Subshells, quantum mechanical model

The VSEPR approach is largely restricted to Main Group species (as is Lewis theory). It can be applied to compounds of the transition elements where the nd subshell is either empty or filled, but a partly-filled nd subshell exerts an influence on stereochemistry which can often be interpreted satisfactorily by means of crystal field theory. Even in Main Group chemistry, VSEPR is by no means infallible. It remains, however, the simplest means of rationalising molecular shapes. In the absence of experimental data, it makes a reasonably reliable prediction of molecular geometry, an essential preliminary to a detailed description of bonding within a more elaborate, quantum-mechanical model such as valence bond or molecular orbital theory. 

The model that we have developed for the structure of atoms has been further refined. This more sophisticated model, known as the quantum mechanical model, retains most of the general features that we have deduced for atomic structure. Within this model, the electrons in atoms occupy specific regions of space known as orbitals, with a maximum of two electrons occupying each orbital. There are three orbitals in a/ subshell and one orbital in each s subshell. The idea that the two electrons in a given orbital must have opposite spins was first proposed by Wolfgang Pauli in 1925, and is known as the Pauli Exclusion Principle. Most general chemistry texts have some discussion of these ideas. An interesting introduction to the ideas of quantum mechanics can be found in Sections 3.13 and 3.15 of Chemistry Structure Dynamics, by J. N. Spencer, G. M. Bodner, and L. H. Rickard (Fourth Edition). You should read the appropriate sections of your text to become familiar with the terms and basic ideas of this model. 

Figure 3-5 is a blank energy level diagram you can use to depict electrons for any particular atom. Not all the known orbitals and subshells are shown. But with this diagram, you should be able to do most anything you need to. (If you don t have a clue what orbitals, subshells, or all those numbers and letters in the figure have to do with the price of beans, check out the Quantum mechanical model section, earlier in this chapter. Fun read, lemme tell ya.)... 

The next orbitals in the quantum-mechanical model are those with principal quantum niunber n = 2. Unlike the n = 1 principal shell, which contains only one subshell (specified by s), the n = 2 principal shell contains two subshells, specified by s and p. 

The Quantum-Mechanical Model The quantum-mechanical model for the atom describes electron orbitals, which are electron probability maps that show the relative probability of finding an electron in various places surrounding the atomic nucleus. Orbitals are specified with a number (n), called the principal quantum number, and a letter. The principal quantum number (n = 1,2,3. . . ) specifies the principal shell, and the letter (s, p, d, or f) specifies the subshell of the orbital. In the hydrogen atom, the energy of orbitals depends only on n. In multi-electron atoms, the energy ordering is Is 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s. 

List the four possible subshells in the quantum-mechanical model, the number of orbitals in each subshell, and the maximum number of electrons that can be contained in each subshell. 

Thus, the Bohr model was further refined by wave mechanics, in which the introduction of three new quantum numbers gives rise to eleetron subshells within each shell. A comparison of these two models on this basis is illustrated, for the hydrogen atom, in Figures 2.2a and 2.2b. 

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