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Chapter 11: Problem 50

In what type of material is the energy gap between the valence band and the conduction band greatest: metal, semiconductor, or insulator? Explain.

Short Answer

Expert verified
The energy gap between the valence band and the conduction band is greatest in an insulator.

Step by step solution

01

Understanding Band Theory

Band theory describes how electrons inhabit energy bands, and in a material, there are two main bands: the valence band, which is the band containing the highest energy electrons that are involved in bonding of the material, and the conduction band, which is higher in energy and usually empty. The gap between these two bands is known as the band gap.
02

Identifying Band Gaps in different materials

In metals, this band gap is non-existent or very small, meaning that electrons can move freely between the valence and conduction bands, which allows metals to conduct electricity. Semiconductors have a moderate band gap, and when this band gap is overcome (often by heat), they can conduct electricity. Insulators, on the other hand, have a large band gap, which prevents electrons from moving to the conduction band, making them poor conductors of electricity.
03

Conclusion

Therefore, based on the properties and definition of the band theory, the energy gap between the valence band and the conduction band is greatest in an insulator.

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Most popular questions from this chapter

Fluorine nitrate, \(\mathrm{FONO}_{2}\), is an oxidizing agent used as a rocket propellant. A reference source lists the following data for \(\mathrm{FO}_{\mathrm{a}} \mathrm{NO}_{2}\). (The subscript "a" shows that this O atom is different from the other two.) Bond lengths: \(\mathrm{N}-\mathrm{O}=129 \mathrm{pm}\) $$ \mathrm{N}-\mathrm{O}_{\mathrm{a}}=139 \mathrm{pm} ; \mathrm{O}_{\mathrm{a}}-\mathrm{F}=142 \mathrm{pm} $$ Bond angles: \(\mathrm{O}-\mathrm{N}-\mathrm{O}=125^{\circ}\) $$ \mathrm{F}-\mathrm{O}_{\mathrm{a}}-\mathrm{N}=105^{\circ} $$ \(\mathrm{NO}_{\mathrm{a}} \mathrm{F}\) plane is perpendicular to the \(\mathrm{O}_{2} \mathrm{NO}_{\mathrm{a}}\) plane Use these data to construct a Lewis structure(s), a three-dimensional sketch of the molecule, and a plausible bonding scheme showing hybridization and orbital overlaps.

Describe the bond order of diatomic carbon, \(\mathrm{C}_{2},\) with Lewis theory and molecular orbital theory, and explain why the results are different.

Describe the molecular geometry of \(\mathrm{CCl}_{4}\) suggested by each of the following methods: (a) Lewis theory; (b) valence-bond method using simple atomic orbitals; (c) VSEPR theory; (d) valence-bond method using hybridized atomic orbitals.

Construct a molecular orbital diagram for \(\mathrm{HF}\), and label the molecular orbitals as bonding, antibonding, or nonbonding.

Borazine, \(\mathrm{B}_{3} \mathrm{N}_{3} \mathrm{H}_{6}\) is often referred to as inorganic benzene because of its similar structure. Like benzene, borazine has a delocalized \(\pi\) system. Describe the molecular orbitals of the \(\pi\) system. Identify the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). How many nodes does the LUMO possess?
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