) How does BAND theory explains metallic character
of Lithium?
Answers
Answer:
Most metals have very compact crystal structures involving either the body-centered cubic, face-centered cubic, or hexagonal closest-packed lattices. Thus every atom in a metal is usually surrounded by 8 or 12 equivalent nearest neighbors. How can each atom be bonded to so many of its fellow atoms? Although there are plenty of electropositive atoms to donate electrons, there are no electronegative atoms to receive them, and so ionic bonding seems unlikely. Ordinary covalent bonding can also be ruled out. Each covalent bond would require one electron from each atom, and no metal has 12 valence electrons.
A valuable clue to the nature of bonding in metals is provided by their ability to conduct electricity. Electrons can be fed into one end of a metal wire and removed from the other end without causing any obvious change in the physical and chemical properties of the metal. To account for this freedom of movement modern theories of metallic bonding assume that the valence electrons are completely delocalized; that is, they occupy molecular orbitals belonging to the metallic crystal as a whole. These delocalized electrons are often referred to as an electron gas or an electron sea. Positive metal ions produced by the loss of these valence electrons can then be thought of as “floating” in this three-dimensional sea. Each ion is held in place by the attraction of the negatively charged electron sea and the repulsion of its fellow positive ions.
In order to see how MO theory can be applied to metals, let us first consider the simplest case, lithium. If two lithium atoms are brought together, the 1s core electrons remain essentially unchanged since there is virtually no overlap between them. The 2s orbitals, by contrast, overlap extensively and produce both a bonding and an antibonding orbital. Only the bonding orbital will actually be occupied by the two electrons, as shown in Figure 1. Somewhat higher than these two orbitals are a group of six unoccupied orbitals produced by the overlap of six 2p atomic orbitals (three on each atom). Suppose now we add a third atom to the two already considered so that we form a triangular molecule of formula Li3. As shown in the figure, the overlap of three 2s orbitals produces a lower group of three orbitals, while the overlap of three times three 2p orbitals produces a higher group of nine orbitals. Again the total number of molecular orbitals is equal to the number of atomic orbitals from which they are derived.
Continuing to add lithium atoms in this fashion, we soon attain a cluster of 25 lithium atoms. The energy-level situation for a cluster this size is a lower group of 25 MO’s, all deriving from 2s atomic orbitals, and a higher group of 75 MO’s, all deriving from 2p atomic orbitals. Note how closely spaced these energy levels have become. This is in line with the tendency for the energy levels to get closer the greater the degree of delocalization.
Finally, if we add enough lithium atoms to our cluster to make a visible, weigh-able sample of lithium, say 1020 atoms, the energy spacing between the molecular orbitals becomes so small it is impossible to indicate in the figure or even to measure. In effect an electron jumping among these levels can have any energy within a broad band from the lowest to highest. In consequence this view of electronic structure in solids is often referred to as the band theory of solids.
Explanation:
Answer:
The valence band and conduction band serve as the foundation for the band theory of metals. It is often referred to as the zone theory or band theory of solids. It clearly and precisely describes conductors, semiconductors, and insulators.
Explanation:
A metal wire may have electrons introduced into one end and withdrawn from the other without the metal's physical and chemical characteristics changing noticeably.
Since there is almost no overlap between them, if two lithium atoms are brought together, the 1s core electrons largely remain intact.
Conductor, semiconductor, and insulator behavior may all be explained using band theory, in which a solid's molecular orbitals are transformed into a sequence of continuous energy levels. Metallic conductors are the most common.
Hence, the band theory explained the metallic character of lithium is mentioned above.
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