Atoms, with many electrons

Diffraction of x-rays from many atoms with many electrons results in a two-dimensional continuous pattern of peaks and valleys. Diffraction from a hquid or an amorphous (noncrystalline) soHd results in a continuous pattern with few features, mainly broad peaks and valleys. 

Instead of writing out the entire electron configuration of an atom, especially an atom with many electrons, we sometimes abbreviate the configuration by using the configuration of the previous noble gas and represent the rest of the electrons explicitly. For example, the full configuration of iron can be given as... 

For an atom with many electrons, the first electron fills the lowest energy orbital, and the second electron fills the next lowest energy orbital, and so forth. For a one-electron atom or ion, the energy depends only on n, the principal quantum number but for a many-electron atom or ion, the value of I also plays a role in the energy. The order of atomic orbital energy is given by... 

It is possible in any single case to calculate each of the orbital energies in an atom with many electrons. The results may be presented as an energy-level scheme such as is given in Figure 1-5. 

The value of a (ca. 10 5 for H, larger for heavier atoms with many electrons) is dimensionless and field independent. Many advanced texts on NMR tabulate signal positions in terms of a rather than in terms of 5 (chemical shift). See Example 6.4. 

Note from Table 16.2 that the freezing point rises going down the group. The principal cause for this trend is that as the mass (and the atomic number) increases, the number of electrons increases, so there is an increased chance of the occurrence of momentary dipoles. We say that large atoms with many electrons exhibit a higher polarizability than small atoms. Thus the importance of London dispersion forces greatly increases as atomic size increases. 

Explain the meaning of the aufbau principle as it applies to atoms with many electrons. (5.3)... 

Atoms with many electrons are described by Hartree s SCF method, in which each electron is assumed to move under the influence of an effective field Veff (r) due to the average positions of all the other electrons. This method generates a set of one-electron wave functions called the Hartree orbitals ip (f) with energy values where a represents the proper set of quantum numbers. Hartree orbitals bear close relation to the hydrogen atomic orbitals but are not the same objects. 

E1.17 In an atom with many electrons like beryllium, the outer electrons (the 2s electrons in this case) are simultaneously attracted to the positive nucleus (the protons in the nucleus) and repelled by the negatively charged electrons occupying the same orbital (in this case, the 2s orbital). The two electrons in the Is orbital on average are statically closer to the nucleus than the 2s electrons, thus the Is electrons feel more positive charge than the 2s electrons. The 1 s electrons also shield that positive charge from the 2s electrons, which are further out from the nucleus than the Is electrons. Consequently, the 2s electrons feel less positive charge than the Is electrons for beryllium. 

The way an atomic orbital varies with direction is known exactly, giving the shape of s, p, d, etc., orbitals. For atoms with many electrons, however, the way the orbital varies with distance from the nucleus can only be approximated, albeit very accurately with modem computational methods. Most calculations start with a set of mathematical functions representing the orbital. This set is called a basis set. 

C tend to make the reactions fast. In consequence, atoms with many electron shells are associated with fast reactions, whether their bonds are broken or whether they make bonds in the reaction. 

We can simplify our problem by dropping out the repulsion term entirely. Similarly, in atoms with many electrons, we will ignore the electron repulsion terms in our first treatment. Then for any multielectron atom we have... 

For atoms with many electrons, the atomic state in question is not always spherically symmetric. The central field approximation is applied, meaning that V(r) is an average over 0 and cp. Variable separation can still be made in Equation 2.2. 

Hartree set forth to calculate wave functions for atoms with many electrons soon after the discovery of the SE of the hydrogen atom. His idea was to write down the repulsive average potential for the electrons, which is easily done using electrostatic... 

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