Ch.13 - Solids & Modern Materials

Tro - Chemistry: A Molecular Approach 6th Edition

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Tro 6th Edition

Ch.13 - Solids & Modern Materials

Problem 67

Chapter 13, Problem 67

A substance has a band gap of 5.8 eV at 273 K. Is this substance best classified as an insulator, a semiconductor, or a metal?

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Understand the concept of band gap: The band gap is the energy difference between the valence band and the conduction band in a material. It determines the electrical conductivity of the material.

Classify materials based on band gap: Metals have no band gap (or a very small one), semiconductors have a moderate band gap (typically 0.5 to 3 eV), and insulators have a large band gap (greater than 3 eV).

Analyze the given band gap: The problem states that the substance has a band gap of 5.8 eV.

Compare the given band gap to typical values: Since 5.8 eV is greater than 3 eV, it falls into the range typical for insulators.

Conclude the classification: Based on the band gap value of 5.8 eV, classify the substance as an insulator.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Band Gap

The band gap is the energy difference between the valence band and the conduction band in a material. It determines how easily electrons can be excited from the valence band to the conduction band, influencing the electrical conductivity of the material. A larger band gap typically indicates that a material is less conductive, as more energy is required to promote electrons.

Classification of Materials

Materials are classified based on their electrical conductivity into three main categories: conductors, semiconductors, and insulators. Conductors have little to no band gap, allowing easy electron flow; semiconductors have a moderate band gap, enabling conductivity under certain conditions; and insulators have a large band gap, preventing electron flow under normal conditions.

Temperature Effects on Band Gap

The band gap can be influenced by temperature, as thermal energy can help electrons overcome the band gap. At absolute zero, the band gap remains constant, but as temperature increases, some materials may experience a reduction in band gap, affecting their conductivity. Understanding the temperature dependence is crucial for determining the behavior of materials in different conditions.

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Which solid would you expect to have the largest band gap? a. As(s) b. Sb(s) c. Bi(s)

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Which solid would you expect to have little or no band gap? a. Cu(s) b. Si(s) c. As(s)

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Does a photon of red light with a frequency of 4.29⨉10¹⁴ Hz have sufficient energy to promote an electron from the valence band to the conduction band in a sample of silicon (the band gap in silicon is 1.11 eV)?

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Indicate if each solid forms an n-type or a p-type semiconductor. b. germanium doped with gallium