Atomic orbital energy

Absorption of a photon is accompanied by the excitation of an electron from a lower-energy atomic orbital to an orbital of higher energy. Not all possible transitions between atomic orbitals are allowed. For sodium the only allowed transitions are those in which there is a change of +1 in the orbital quantum number ) thus transitions from s—orbitals are allowed, but transitions from s d orbitals are forbidden. The wavelengths of electromagnetic radiation that must be absorbed to cause several allowed transitions are shown in Figure 10.18. 

The Is orbital is the lowest-energy atomic orbital. It has no nodes—that is. the math sign of the function is positive everywhere. 

The next orbital requires one node, just as higher-energy atomic orbitals have extra nodes (Chapter 4). The only "y to include a node and maintain the symmetry of the system is to put the node through the central atom. This means that when this orbital is occupied there will be no electron density on this cen-... 

Relative orbital energies. Atomic orbitals that are close in energy will interact more strongly than those widely separated in energy. 

Figure 8.1 also illustrates that the band width depends on the j(,(r) function being used in the Bloch states (17). The 0(2s) orbital is the lowest energy atomic orbital and forms a low-lying band with little dispersion, that is, the band width is small. This orbital is relatively hghtly bound to the atomic core and the overlap between 0(2s) orbitals in neighboring unit cells wiU be small. The 0(2p) orbital on the other hand is more diffuse and so the overlap between neighboring cells leads to a calculated band width of around 5 eV. 

Photoexcited higher energies, which arise froni the higher-energy atomic orbitals. For example. 

By this mechanism the negative charge is not localized on the high energy atomic orbitals the nonbonding d electrons of the metal are stabilized, which easily explains why d systems such as the Ni(0), Pd(0), and Pt(0) derivatives are stable. 

According to the Bohr model of the atom, hydrogen s atomic emission spectrum results from electrons dropping from higher-energy atomic orbits to lower-energy atomic orbits. 

Molecular orbitals for polyatomic molecules can be constructed using the same principles (overlap of similar energy atomic orbitals) as for diatomic molecules. 

Optical electrons are electrons which can undergo optical transitions. In atoms the optical electrons are located in the outer, highest energy atomic orbitals. In the cases of interest to us in this paper, the optical electrons are located in the highest n and tt molecular orbitals. 

The principle of X-ray photoelectron spectroscopy (XPS) is a well-known photoelectric effect, in which the sample is irradiated by a source of low-energy X-rays that leads to the emission of electrons from the lower energy atomic orbitals, as shown schematically in Fig. 4.9b. The kinetic energy of the emitted photo-electrons, Ek, is given by ... 

---