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Ch.12 - Solids and Modern Materials
Chapter 12, Problem 77

The semiconductor CdSe has a band gap of 1.74 eV. What wavelength of light would be emitted from an LED made from CdSe? What region of the electromagnetic spectrum does this correspond to?

Verified step by step guidance
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Step 1: Understand the relationship between energy and wavelength. The energy of a photon is related to its wavelength by the equation: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy in electron volts (eV), \( h \) is Planck's constant (\( 4.1357 \times 10^{-15} \) eV·s), \( c \) is the speed of light (\( 3.00 \times 10^8 \) m/s), and \( \lambda \) is the wavelength in meters.
Step 2: Rearrange the equation to solve for wavelength \( \lambda \). The equation becomes: \( \lambda = \frac{hc}{E} \).
Step 3: Substitute the given values into the equation. Use \( E = 1.74 \) eV, \( h = 4.1357 \times 10^{-15} \) eV·s, and \( c = 3.00 \times 10^8 \) m/s.
Step 4: Calculate the wavelength \( \lambda \) in meters. After substituting the values, perform the calculation to find \( \lambda \).
Step 5: Convert the wavelength from meters to nanometers (1 m = 10^9 nm) and determine the region of the electromagnetic spectrum it corresponds to. Typically, visible light ranges from about 400 nm to 700 nm.

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 energy required for an electron to jump from the valence band to the conduction band, allowing for electrical conduction. In the case of CdSe, a band gap of 1.74 eV indicates the energy of photons that can be absorbed or emitted by the material.
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Photon Energy and Wavelength Relationship

The energy of a photon is inversely related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. By rearranging this equation, one can calculate the wavelength of light emitted by a semiconductor when an electron transitions from the conduction band to the valence band, releasing energy in the form of a photon.
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Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, ranging from radio waves to gamma rays. Each type of radiation is characterized by its wavelength and frequency. The visible light region, which is relevant for LEDs, typically ranges from about 400 nm (violet) to 700 nm (red). Understanding where the emitted wavelength falls within this spectrum helps identify its color and potential applications.
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