Energy bands spreading

The origin of the cohesive energy of a metal can now be obtained. Suppose that the energy band spreads out symmetrically from the original atomic orbital energy and that the energy levels in the band are all equally spaced. (This is not true, but it is a... 

For purposes of illustration, consider a lithium crystal weighing one gram, which contains roughly 1023 atoms. Each Li atom has a half-filled 2s atomic orbital (elect conf. Li = ls22s1). When these atomic orbitals combine, they form an equal number, 1023, of molecular orbitals. These orbitals are spread over an energy band covering about 100 kJ/moL It follows that the spacing between adjacent MOs is of the order of... 

The absorption and emission spectra of a fluorophore are bands spread over a range of wavelengths with at least one peak of maximal absorbance and emission that corresponds to the So-Si and Si—S0 transitions, respectively. There are several vibrational levels within an electronic state and transitions from one electronic to several vibrational states are potentially possible. This determines that the spectra are not sharp but consist of broad bands. The emission spectrum is independent of the excitation wavelength. The energy used to excite the fluorophore to higher electronic and vibrational levels is very rapidly dissipated, sending the fluorophore to the lowest vibrational level of the first electronic excited state (Si) from where the main fluorescent transition occurs [3] (see Fig. 6.1). 

In ultraviolet photoelectron spectroscopy (UPS or U-PES), the irradiation (usually a He(I) (21.2 eV) or He(II) (40.8 eV) source) causes the displacement of a valence electron. Although an important method of studying the electronic nature of molecules in the gas phase, it is less useful for studying the surfaces of metals, since the valence electrons are in a continuous (conducting) energy band with a spread of about 10 eV. Adsorbed layers can, however, usefully be investigated in terms of the difference between the spectrum following adsorption and that for the clean metal surface. 

Where (in energy) the bands are The bands spread out, more or less dispersed, around a center of gravity. This is the energy of that... 

As the 2s orbitals combine and spread out to form a band, it will overlap with the band generated by the combination of 2p orbitals. So, in solid beryllium (and similarly in other solid elements in Groups I—III (1,2 and 13)), the band generated by combination of atomic orbitals is not a pure 2s band, but one continuous band made by combination of both 2s and 2p orbitals. In consequence, there are unoccupied levels available in the energy band of solid beryllium into which electrons may be excited. This allows the development of metallic properties. 

From a quantum-mechanical point of view, it is said that electron wave functions are spread out over the entire solid atomic levels are transformed into an energy band, where differences between energy levels are so small that it can be thought of as a continuous distribution of states. Electrons in a band can no longer be assigned to a particular cation. They are delocalised and become free, in the sense that having energy states available, they can easily be excited by an external electrical field to transport current, for example. 

The spreading of the energy bands associated with the outer orbitals increases for the heavier elements, simply because of their larger size and consequently greater interaction. Because of this, the outer orbitals on most of the heavier elements in... 

An energy band is due to the spreading out of energy levels as a result of ... 

In the earliest theories of the solid state, electrons were perceived as being free and non-interacting - an electron gas. In this model, the atomic orbitals of the component atoms are spread out into energy bands, the detailed form of which depends upon the crystal structure of the phase. An upper energy band which is only partly filled with electrons characterises a metal with itinerant (freely moving) non-interacting electrons. 

---