Ch.12 - Solids and Solid-State Materials

McMurry8th EditionChemistryISBN: 9781292336145Not the one you use?Change textbook

McMurry 8th Edition

Ch.12 - Solids and Solid-State Materials

Problem 104

Chapter 12, Problem 104

Gallium arsenide, a material used to manufacture laser printers and compact disc players, has a band gap of 130 kJ/mol. Is GaAs a metallic conductor, a semiconductor, or an electrical insulator? With what group 4A element is GaAs isoelectronic? (Isoelectronic substances have the same number of electrons.)

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Identify the type of material based on the band gap energy. A band gap of 130 kJ/mol is relatively small, indicating that GaAs is a semiconductor.

Recall that semiconductors have a band gap that allows them to conduct electricity under certain conditions, unlike metallic conductors which have no band gap, and insulators which have a large band gap.

Determine the number of valence electrons in GaAs. Gallium (Ga) is in group 3A and has 3 valence electrons, while arsenic (As) is in group 5A and has 5 valence electrons, totaling 8 valence electrons for GaAs.

Identify the group 4A element that is isoelectronic with GaAs. Group 4A elements have 4 valence electrons, and when combined in a compound like silicon (Si) or germanium (Ge), they also have 8 valence electrons, making them isoelectronic with GaAs.

Conclude that GaAs is isoelectronic with silicon (Si) or germanium (Ge), as these group 4A elements have the same number of total electrons in their compounds.

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Key Concepts

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

Band Gap Energy

The band gap energy is the energy difference between the valence band and the conduction band in a material. It determines a material's electrical conductivity; materials with a small band gap (like semiconductors) can conduct electricity under certain conditions, while those with a large band gap (like insulators) do not conduct electricity well. Gallium arsenide (GaAs) has a band gap of 130 kJ/mol, indicating it is a semiconductor.

Semiconductors

Semiconductors are materials that have electrical conductivity between that of conductors and insulators. They can conduct electricity under specific conditions, such as when energy is supplied (e.g., heat or light). GaAs is classified as a semiconductor due to its band gap, which allows it to conduct electricity when energy is applied, making it useful in electronic devices like laser printers and CD players.

Isoelectronic Species

Isoelectronic species are atoms, ions, or molecules that have the same number of electrons, resulting in similar electronic configurations. In the case of GaAs, it is isoelectronic with silicon (Si), a group 4A element, meaning they both have the same number of electrons in their outer shells. This property is significant in understanding the behavior of materials in electronic applications.

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Amphoteric Species

Related Practice

Textbook Question

A photovoltaic cell contains a p–n junction that that converts solar light to electricity. An optimum semiconductor would have its band-gap energy matched to the wavelength of maximum solar intensity at the Earth's surface. (a) What is the color and approximate wavelength of maximum solar intensity at the Earth's surface? Refer to the figure for Problem 12.102.

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Textbook Question

The YBa₂Cu₃O₇ superconductor can be synthesized by the solgel method from a stoichiometric mixture of metal ethoxides followed by heating in oxygen. How many grams of Y(OCH₂CH₃)₃ and how many grams of Ba(OCH₂CH₃)₂ are required to react with 75.4 g of Cu(OCH₂CH₃)₂ and an excess of water? Assuming a 100% yield, how many grams of YBa₂Cu₃O₇ are obtained?

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Textbook Question

What is the coordination environment of the K+ ions in thefullerene-based superconductor K3C60?

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Textbook Question

Looking at Figure 12.27 identify the coordination numbers of the Cu, Y, and Ba atoms.

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Textbook Question

A photovoltaic cell contains a p–n junction that that converts solar light to electricity. An optimum semiconductor would have its band-gap energy matched to the wavelength of maximum solar intensity at the Earth's surface. (b) Which of the following semiconductors absorb at a wavelength matched with maximum solar intensity? CdTe with a band-gap energy of 145 kJ/mol or ZnSe with a band-gap energy of 248 kJ/mol.

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Textbook Question

A photovoltaic cell contains a p–n junction that converts solar light to electricity. (a) Silicon semiconductors with a band-gap energy of 107 kJ/mol are commonly used to make photovoltaic cells. Calculate the wavelength that corresponds to the band-gap energy in silicon.

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