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Principles of Electronic
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University of Saskatchewan
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Louis
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PRINCIPLES OF ELECTRONIC MATERIALS AND DEVICES, SECOND EDITION
S.O. KASAP
Published by McGraw-Hill Higher Education, an imprint of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas,
New York, NY 10020. Copyright © The McGraw-Hill Companies, Inc., 2002, 1997. All rights reserved.
The contents, or parts thereof, may be reproduced in print form solely for classroom use with PRINCIPLES OF ELECTRONIC
MATERIALS AND DEVICES, Second Edition by S.O. Kasap, provided such reproductions bear copyright notice, but may not be
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Solutions to Principles of Electronic Materials and Devices: 2nd Edition (Summer 2001) Chapter 1
Second Edition ( 2001 McGraw-Hill)
Chapter 1
1.1 The covalent bond
Consider the H2 molecule in a simple way as two touching H atoms as depicted in Figure 1Q1-1. Does
this arrangement have a lower energy than two separated H atoms? Suppose that electrons totally
correlate their motions so that they move to avoid each other as in the snapshot in Figure 1Q1-1. The
radius ro of the hydrogen atom is 0.0529 nm. The electrostatic potential energy PE of two charges Q1
and Q2 separated by a distance r is given by Q1Q2/(4πεor).
Using the Virial Theorem stated in Example 1.1 (in textbook) consider the following:
a. Calculate the total electrostatic potential energy (PE) of all the charges when they are arranged as
shown in Figure 1Q1-1. In evaluating the PE of the whole collection of charges you must consider
all pairs of charges and, at the same time, avoid double counting of interactions between the same pair
of charges. The total PE is the sum of the following: electron 1 interacting with the proton at a
distance ro on the left, proton at ro on the right, and electron 2 at a distance 2ro + electron 2 interacting
with a proton at ro and another proton at 3ro + two protons, separated by 2ro, interacting with each
other. Is this configuration energetically favorable?
b. Given that in the isolated H-atom the PE is 2 × (–13.6 eV), calculate the change in PE with respect to
two isolated H-atoms. Using the Virial theorem, find the change in the total energy and hence the
covalent bond energy. How does this compare with the experimental value of 4.51 eV?
Solution
2 Nucleus e– Nucleus
e– ro ro
1
Hydrogen Hydrogen
Figure 1Q1-1 A simplified view of the covalent bond in H : a snap shot at one instant in time. The
2
electrons correlate their motions and avoid each other as much as possible.
a Consider the PE of the whole arrangement of charges shown in the figure. In evaluating the PE of
all the charges, we must avoid double counting of interactions between the same pair of charges. The total
PE is the sum of the following:
Electron 1 interacting with the proton at a distance ro on the left, with the proton at ro on the
right and with electron 2 at a distance 2ro
+ Electron 2 on the far left interacting with a proton at ro and another proton at 3ro
+ Two protons, separated by 2ro, interacting with each other
1.1
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Materials and Devices Second Edition S.O. Kas
Solutions Manual
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Principles of Electronic
Materials and Devices
Second Edition
S.O. Kasap
University of Saskatchewan
Boston Burr Ridge, IL Dubuque, IA
Madison, WI New York San Francisco St.
Louis
Bangkok Bogotб Caracas Kuala Lumpur Lisbon London Madrid Mexico City
Milan Montreal New Delhi Santiago Seoul Singapore Sydney Taipei Toronto
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Materials and Devices Second Edition S.O. Kas
Solutions Manual to accompany
PRINCIPLES OF ELECTRONIC MATERIALS AND DEVICES, SECOND EDITION
S.O. KASAP
Published by McGraw-Hill Higher Education, an imprint of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas,
New York, NY 10020. Copyright © The McGraw-Hill Companies, Inc., 2002, 1997. All rights reserved.
The contents, or parts thereof, may be reproduced in print form solely for classroom use with PRINCIPLES OF ELECTRONIC
MATERIALS AND DEVICES, Second Edition by S.O. Kasap, provided such reproductions bear copyright notice, but may not be
reproduced in any other form or for any other purpose without the prior written consent of The McGraw-Hill Companies, Inc.,
including, but not limited to, network or other electronic storage or transmission, or broadcast for distance learning.
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Materials and Devices Second Edition S.O. Kas
Solutions to Principles of Electronic Materials and Devices: 2nd Edition (Summer 2001) Chapter 1
Second Edition ( 2001 McGraw-Hill)
Chapter 1
1.1 The covalent bond
Consider the H2 molecule in a simple way as two touching H atoms as depicted in Figure 1Q1-1. Does
this arrangement have a lower energy than two separated H atoms? Suppose that electrons totally
correlate their motions so that they move to avoid each other as in the snapshot in Figure 1Q1-1. The
radius ro of the hydrogen atom is 0.0529 nm. The electrostatic potential energy PE of two charges Q1
and Q2 separated by a distance r is given by Q1Q2/(4πεor).
Using the Virial Theorem stated in Example 1.1 (in textbook) consider the following:
a. Calculate the total electrostatic potential energy (PE) of all the charges when they are arranged as
shown in Figure 1Q1-1. In evaluating the PE of the whole collection of charges you must consider
all pairs of charges and, at the same time, avoid double counting of interactions between the same pair
of charges. The total PE is the sum of the following: electron 1 interacting with the proton at a
distance ro on the left, proton at ro on the right, and electron 2 at a distance 2ro + electron 2 interacting
with a proton at ro and another proton at 3ro + two protons, separated by 2ro, interacting with each
other. Is this configuration energetically favorable?
b. Given that in the isolated H-atom the PE is 2 × (–13.6 eV), calculate the change in PE with respect to
two isolated H-atoms. Using the Virial theorem, find the change in the total energy and hence the
covalent bond energy. How does this compare with the experimental value of 4.51 eV?
Solution
2 Nucleus e– Nucleus
e– ro ro
1
Hydrogen Hydrogen
Figure 1Q1-1 A simplified view of the covalent bond in H : a snap shot at one instant in time. The
2
electrons correlate their motions and avoid each other as much as possible.
a Consider the PE of the whole arrangement of charges shown in the figure. In evaluating the PE of
all the charges, we must avoid double counting of interactions between the same pair of charges. The total
PE is the sum of the following:
Electron 1 interacting with the proton at a distance ro on the left, with the proton at ro on the
right and with electron 2 at a distance 2ro
+ Electron 2 on the far left interacting with a proton at ro and another proton at 3ro
+ Two protons, separated by 2ro, interacting with each other
1.1
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