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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
All textbooksBrown 15th EditionCh.12 - Solids and Modern MaterialsProblem 78
Chapter 12, Problem 78

The first LEDs were made from GaAs, which has a band gap of 1.43 eV. What wavelength of light would be emitted from an LED made from GaAs? What region of the electromagnetic spectrum does this light correspond to: ultraviolet, visible, or infrared?

Verified step by step guidance
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Step 1: Understand that the energy of the emitted light from an LED is equal to the band gap energy of the semiconductor material, which in this case is 1.43 eV for GaAs.
Step 2: Convert the energy from electron volts (eV) to joules (J) using the conversion factor: 1 eV = 1.602 x 10^-19 J.
Step 3: 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.
Step 4: Rearrange the equation to solve for wavelength: \( \lambda = \frac{hc}{E} \). Substitute the values for \( h \), \( c \), and the converted energy \( E \) 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 falls into by comparing the wavelength to known ranges: ultraviolet (10-400 nm), visible (400-700 nm), or infrared (700 nm and above).

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, which is crucial for the emission of light in LEDs. The band gap is typically measured in electron volts (eV), and for GaAs, it is 1.43 eV.
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Wavelength and Energy Relationship

The wavelength of light emitted by a semiconductor can be calculated using the relationship between energy and wavelength, given 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 determine the wavelength corresponding to the band gap energy of the material.
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Electromagnetic Spectrum Regions

The electromagnetic spectrum is divided into various regions based on wavelength, including ultraviolet, visible, and infrared light. Visible light ranges from approximately 400 nm to 700 nm, while infrared light has longer wavelengths, typically from 700 nm to 1 mm. Understanding where the emitted light falls within this spectrum helps classify the type of light produced by the LED.
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(a) What is a monomer? (b) Which of these molecules can be used as a monomer: ethanol, ethene (also called ethylene), methane?

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If you want to dope GaAs to make an n-type semiconductor with an element to replace Ga, which element would you pick? a. Zn b. Al c. In or d. Si