An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 6.7, Problem 49P
To determine
The value of given following quantities.
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1.7 A crystal has a basis of one atom per lattice point and a set of primitive translation
vectors (in A):
c = 1.5(i + j+ k),
a = 3i,
where i, j and k are unit vectors in the x, y and z directions of a Cartesian coordinate
system. What is the Bravais lattice type of this crystal, and what are the Miller indices
of the set of planes most densely populated with atoms? Calculate the volumes of the
primitive unit cell and the conventional unit cell.
b= 3j.
a) Starting from a general fornula of
desity of
States.
g(k) dk= Vkdk
272
Show that
g(w) dw= 3x Vw°dw for
Phonons under the assumption thait the phonoh
dre aicoustic, meaning U = does not depend
3.
on
W or k.
3N
b) In a solid of N
atoms, there are
vibrational modes(phonons) with the highat
frequercy Wp.
In this and following questions, we develop a model for spontaneous
emission of a photon by a diatomic molecule AB (a model molecule),
which rotates and vibrates. In intermediate calculations, atomic units
(a.u.) will be used: unit of mass = the mass of electron, unit of charge
is the proton charge e, (e is a positive constant so that the charge of
electron is -e). The initial state of the molecule is an excited
rotational (1=1) and excited vibrational state (v=1). We consider a
molecule with the reduced mass µ = 10,000 a.u. (it is similar to the
mass of CO). After emitting a photon, the molecule will go to the 1=0,
v=0 state. The first question is about the model potential of the
molecule. It is represented by a potential of the form:
V(r)
=
C6
p12
C12
p6
"
where r is the distance between A and B in the molecule, C6 and C12
are positive constants (C6 =2 and C₁2-1). This potential has a well
meaning that the molecule is bound. The first thing to do is find
vibrational states of the…
Chapter 6 Solutions
An Introduction to Thermal Physics
Ch. 6.1 - Prob. 2PCh. 6.1 - Prob. 4PCh. 6.1 - Prob. 5PCh. 6.1 - Prob. 6PCh. 6.1 - Prob. 7PCh. 6.1 - Prob. 8PCh. 6.1 - Prob. 9PCh. 6.1 - Prob. 10PCh. 6.1 - Prob. 11PCh. 6.1 - Prob. 12P
Ch. 6.1 - Prob. 13PCh. 6.1 - Prob. 14PCh. 6.2 - Prob. 15PCh. 6.2 - Prob. 16PCh. 6.2 - Prob. 17PCh. 6.2 - Prob. 18PCh. 6.2 - Prob. 19PCh. 6.2 - Prob. 20PCh. 6.2 - For an O2 molecule the constant is approximately...Ch. 6.2 - The analysis of this section applies also to...Ch. 6.3 - Prob. 31PCh. 6.4 - Calculate the most probable speed, average speed,...Ch. 6.4 - Prob. 35PCh. 6.4 - Prob. 36PCh. 6.4 - Prob. 37PCh. 6.4 - Prob. 39PCh. 6.4 - Prob. 40PCh. 6.5 - Prob. 42PCh. 6.5 - Some advanced textbooks define entropy by the...Ch. 6.6 - Prob. 44PCh. 6.7 - Prob. 45PCh. 6.7 - Equations 6.92 and 6.93 for the entropy and...Ch. 6.7 - Prob. 47PCh. 6.7 - For a diatomic gas near room temperature, the...Ch. 6.7 - Prob. 49PCh. 6.7 - Prob. 50PCh. 6.7 - Prob. 51PCh. 6.7 - Prob. 52PCh. 6.7 - Prob. 53P
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