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Chapter 12: Problem 91

Explain why "bands" may not be the most accurate description of bonding in a solid when the solid has nanoscale dimensions.

Short Answer

Expert verified
In nanoscale materials, the quantum confinement effect causes the energy states to become more discrete, resembling atomic energy levels rather than continuous bands found in bulk solid-state materials. Thus, the term "bands" is not the most accurate description of bonding in a solid with nanoscale dimensions, as their electronic structure is better described as discrete energy states akin to atomic levels.

Step by step solution

01

Introduction to Energy Bands and Bonding in Solids

In a crystalline solid, the atoms are arranged in a periodic lattice structure. When the atoms are close to each other, their discrete energy levels interact due to wavefunction overlap and form energy bands. These overlap regions are called molecular orbitals. The electronic structure of the entire crystal can be described by these bands, with the valence band including the occupied orbitals (filled with electrons) and the conduction band being the unoccupied orbitals (empty at absolute zero).
02

Quantum Confinement

Quantum confinement refers to a phenomenon observed in nanoscale materials in which the behavior of electrons is confined within the dimensions of the material. This effect occurs when the size of the material is comparable or smaller than the particle's de Broglie wavelength, which influences the energy states of electrons.
03

Energy States in Nanoscale Materials

When a solid has nanoscale dimensions, the quantum confinement effect results in the breakdown of the traditional energy band picture. The energy states become more discrete, as observed in individual quantum wells, wires, or dots, and the bands are no longer continuous. Instead, they appear as a series of discrete energy levels, resembling the atomic energy levels of individual atoms rather than continuous bands.
04

"Bands" in Nanoscale Materials

The term "bands" may not be the most accurate description of bonding in nanoscale solid materials due to quantum confinement. As mentioned earlier, the continuous energy bands split into discrete levels as a result of size reduction in the material. Therefore, the electronic structure in nanoscale materials is better described as discrete energy states akin to atomic levels than continuous energy bands found in bulk solid-state materials.
05

Conclusion

In conclusion, the term "bands" is not particularly accurate when describing the bonding in a solid with nanoscale dimensions. The quantum confinement effect in these materials causes the energy states to become more discrete, resembling atomic energy levels rather than continuous bands. Hence, it is more appropriate to refer to the electronic structure of nanoscale materials as a series of discrete energy states rather than energy bands.

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Most popular questions from this chapter

Besides the cubic unit cell, which other unit cell(s) has edge lengths that are all equal to each other? (a) Orthorhombic, (b) hexagonal, (c) rhombohedral, (d) triclinic, (e) both rhombohedral and triclinic.

Indicate the type of solid (molecular, metallic, ionic, or covalent-network) for each compound: (a) \(\mathrm{CaCO}_{3}\), (b) \(\mathrm{Pt}\), (c) \(\mathrm{ZrO}_{2}\) (melting point, \(\left.2677^{\circ} \mathrm{C}\right)\), (d) table sugar \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\), (e) benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\), (f) \(\mathrm{I}_{2}\).

Proteins are naturally occurring polymers formed by condensation reactions of amino acids, which have the general structure In this structure, \(-\mathrm{R}\) represents \(-\mathrm{H},-\mathrm{CH}_{3}\), or another group of atoms; there are 20 different natural amino acids, and each has one of 20 different \(R\) groups. (a) Draw the general structure of a protein formed by condensation polymerization of the generic amino acid shown here. (b) When only a few amino acids react to make a chain, the product is called a "peptide" rather than a protein; only when there are 50 amino acids or more in the chain would the molecule be called a protein. For three amino acids (distinguished by having three different \(R\) groups, R1, R2, and \(R 3\) ), draw the peptide that results from their condensation reactions. (c) The order in which the \(\mathrm{R}\) groups exist in a peptide or protein has a huge influence on its biological activity. To distinguish different peptides and proteins, chemists call the first amino acid the one at the " \(\mathrm{N}\) terminus" and the last one the one at the "C terminus." From your drawing in part (b) you should be able to figure out what " \(\mathrm{N}\) terminus" and " \(\mathrm{C}\) terminus" mean. How many different peptides can be made from your three different amino acids?

What kinds of attractive forces exist between particles (atoms, molecules, or ions) in (a) molecular crystals, (b) covalentnetwork crystals, (c) ionic crystals, (d) and metallic crystals?

What is the minimum number of atoms that could be contained in the unit cell of an element with a body-centered cubic lattice? (a) 1, (b) 2, (c) 3, (d) 4, (e) 5 .
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