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Further Development of the Polyelectronic Model

The next step involves solving the Schrodinger equation for electron 1, which is moving in a potential field created by the nucleus and the electrons in orbitals 1/ 2, tfis,, 4 n- The repulsions between electron 1 and the other electrons are computed at each point in space from the sum of the average electron densities (probabilities) corresponding to 0 213, in volume element dv around that point. With the aid of a computer, the problem is solved to yield the wave function for electron 1, which we will label 4 i- [Pg.569]

The next step is to do the same type of calculation to obtain a new wave function for electron 2 moving in a field of electrons described by the wave functions tf/ i, tf/, if/4,. . . , i/ n- This step leads to a new function 2 for electron 2. Now the process is carried out for electron 3 interacting with electrons described by the wave functions i/ i, tif x, 4,. . ., ilfN to produce a new function This procedure continues until all electrons have been covered to yield the wave functions i/ 2, / a, , iAn- Then the entire process starts again with electron 1 and continues through electron N to give the new functions i/ 2, 1 3, , N- The procedure is diagramed in Fig. 12.32. When a given cycle produces a set of wave functions that are virtually identical to the previous set, a self-consistent field is achieved and the procedure is terminated. [Pg.569]

Finally, although it is not precisely correct to assume that the N electrons in an atom occupy N independent one-electron orbitals, this remains a very useful idea for understanding many atomic properties, including the organization [Pg.569]

A schematic of the SCF method for obtaining the orbitals of a polyelectronic atom. [Pg.569]

Repeat cycle until new set of functions is virtually the same as the previous set [Pg.569]

Radium, element 88, is in Period 7 (and Group 2A), as shown in Fig. 12.31. Thus radium has two electrons in the 7s orbital, and the configuration is [Pg.557]

In contrast to the Schrodinger equation for the hydrogen atom, the Schrodinger equation for a polyelectronic atom cannot be solved exactly. For example, although the hydrogen and helium atoms are similar in many respects, the mathematical descriptions of these atoms are fundamentally [Pg.557]

The orbitals that arise from the SCF method are quite similar to hydrogen orbitals. They have the same angular characteristics (same type of bound- [Pg.558]


See other pages where Further Development of the Polyelectronic Model is mentioned: [Pg.510]    [Pg.557]    [Pg.557]    [Pg.559]    [Pg.521]    [Pg.568]    [Pg.569]    [Pg.510]    [Pg.557]    [Pg.557]    [Pg.559]    [Pg.521]    [Pg.568]    [Pg.569]   


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Developing the model further

Further Developments

Further development of the

Model developed

Polyelectronic

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