Chemistry: An Atoms-Focused Approach
Chemistry: An Atoms-Focused Approach
14th Edition
ISBN: 9780393912340
Author: Thomas R. Gilbert, Rein V. Kirss, Natalie Foster
Publisher: W. W. Norton & Company
Question
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Chapter 18, Problem 18.34QA
Interpretation Introduction

To find:

The wavelength of light emitted by the semiconducting phosphides from the band gaps values.

Expert Solution & Answer
Check Mark

Answer to Problem 18.34QA

Solution:

a) λAlP =496.4 nm

b) λGaP =554.0 nm

c) λInP =977.3 nm

 

Explanation of Solution

1) Concept:

To find the wavelength corresponding to band gaps for semiconducting phosphides, we need to use the Eg absorbed by the semiconductor.  We need to convert the given Eg into Joule by using an appropriate unit conversion factor. We can calculate the wavelengthby using Eg band gap and the formula.

2) Formula:

Eg=h×   cλ

3) Given:

i) Eg(AlP)=241.1 kJmol

ii) Eg(GaP)=216.0 kJmol

iii) Eg(InP)=122.5 kJmol

iv) h=6.626 ×10-34 J.s

v) c= 3 × 108 ms

vi) Avogadro’s number 1 mol=6.022 ×1023 photons

      

4) Calculations:

a) Wavelength of AlP:

The energy gap is the minimum energy needed to excite the electrons from the ground state for the conduction. From this energy, we can calculate the light energy needed to excite the electrons from their ground state to conduction band.

First we will calculate the energy, J/photons, by using Avogadro’s number.

241.1 kJmol×  1000 J1 kJ × 1 mol 6.022 × 1023 photons=4.004 ×10-19 Jphotons

Eg per photon= 4.004 ×10-19 J

Wavelength of AlN is calculated as follows:

Eg=h×   cλ

λ= h×  cEg

λ=  6.626 × 10-34 J.s ×  3 × 108 ms4.004 ×10-19 J = 4.964 × 10-7 m

λ =4.964 × 10-7 m × 1 ×109nm1 m  =496.4 nm

λ =496.4 nm

b) Wavelength of GaP:

First we will calculate the energy, J/photons, by using Avogadro’s number.

216.0 kJmol×  1000 J1 kJ × 1 mol 6.022 × 1023 photons=3.59 ×10-19 Jphotons

Eg per photon= 3.59 ×10-19 J

Wavelength of AlN is calculated as follows:

Eg=h×   cλ

λ= h×  cEg

λ=  6.626 × 10-34 J.s ×  3 × 108 ms3.59 ×10-19 J = 5.54 × 10-7 m

λ =5.540 × 10-7 m × 1 ×109nm1 m  =554.0 nm

λ =554.0 nm

c) Wavelength of InP:

First we will calculate the energy, J/photons, by using Avogadro’s number.

122.5 kJmol×  1000 J1 kJ × 1 mol 6.022 × 1023 photons=2.034 ×10-19 Jphotons

Eg per photon= 2.034 ×10-19 J

Wavelength of AlN is calculated as follows:

Eg=h×   cλ

λ= h×  cEg

λ=  6.626 × 10-34 J.s ×  3 × 108 ms2.034 ×10-19 J = 9.773 × 10-7 m

λ =9.773 × 10-7 m × 1 ×109nm1 m  =977.3 nm

λ =977.3 nm

Conclusion:

The wavelength is calculated from the energy gaps present in the semiconductors and Avogadro’s value.

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Chapter 18 Solutions

Chemistry: An Atoms-Focused Approach

Ch. 18 - Prob. 18.11VPCh. 18 - Prob. 18.12VPCh. 18 - Prob. 18.13VPCh. 18 - Prob. 18.14VPCh. 18 - Prob. 18.15VPCh. 18 - Prob. 18.16VPCh. 18 - Prob. 18.17VPCh. 18 - Prob. 18.18VPCh. 18 - Prob. 18.19QACh. 18 - Prob. 18.20QACh. 18 - Prob. 18.21QACh. 18 - Prob. 18.22QACh. 18 - Prob. 18.23QACh. 18 - Prob. 18.24QACh. 18 - Prob. 18.25QACh. 18 - Prob. 18.26QACh. 18 - Prob. 18.27QACh. 18 - Prob. 18.28QACh. 18 - Prob. 18.29QACh. 18 - Prob. 18.30QACh. 18 - Prob. 18.31QACh. 18 - Prob. 18.32QACh. 18 - Prob. 18.33QACh. 18 - Prob. 18.34QACh. 18 - Prob. 18.35QACh. 18 - Prob. 18.36QACh. 18 - Prob. 18.37QACh. 18 - Prob. 18.38QACh. 18 - Prob. 18.39QACh. 18 - Prob. 18.40QACh. 18 - Prob. 18.41QACh. 18 - Prob. 18.42QACh. 18 - Prob. 18.43QACh. 18 - Prob. 18.44QACh. 18 - Prob. 18.45QACh. 18 - Prob. 18.46QACh. 18 - Prob. 18.47QACh. 18 - Prob. 18.48QACh. 18 - Prob. 18.49QACh. 18 - Prob. 18.50QACh. 18 - Prob. 18.51QACh. 18 - Prob. 18.52QACh. 18 - Prob. 18.53QACh. 18 - Prob. 18.54QACh. 18 - Prob. 18.55QACh. 18 - Prob. 18.56QACh. 18 - Prob. 18.57QACh. 18 - Prob. 18.58QACh. 18 - Prob. 18.59QACh. 18 - Prob. 18.60QACh. 18 - Prob. 18.61QACh. 18 - Prob. 18.62QACh. 18 - Prob. 18.63QACh. 18 - Prob. 18.64QACh. 18 - Prob. 18.65QACh. 18 - Prob. 18.66QACh. 18 - Prob. 18.67QACh. 18 - Prob. 18.68QACh. 18 - Prob. 18.69QACh. 18 - Prob. 18.70QACh. 18 - Prob. 18.71QACh. 18 - Prob. 18.72QACh. 18 - Prob. 18.73QACh. 18 - Prob. 18.74QACh. 18 - Prob. 18.75QACh. 18 - Prob. 18.76QACh. 18 - Prob. 18.77QACh. 18 - Prob. 18.78QACh. 18 - Prob. 18.79QACh. 18 - Prob. 18.80QACh. 18 - Prob. 18.81QACh. 18 - Prob. 18.82QACh. 18 - Prob. 18.83QACh. 18 - Prob. 18.84QACh. 18 - Prob. 18.85QACh. 18 - Prob. 18.86QACh. 18 - Prob. 18.87QACh. 18 - Prob. 18.88QACh. 18 - Prob. 18.89QACh. 18 - Prob. 18.90QACh. 18 - Prob. 18.91QACh. 18 - Prob. 18.92QACh. 18 - Prob. 18.93QACh. 18 - Prob. 18.94QACh. 18 - Prob. 18.95QACh. 18 - Prob. 18.96QACh. 18 - Prob. 18.97QACh. 18 - Prob. 18.98QACh. 18 - Prob. 18.99QACh. 18 - Prob. 18.100QACh. 18 - Prob. 18.101QACh. 18 - Prob. 18.102QACh. 18 - Prob. 18.103QACh. 18 - Prob. 18.104QACh. 18 - Prob. 18.105QACh. 18 - Prob. 18.106QACh. 18 - Prob. 18.107QACh. 18 - Prob. 18.108QACh. 18 - Prob. 18.109QACh. 18 - Prob. 18.110QACh. 18 - Prob. 18.111QACh. 18 - Prob. 18.112QACh. 18 - Prob. 18.113QACh. 18 - Prob. 18.114QACh. 18 - Prob. 18.115QACh. 18 - Prob. 18.116QACh. 18 - Prob. 18.117QACh. 18 - Prob. 18.118QACh. 18 - Prob. 18.119QACh. 18 - Prob. 18.120QACh. 18 - Prob. 18.121QACh. 18 - Prob. 18.122QACh. 18 - Prob. 18.123QACh. 18 - Prob. 18.124QACh. 18 - Prob. 18.125QACh. 18 - Prob. 18.126QACh. 18 - Prob. 18.127QACh. 18 - Prob. 18.128QACh. 18 - Prob. 18.129QACh. 18 - Prob. 18.130QACh. 18 - Prob. 18.131QACh. 18 - Prob. 18.132QACh. 18 - Prob. 18.133QA
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