Atomic orbitals quantum number combinations, Table

Table 2.1 Quantum number combinations and atomic orbitals...

The hierarchy of shells, subshells, and orbitals is summarized in Fig. 1.30 and Table 1.3. Each possible combination of the three quantum numbers specifies an individual orbital. For example, an electron in the ground state of a hydrogen atom has the specification n = 1, / = 0, nij = 0. Because 1=0, the ground-state wavefunction is an example of an s-orbital and is denoted Is. Each... 

Using the above definitions for the four quantum numbers, we can list what combinations of quantum numbers are possible. A basic rule when working with quantum numbers is that no two electrons in the same atom can have an identical set of quantum numbers. This rule is known as the Pauli Exclusion Principle named after Wolfgang Pauli (1900-1958). For example, when n = 1,1 and mj can be only 0 and m can be + / or -1/ This means the K shell can hold a maximum of two electrons. The two electrons would have quantum numbers of 1,0,0, + / and 1,0,0,- /, respectively. We see that the opposite spin of the two electrons in the K orbital means the electrons do not violate the Pauli Exclusion Principle. Possible values for quantum numbers and the maximum number of electrons each orbital can hold are given in Table 4.3 and shown in Figure 4.7. 

Explicit formulas and numerical tables for the overlap integral S between AOs (atomic orbitals) of two overlapping atoms a and b are given. These cover all the most important combinations of AO pairs involving ns, npSlater type, each containing two parameters i [equal to Z/( - 5)], and n — S, where n — S is an effective principal quantum number. The S formulas are given as functions of two parameters p and t, where p = p- + p,s)R/ao, R being the interatomic distance, and t = — Mb)/(ma + Mb)- Master tables of... 

We can see the relationship between these terms and quantum numbers by looking carefully at Table 4.3. First, each unique value of n represents an energy level. Each 7 value represents a specific sublevel within an energy level. Recall from the previous section that these sublevels are typically referred to using their common names s, p, d, and f. Each unique combination of n and 1 values corresponds to a different sublevel. For example, for n = 3 and 7=2, this corresponds to the 3dsublevel of the atom. The rn values tell us how many orbitals are found in a given sublevel. For instance, in the 3d sublevel there are 5 orbitals possible (for 3d, rn —2, — 1, 0, 1, 2). The spin quantum number tells us that there can be no more than 2 electrons in any orbital, which you will learn more about later in this chapter. Let s summarize what we know in a new chart. 

Molecular orbitals (MOs) were constructed using linear combinations of basis functions of atomic orbitals. The MO eigenfunctions were obtained by solving the Schrodinger equations in numerical form, including Is— (n+l)p, that is to say, Is, 2s, 2p, -ns, np, nd, (n+l)s, (n+l)p orbitals for elements from n-th row in the periodic table and ls-2p orbitals for O, where n—1 corresponded to the principal quantum number of the valence shell. 

TERM SYMBOLS FOR LINEAR MOLECULES Electronic states of a linear molecule may be classified conveniently in terms of angular momentum and spin, analogous to the Russell-Saunders term-symbol scheme for atoms. The unique molecular axis in linear molecules is labeled the axis. The combining atomic orbitals in any given molecular orbital have the same mi value. Thus an mi quantum number is assigned to each different type of MO, as indicated in Table 2-3. The term designations are of the form... 

As already mentioned, neither Mendeleev nor his successors could place the lanthanides in the Periodic Table. Not only was there no recognizable atomic theory until many years afterwards, but, more relevant to how groupings of elements were made in those days, there was no comparable block of elements for making comparisons. The lanthanides were sui generis. The problem was solved by the combined (but separate) efforts of Moseley and Bohr, the former showing that La-Lu was composed of 15 elements with atomic numbers from 57 to 71, whilst the latter concluded that the fourth quantum shell could accommodate 32 electrons, and that the lanthanides were associated with placing electrons into the 4f orbitals. 

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