Ch.12 - Solids and Modern Materials

Brown - Chemistry: The Central Science 15th Edition

Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook

Brown 15th Edition

Ch.12 - Solids and Modern Materials

Problem 96a

Chapter 12, Problem 96a

CdS has a band gap of 2.4 eV. If large crystals of CdS are illuminated with ultraviolet light, they emit light equal to the band gap energy. (a) What color is the emitted light?

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Understand that the band gap energy of CdS is 2.4 eV, which is the energy of the emitted light when illuminated with UV light.

Convert the energy from electron volts (eV) to joules (J) using the conversion factor: 1 eV = 1.602 x 10^{-19} J.

Use the energy-wavelength relationship given by the equation: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy in joules, \( h \) is Planck's constant (6.626 x 10^{-34} J·s), \( c \) is the speed of light (3.00 x 10^8 m/s), and \( \lambda \) is the wavelength in meters.

Rearrange the equation to solve for wavelength: \( \lambda = \frac{hc}{E} \). Substitute the values for \( h \), \( c \), and the energy in joules to find the wavelength.

Determine the color of the emitted light by comparing the calculated wavelength to the visible light spectrum, where different wavelengths correspond to different colors.

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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 semiconductor or insulator. It determines the wavelengths of light that a material can absorb or emit. In the case of CdS, a band gap of 2.4 eV indicates that it can absorb photons with energy equal to or greater than this value, leading to the emission of light when excited.

Photon Energy and Color

The energy of a photon is directly related to its wavelength and frequency, as described by the equation E = hf, where E is energy, h is Planck's constant, and f is frequency. The color of light emitted by a material corresponds to its photon energy; for CdS, a band gap of 2.4 eV corresponds to a wavelength of approximately 517 nm, which falls within the green region of the visible spectrum.

Ultraviolet Light and Excitation

Ultraviolet (UV) light has higher energy than visible light and can excite electrons in a semiconductor like CdS. When large crystals of CdS are illuminated with UV light, electrons are promoted from the valence band to the conduction band, creating electron-hole pairs. When these electrons return to their ground state, they release energy in the form of light, which corresponds to the band gap energy.

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Textbook Question

CdS has a band gap of 2.4 eV. If large crystals of CdS are illuminated with ultraviolet light, they emit light equal to the band gap energy. (b) Would appropriately sized CdS quantum dots be able to emit blue light?

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Textbook Question

Which statement correctly describes a difference between graphene and graphite? (a) Graphene is a molecule but graphite is not. (b) Graphene is a single sheet of carbon atoms and graphite contains many, and larger, sheets of carbon atoms. (c) Graphene is an insulator but graphite is a metal. (d) Graphite is pure carbon but graphene is not. (e) The carbons are sp2 hybridized in graphene but sp3 hybridized in graphite.

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Textbook Question

CdS has a band gap of 2.4 eV. If large crystals of CdS are illuminated with ultraviolet light, they emit light equal to the band gap energy. (c) What about red light?

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Textbook Question

Write the chemical equation that represents the formation of (b) polyacrylonitrile from acrylonitrile (polyacrylonitrile is used in home furnishings, craft yarns, clothing, and many other items).

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