Resultant orbital quantum number

In addition to the magnetism due to the electron spin, the magnetism of the orbital motion has to be considered. For this purpose the magnetic quantum numbers of the electrons are added to a resultant orbital quantum number L = beginning with the highest magnetic quantum number. For example ... 

Spin Orbit Coupling of p2 With a p2 arrangement, resultant orbital quantum number values of L = 2,1 and 0, and also resultant quantum number values S = 1 and 0 are obtained. These may be coupled to give the total angular quantum number J. Each of these arrangement corresponds to an electronic arrangement called a spectroscopic state. 

Total spin quantum number, 5 = 4 x j = 2 Spin multiplicity, 25 + 1 = 5 Resultant orbital quantum number,... 

L total (resultant) orbital quantum number MOCVD metal-organic chemical vapour deposition... 

The modern theory of the behavior Of matter, called quantum mechanics, was developed by several workers in the years 1925-1927. For our purposes the most important result of the quantum mechanical theory is that the motion of an electron is described by the quantum numbers and orbitals. Quantum numbers are integers that identify the stationary states of an atom the word orbital means a spatial description of the motion of an electron corresponding to a particular stationary state. 

Any determinant changes sign when any two columns are interchanged. Moreover, no two of the product functions (columns) can be the same since that would cause the determinant to vanish. Thus, in all nonvanishing completely anti-symmetric wave functions, each electron must be in a different quantum state. This result is known as Pauli s exclusion principle, which states that no two electrons in a many-electron system can have all quantum numbers the same. In the case of atoms it is noted that since there are only two quantum states of the spin, no more than two electrons can have the same set of orbital quantum numbers. 

The resulting RPAE equation for the photoionization amplitude Dn from an initial state i i into a final state V2, (v is the total set of quantum numbers that characterize a single-electron state the principal quantum number n, orbital quantum number /, magnetic quantum number mi, and the z projection of the electron spin sz) is given by [55]... 

An important question that arises is how the orbital and spin angular momenta of the individual electrons in a shell are coupled. One possibility is that the spin and orbital momenta for an individual electron couple into a resultant and that, in turn, the resultants for each electron in the shell couple. The other extreme possibility is that the spin momenta for individual electrons couple together to give a resultant spin quantum number S, as do the orbital momenta to give a resultant quantum number L the resultants. S and L then couple to give a final resultant quantum number J. In the brief discussion that follows the latter coupling is assumed to occur. 

The contribution of the orbital motion depends for one electron, as in hydrogen, on the orbital quantum number / [x = f 1) B.M. for an s electron there is thus no contribution from the orbital motion. With more electrons the total quantum number L appears, resulting from the vector summation of the individual l values. 

The atomic terms are characterized by the orbital angular momentum which is reflected in the value of the total orbital quantum number L. Just as the individual angular momenta are quantized, so are the resultants. For the example above, with = 1 for two p electrons, the maximum value of the resultant angular momentum is represented by the sum of the quantum numbers, and the minimum value is represented by the difference. Intermediate values are allowed too, provided they differ from the extremes by a whole number ... 

The symmetrical spin functions have been seen to be triplet and the antisymmetrical to be singlet. Furthermore, the singlet states include the lowest or ground state, where presumably the two electrons have their orbital quantum numbers equal. Thus the antisymmetrical spin combination is associated with the symmetrical orbital wave function to give a total wave function which is antisymmetrical. This result verifies the principle of the antisymmetrical character of electron wave functions. 

Conversely, since totai bas this character when orbital antisymmetrical (different electronic orbital quantum numbers), the spin combinations must be symmetrical. There are three of them and the triplet ortho states result. 

The A values resulting from the combination of Lj and the orbital quantum numbers of two unlike atoms, are... 

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