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Chapter 12: Problem 95

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 a solid with nanoscale dimensions, the concept of "bands" may not be the most accurate description of bonding, as quantum confinement effects come into play, leading to discrete energy levels instead of continuous energy bands found in bulk materials. This discreteness in energy levels is a result of electron wave functions being confined to a smaller spatial region, limiting the overlap between molecular orbitals. Therefore, band theory does not accurately represent the electronic structure or bonding in nanoscale solids.

Step by step solution

01

Introducing Band Theory

Band theory is used to describe the energy states of electrons in a solid. In a solid, the valence electrons of the atoms are shared with neighboring atoms, forming numerous molecular orbitals that overlap with each other. When there are a large number of overlapping orbitals, they effectively merge to form continuous energy bands. The band structure ultimately depends on the distribution of the electron density and the atomic arrangement. There are two types of energy bands: valence bands filled with electrons and conduction bands that are empty or partially filled.
02

Understanding Nanoscale Dimensions

Nanoscale dimensions refer to solids where at least one of their dimensions is on the order of nanometers, typically between 1 and 100 nanometers in size. In such small scales, the properties of materials start to deviate from their bulk counterparts due to quantum confinement effects, which result in electron wave functions being confined in a limited space. This confinement leads to an entirely new set of physical behaviors and properties, which are not accurately described using the traditional band theory.
03

Effects of Quantum Confinement and Discreteness

In a nanoscale solid, quantum confinement results in electron wave functions being confined to a much smaller spatial region than in bulk materials. This confinement manifests itself through the discreteness of energy levels, meaning that the continuous energy bands seen in bulk materials are replaced by discrete energy states or levels. As the size of the solid reduces to the nanoscale, the overlap between molecular orbitals is limited, diminishing the formation of continuous energy bands. Instead, these discrete orbitals or quantum states are more representative of the bonding in nanoscale solids.
04

Conclusion

In conclusion, the term "bands" may not be the most accurate description for bonding in a solid with nanoscale dimensions. This is mainly due to the quantum confinement effects, which lead to discrete energy levels instead of continuous energy bands typically found in bulk materials. Hence, band theory does not accurately describe the electronic structure or bonding in nanoscale solids.

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