Subshells, atomic relative energies

FIGURE 1.41 The relative energies of the shells, subshells, and orbitals in a many-electron atom. Each of the boxes can hold at most two electrons. Note the change in the order of energies of the 3d- and 4s-orbitals after Z = 20. 

In looking for other trends in the data of Figure 6.6, the near-zero Eea s of the alkaline earth metals (Be, Mg, Ca, Sr, Ba) are particularly striking. Atoms of these elements have filled s subshells, which means that the additional electron must go into a p subshell. The higher energy of the p subshell, together with a relatively low Zeff for elements on the left side of the periodic table, means that alkaline earth atoms accept an electron reluctantly and have Eea values near zero. 

Table 1. Stability, size, and magnetic moments for selected central atoms in icosahedral Fe12X clusters, that have all electrons in either filled or half-filled and maximally spin-polarized icosahedral electronic subshells. The binding energy (relative to Fe12 + X) is in Hartrees and radial bond distance in Bohr.

Before continuing the discussion of bonding theory, it is necessary to review briefly the electronic structure of the atom. Note that electrons in atoms are described as occupying orbitals which in turn constitute subshells and shells. Each orbital can hold no more than two electrons and electrons occupy the lowest energy orbitals of the atom. Figure 2.1 illustrates relative energies of atomic orbitals, where small circles represent orbitals. Note there is one s orbital in each shell, and three p orbitals, five d orbitals, and seven / orbitals in each shell. 

The Quantum-Mechanical Model The quantum-mechanical model for the atom describes electron orbitals, which are electron probability maps that show the relative probability of finding an electron in various places surrounding the atomic nucleus. Orbitals are specified with a number (n), called the principal quantum number, and a letter. The principal quantum number (n = 1,2,3. . . ) specifies the principal shell, and the letter (s, p, d, or f) specifies the subshell of the orbital. In the hydrogen atom, the energy of orbitals depends only on n. In multi-electron atoms, the energy ordering is Is 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s. 

FIGURE 4.5 Approximate relative energies of the subshells in the many-electron atom, reflecting the shifts due to nuclear shielding. The Is and 2s orbital energies are too low to appear in this plot. Actual relative energies will vary with number and excitation of electrons. 

An electron band is a series of electron states that are closely spaced with respect to energy, and one such band may exist for each electron subshell found in the isolated atom. Electron energy band structure refers to the manner in which the outermost bands are arranged relative to one another and then filled with electrons. 

Continuing this pattern, the first and second lEs of the actinides are less sensitive to increasing atomic number than the third lEs (Figure 2.6). However, owing to the similarity in energies between the 6d and 5f subshells, the behaviour of the third lEs is less simple than for the lanthanides, although maxima do appear at Am and No ". The behaviour of the actinide elements is also complicated by the effects of relativity. These result in a contraction of the 7s and 7p orbitals but an expansion and destabilization of the 6d and 5f orbitals. As a consequence, the actinide valence shell 6d and 5f electrons are more easy to ionize than would be predicted by a non-relativistic model. 

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