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Chapter 12: Problem 87

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 solids, fewer electrons interact with one another, resulting in less densely packed and distinguishable individual energy levels. The confinement of electrons also leads to distinct energy level changes compared to bulk materials; thus, the concept of "bands" is less relevant. Instead, terms like "energy levels" or "quantum states" more accurately describe bonding and electronic properties in nanoscale materials.

Step by step solution

01

Understand electron energy bands

Basically, electron energy bands are formed in a solid due to the interaction of electron wave-functions from neighboring atoms. When the size of the solid increases, the number of interacting electrons increases, allowing energy levels to be divided into smaller intervals and form continuous bands. In a bulk solid, the bands (energy levels) are densely spaced, making it difficult to identify individual energy levels. Instead, they form a collective band structure that determines the material's conductivity and other electronic properties.
02

Consider nanoscale dimensions

In contrast, a solid with nanoscale dimensions has fewer atoms, which results in fewer electrons interacting with one another. As a result, the individual energy levels are less densely packed and are easier to identify. Additionally, the confinement of electrons due to the small size of the solid can lead to distinct changes in energy levels compared to bulk materials, which cannot be classified within the same band structure.
03

Assess the term "bands" in nanoscale solids

Since the energy levels are no longer densely packed and continuous in nanoscale solids, the concept of "bands" becomes less relevant. Therefore, we may need to use a different term to describe bonding in nanoscale materials, such as "energy levels" or "quantum states," which acknowledge their discrete nature.
04

Conclusion

In conclusion, the notion of defined energy bands becomes less accurate when discussing solids of nanoscale dimensions due to the fewer electrons interactions and discrete energy levels. Instead, the concepts of individual energy levels or quantum states are more appropriate to describe bonding and electronic properties in such materials.

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The first LEDs were made from GaAs, which has a band gap of \(1.43 \mathrm{eV}\). What wavelength of light would be emitted from an LED made from GaAs? What region of the electromagnetic spectrum does this light correspond to: UV, visible, or IR?

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