequential manner there would be no problem and the explanation would in fact be complete. But as everyone is aware, the electron shells do not fill in the expected sequential manner. The configuration of element number 18, or argon is,... 

The number of energy levels found to date, with the aid of the Zeeman effect and the isotope shift data, is 605 even and 586 odd levels for Pu I and 252 even and 746 odd for Pu II. The quantum number J has been determined for all these levels, the Lande g-factor for most of them, and the isotope shift for almost all of the Pu I levels and for half of those of Pu II. Over 31000 lines have been observed of which 52% have been classified as transitions between pairs of the above levels. These represent 23 distinct electron configurations. 

Quantum number J, lowest level of each configuration of Pu(I)... 

The nuclear spin product functions will be represented by where n represents a given nuclear spin configuration characterized by nuclear spin quantum number Wj and for nuclei j and k, respectively. 

A complete specification of how an atom s electrons are distributed in its orbitals is called an electron configuration. There are three common ways to represent electron configurations. One is a complete specification of quantum numbers. The second is a shorthand notation from which the quantum numbers can be inferred. The third is a diagrammatic representation of orbital energy levels and their occupancy. 

As the number of electrons In an atom Increases, a listing of all quantum numbers quickly becomes tedious. For example. Iron, with 26 electrons, would require the specification of 26 sets of 4 quantum numbers. To save time and space, chemists have devised a shorthand notation to write electron configurations. The orbital symbols (1 5, 2 p,... 

A neutral helium atom has two electrons. To write the ground-state electron configuration of He, we apply the aufbau principle. One unique set of quantum numbers is assigned to each electron, moving from the most stable orbital upward until all electrons have been assigned. The most stable orbital is always ly( = l,/ = 0, JW/ = 0 ). 

---