/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 24 The first LEDs were made from Ga... [FREE SOLUTION] | 91影视

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Chapter 12: Problem 24

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: UV, Visible, or IR?

Short Answer

Expert verified
The GaAs LED emits light with a wavelength of 866 nm, corresponding to the infrared region of the electromagnetic spectrum.

Step by step solution

01

Convert energy to Joules

First, we have to convert the energy from electron volts (eV) to Joules (J) using the conversion factor 1 eV = \(1.602 \times 10^{-19}\) J. Thus: \(E = 1.43 \ \text{eV} \times 1.602 \times 10^{-19} \frac{\text{J}}{\text{eV}} = 2.29 \times 10^{-19} \ \text{J}\)
02

Rearrange the formula to solve for wavelength

Now, we can rearrange the formula: \(\lambda = \dfrac{hc}{E}\)
03

Plug in values to find the wavelength

We know the values of h and c, so we can plug them in: \(\lambda = \dfrac{(6.626 \times 10^{-34} \ \text{J} \cdot \text{s})(2.998 \times 10^8 \ \frac{\text{m}}{\text{s}})}{2.29 \times 10^{-19} \ \text{J}}\)
04

Calculate the wavelength

Now, we can calculate the wavelength: \(\lambda = \dfrac{(6.626 \times 10^{-34} \ \text{J} \cdot \text{s})(2.998 \times 10^8 \ \frac{\text{m}}{\text{s}})}{2.29 \times 10^{-19} \ \text{J}} \approx 8.66 \times 10^{-7} \ \text{m}\)
05

Convert wavelength to nanometers

For convenience, we can convert the wavelength to nanometers (nm): \(\lambda = 8.66 \times 10^{-7} \ \text{m} \times \dfrac{10^9 \ \text{nm}}{1 \ \text{m}} = 866 \ \text{nm}\)
06

Identify the region of the electromagnetic spectrum

With the wavelength calculated, we can identify the region of the electromagnetic spectrum it falls into: - UV: 10 nm - 400 nm - Visible: 400 nm - 700 nm - IR: 700 nm - 1,000,000 nm The wavelength of 866 nm falls in the infrared (IR) region. Hence, the GaAs LED emits light with a wavelength of 866 nm, corresponding to the infrared region of the electromagnetic spectrum.

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Most popular questions from this chapter

Silicon has diamond structure (Figure 12.3) with unit cell edge length of \(5.43 \AA\) and eight atoms per unit cell. (a) How many silicon atoms are there in \(1 \mathrm{~cm}^{3}\) of material? (b) Suppose you dope that \(1-\mathrm{cm}^{3}\) sample of silicon with 1 ppm of phosphorus that will increase the conductivity by a factor of a million. How many milligrams of phosphorus are required?

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