Principal shell

The principal shell arrangements are shown in Figure 12.12a-e. The letters E, F, G, H, J are those used in the TEMA standards to designate the various types. The E shell is the most commonly used arrangement. 

The quantum number / occurs in the 0(0) factor of the wave function. It may be thought of as representing the angular momentum of the electron, in units of /i/27t, because of its orbital motion, and we shall call it the orbital momentum quantum number. It may take all values 0, 1, 2,. .., / — 1, where n is the principal quantum number. Thus, in the first principal shell, there exist only wave functions with / = 0 in the second shell there are wave functions with 1 = 0 and 1 and so on. For historical reasons, letter symbols are given to orbitals according to the value of /, as shown in the following scheme ... 

For given n and / = 0 there is only one possible orbital, namely, one with m = 0. Thus there is only one s orbital of each principal quantum shell. For given n and / = 1 there are three possible m values. Hence each principal shell has three different p orbitals. Similarly, d orbitals come in sets of five, / orbitals in sets of seven, and so on. In the absence of any external forces, the energy of an orbital is independent of its m value. Hence all three np orbitals, all five nd orbitals, and so on, are of the same energy. 

In order to find expressions for the submatrix elements of these transitions, we have to transform them, using the CFP with one detached electron, to the form in which the electrons of the principal shell (/f1-1 for (25.25)-(25.27)) do not participate in the transition under consideration. 

Two trends are apparent in Table 2.8. Firstly, in going from Sc to to La there is a stepwise increase in radius as principal shells of electrons are added. However, in all of the other groups the increase between the first and second row is not repeated in the second to third row. This is a result of the lanthanide contraction and the filling of the 4f subshell between La and Hf. This reflects the poor screening of 4f electrons one by another, leading to an increase in and a decrease in radius. Secondly, for metals in the same oxidation state, there is a d-block contraction across the rows as a result of the increase in Z... 

Principal Quantum Number. This is designated as n and gives the number of principal shell in which the electron is revolving around the nucleus. It designates the average distance of the electron from the nucleus. Hence this quantum number represents the size of electron orbit. 

The Quantum Mechanical Atom Principal Shells, Subshells, and Orbitals... 

The quantum mechanical description of the hydrogen atom is more complex than Bohr s picture, but it is a better picture. In the quantum mechanical model, there are several principal shells... 

To help you get a better idea of this nested structure, the general characteristics of principal shells, subshells, and orbitals are described below. 

Within each principal shell are subshells. The number of subshells in a principal shell equals the value of its quantum number, n. Each subshell is identified with a one-letter label s, p, d, or f. Within known elements, the s-, p-, and d-subshells are encountered most often. 

The n = 1 principal shell contains one subshell, an s-subshell. It is identified as the ls-subshell. 

The n = 2 principal shell contains two subshells, an s-subshell and a p-subshell. They are identified as the 2s-subshell and the 2p-subshell. 

The n = 3 principal shell contains three subshells, an s-, p-, and a d-subshell. They are called the 3s-subshell, 3p-subshell, and the 3d-subshell. 

The orbital is a region of space where an electron assigned to that orbital is most likely to be found. Each orbital can hold a maximum of two electrons. The subshells are composed of one or more orbitals. There is one orbital in an s-subshell. There are three orbitals in a p-subshell, five in a d-subshell, and seven in an f-subshell. The number of orbitals in a principal shell equals n2. There are nine orbitals in the n = 3 principal shell, 32 = 9. 

The following figure shows the hierarchy of principal shells, subshells, and the orbitals in each subshell. The orbitals are represented by small boxes. 

Every principal shell contains one s-orbital in an s-subshell. The labels used to identify the s-subshells, Is, 2s, 3s, etc., are also used to identify the s-orbital they contain. The 1 s-orbital is in the 1 s-subshell, and so forth. An s-orbital can hold a minimum of 2 electrons. 

Since d-subshells first appear in the n = 3 principal shell, d-orbitals are first encountered in the n = 3 principal shell. The d-orbitals in the 3d-subshell are referred to as the 3d-orbitals. d-orbitals are always kept together as a set and they all have the same energy. A d-subshell can contain a maximum often electrons, two in each of the five d-orbitals. 

Principal Shell (n) Number of Subshells in the Principal Shell Identity of Subshells Number of Orbitals in the Subshell... 

The symbols used to indicate the number of electrons in a subshell include the number of the principal shell (1,2, 3...), the letter designation of the subshell (s, p, d, f), with a superscript number indicating the number of electrons. 

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