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. (a) What color is the emitted light?
Ch.12 - Solids and Modern Materials
Chapter 12, Problem 97
Indicate whether each statement is true or false: (a) The band gap of a semiconductor decreases as the particle size decreases in the 1–10-nm range. (b) The light that is emitted from a semiconductor, upon external stimulation, becomes longer in wavelength as the particle size of the semiconductor decreases.
Verified step by step guidance1
Step 1: Understand the relationship between particle size and band gap in semiconductors. In the 1–10 nm range, as the particle size decreases, the band gap typically increases due to quantum confinement effects.
Step 2: Analyze statement (a). Given the relationship from Step 1, if the band gap increases as the particle size decreases, then the statement 'The band gap of a semiconductor decreases as the particle size decreases in the 1–10-nm range' is false.
Step 3: Understand the relationship between band gap and emitted light wavelength. The energy of emitted light is inversely related to its wavelength (E = hc/λ). A larger band gap corresponds to higher energy and thus shorter wavelength.
Step 4: Analyze statement (b). If the band gap increases with decreasing particle size, the emitted light should have higher energy and shorter wavelength. Therefore, the statement 'The light that is emitted from a semiconductor, upon external stimulation, becomes longer in wavelength as the particle size of the semiconductor decreases' is false.
Step 5: Conclude that both statements (a) and (b) are false based on the analysis of the relationship between particle size, band gap, and emitted light wavelength in semiconductors.
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. It determines the electrical conductivity and optical properties of the material. In nanomaterials, the band gap can change due to quantum confinement effects, where smaller particle sizes can lead to an increase in band gap energy.
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Quantum Confinement
Quantum confinement occurs when the dimensions of a semiconductor are reduced to the nanoscale, typically below 10 nm. This phenomenon leads to discrete energy levels and affects the electronic and optical properties of the material. As particle size decreases, the energy levels become more spaced out, which can increase the band gap and affect the wavelength of emitted light.
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Photoluminescence
Photoluminescence is the emission of light from a semiconductor after it absorbs photons and re-emits them. The wavelength of the emitted light is influenced by the band gap energy; a larger band gap results in shorter wavelengths (higher energy), while a smaller band gap leads to longer wavelengths (lower energy). Thus, changes in particle size can significantly impact the photoluminescent properties of semiconductors.
Related Practice
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?
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?
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.