/*! 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 23 The semiconductor GaP has a band... [FREE SOLUTION] | 91影视

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Chapter 12: Problem 23

The semiconductor GaP has a band gap of \(2.2 \mathrm{eV}\). Green LEDs are made from pure GaP. What wavelength of light would be emitted from an LED made from GaP?

Short Answer

Expert verified
The emitted wavelength of light from a GaP LED can be calculated using the energy-wavelength relationship: \(E = h \times f\) and the frequency-wavelength relationship: \(c = f \times \lambda\). Firstly, convert the given band gap energy of 2.2 eV to Joules: 2.2 eV = 2.2 脳 \(1.60218 \times 10^{-19}\) J. Then, calculate the frequency of the emitted light: \(f = \dfrac{E}{h}\), where h is Planck's constant (\(6.626 \times 10^{-34}\) J路s). Finally, calculate the emitted wavelength: \(\lambda = \dfrac{c}{f}\), where c is the speed of light in vacuum (\(3 \times 10^8\) m/s). To express the wavelength in nanometers (nm), multiply the result by \(10^9\).

Step by step solution

01

Given Values

The band gap energy of GaP is given as 2.2 eV.
02

Convert energy from eV to Joules

First, we need to convert the energy value from electron volts (eV) to Joules (J) by using the conversion factor: 1 eV = \(1.60218 \times 10^{-19}\) J So, 2.2 eV = 2.2 脳 \(1.60218 \times 10^{-19}\) J
03

Find the energy-frequency relation

We can use the energy-frequency relation, which is derived from Planck's equation: E = h 脳 f Where E represents energy, f represents frequency, and h is Planck's constant (\(6.626 \times 10^{-34}\) J路s).
04

Calculate the frequency of emitted light

Now, we can calculate the frequency of emitted light using the energy-frequency relation: f = E / h Where E is the energy in Joules, and h is Planck's constant (\(6.626 \times 10^{-34}\) J路s). f = (2.2 脳 \(1.60218 \times 10^{-19}\) J) / (\(6.626 \times 10^{-34}\) J路s)
05

Finding the frequency-wavelength relation

We can relate the frequency and wavelength using the speed of light (c) in vacuum: c = f 脳 位 Where c is the speed of light in vacuum (\(3 \times 10^8\) m/s), f is frequency, and 位 is wavelength.
06

Calculate the emitted wavelength

Finally, we can rearrange the frequency-wavelength equation to find the wavelength of emitted light: 位 = c / f 位 = (\(3 \times 10^8\) m/s) / ((2.2 脳 \(1.60218 \times 10^{-19}\) J) / (\(6.626 \times 10^{-34}\) J路s)) Now, calculate the emitted wavelength, which will be in meters. To express the wavelength in nanometers (nm), multiply the result by \(10^9\).

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