Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 78

The first LEDs were made from GaAs, which has a band gap of $1.43 \mathrm{eV}$. 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?

Short Answer

Expert verified
The light emitted by a GaAs LED has a wavelength of approximately 865.6 nm, which corresponds to the infrared region of the electromagnetic spectrum.

Step by step solution

01

Convert the band-gap energy from eV to Joules

Given the band-gap energy, E = 1.43 eV, we need to convert it to Joules. We know that 1 eV = 1.6 × 10^(-19) J. So, we have: E (Joules) = E (eV) × 1.6 × 10^(-19) J/eV E (Joules) = 1.43 eV × 1.6 × 10^(-19) J/eV Now, calculate the energy in Joules: E (Joules) = 2.288 × 10^(-19) J
02

Find the wavelength using the energy-wavelength relationship

We will now use the energy-wavelength relationship formula: E = h × c / λ where E = energy (in Joules), h = Planck's constant (6.626 × 10^(-34) Js), c = speed of light (3 × 10^8 m/s), and λ = wavelength (in meters) Rearrange the formula to find λ: λ = h × c / E Now, plug in the values and find the wavelength: λ = (6.626 × 10^(-34) Js × 3 × 10^8 m/s) / (2.288 × 10^(-19) J) Calculate the wavelength λ: λ ≈ 8.656 × 10^(-7) m To express the wavelength in nanometers, we can convert meters to nanometers (1 m = 10^9 nm) λ ≈ 8.656 × 10^(-7) m × 10^9 nm/m ≈ 865.6 nm
03

Determine the region of the electromagnetic spectrum

Compare the calculated wavelength with the range of wavelengths for ultraviolet, visible, and infrared light: 1. Ultraviolet: 10 nm - 400 nm 2. Visible light: 400 nm - 700 nm 3. Infrared: 700 nm - 1 mm As 865.6 nm lies in the range of the infrared region, the emitted light from a GaAs LED corresponds to the infrared region of the electromagnetic spectrum. #Conclusion# The wavelength of the light emitted by a GaAs LED is approximately 865.6 nm, and it corresponds to the infrared region of the electromagnetic spectrum.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Write the chemical equation that represents the formation of (a) polychloroprene from chloroprene (polychloroprene is used in highway- pavement seals, expansion joints, conveyor belts, and wire and cable jackets) (b) polyacrylonitrile from acrylonitrile (polyacrylonitrile is used in home furnishings, craft yarns, clothing, and many other items).

What is the minimum number of atoms that could be contained in the unit cell of an element with a body-centered cubic lattice? $(\mathbf{a}) 1,(\mathbf{b}) 2,(\mathbf{c}) 3,(\mathbf{d}) 4,(\mathbf{e}) 5 .$

Potassium metal (atomic weight \(39.10 \mathrm{~g} / \mathrm{mol}\) ) adopts a body-centered cubic structure with a density of $0.856 \mathrm{~g} / \mathrm{cm}^{3}\(. (a) Use this information and Avogadro's number \)(6.022 \times\( \)10^{23}$ ) to estimate the atomic radius of potassium. (b) If potassium didn't react so vigorously, it could float on water. Use the answer from part (a) to estimate the density of \(\mathrm{K}\) if its structure were that of a cubic close-packed metal. Would it still float on water?

The karat scale used to describe gold alloys is based on mass percentages. (a) If an alloy is formed that is \(75 \mathrm{~mol} \%\) silver and $25 \mathrm{~mol} \%$ gold, what is the karat number of the alloy? Use Figure 12.18 to estimate the color of this alloy. (b) If an alloy is formed that is 75 mol\% copper and 25 mol\% gold, what is the karat number of the alloy? What is the color of this alloy?

What molecular structural features cause high-density polyethylene to be denser than low-density polyethylene?
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

Chemical Reactions

Read Explanation

Chemistry Branches

Read Explanation

Inorganic Chemistry

Read Explanation

Physical Chemistry

Read Explanation

Chemical Analysis

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free