Ch 42: Molecules and Condensed Matter

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 42: Molecules and Condensed Matter

Problema 42.17b

Capitolo 42, Problema 42.17b

The maximum wavelength of light that a certain silicon photocell can detect is 1.11 mm. (b) Explain why pure silicon is opaque.

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To understand why pure silicon is opaque, we need to consider its electronic structure and band gap. Silicon is a semiconductor with a specific energy band gap.

In a semiconductor, the band gap is the energy difference between the valence band (where electrons are normally present) and the conduction band (where electrons can move freely and conduct electricity).

For silicon, the band gap is about 1.1 eV. This means that photons with energy less than 1.1 eV cannot excite electrons from the valence band to the conduction band.

Light with a wavelength of 1.11 mm corresponds to a photon energy that is much lower than 1.1 eV. Therefore, such light does not have enough energy to bridge the band gap in silicon.

As a result, pure silicon does not absorb this light and is opaque to it, because the photons do not have sufficient energy to excite electrons across the band gap.

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Band Gap Energy

The band gap energy is the energy difference between the valence band and the conduction band in a semiconductor. For silicon, this gap determines the range of photon energies it can absorb. Photons with energy less than the band gap cannot excite electrons to the conduction band, making pure silicon opaque to certain wavelengths.

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04:10

Intro to Energy & Types of Energy

Photon Absorption

Photon absorption in semiconductors occurs when photons have enough energy to move electrons from the valence band to the conduction band. Silicon's band gap requires photons with energies corresponding to wavelengths shorter than its maximum detectable wavelength. Longer wavelengths, like 1.11 mm, lack sufficient energy for absorption, contributing to opacity.

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Radiation Pressure

Material Transparency

Material transparency is determined by its ability to transmit light without significant absorption. In pure silicon, the absence of free charge carriers and the specific band gap result in limited absorption of longer wavelengths, rendering it opaque. Doping or altering the material can change its transparency by modifying the band structure.

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06:37

Ray Diagrams for Converging Lenses

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