Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 5.1, Problem 5.3P
To determine
Show that the vibrational spectrum of
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The three lowest energy levels of a hydrogen atom are -13.6 eV, -3.4 eV, and -1.5 eV. Place this atom in thermal contact with a reservoir and assume that there is only one way to occupy any one of these levels.
Calculate the relative probability that this hydrogen atom at T = 316 K is in its first excited state (at -3.4 eV) relative to its ground state (at -13.6 eV). Write your answer in exponential form.
An "eV" (electron volt) is the energy acquired by an electron accelerated across a 1 volt potential difference. This unit is used to describe electronic energy levels in atoms or solids (semiconductors, etc.).
1 eV = 1.602 x 10-19 J and Boltzmann's constant can be written as 8.617 x 10-5 eV K-1.
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In this site ex is entered as e^x, though exp(x) can also be used. If you haven't used this website before, a convenient tutorial can be found on youtube (for example,…
Problem 3: Chemical potential of an Einstein solid.
Consider an Einstein solid for which both N and q are much greater than 1. Think of each
ocillator as a separate “particle".
a) Show that the chemical potential is
H = -kT In (**e)
b) Discuss this result in the limits N » q and N « q, concentrating on the question of how
much S increases when another particle carrying no energy is added to the system. Does
the formula make intuitive sense?
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.
Chapter 5 Solutions
Introduction To Quantum Mechanics
Ch. 5.1 - Prob. 5.1PCh. 5.1 - Prob. 5.2PCh. 5.1 - Prob. 5.3PCh. 5.1 - Prob. 5.4PCh. 5.1 - Prob. 5.5PCh. 5.1 - Prob. 5.6PCh. 5.1 - Prob. 5.8PCh. 5.1 - Prob. 5.9PCh. 5.1 - Prob. 5.10PCh. 5.1 - Prob. 5.11P
Ch. 5.2 - Prob. 5.12PCh. 5.2 - Prob. 5.13PCh. 5.2 - Prob. 5.14PCh. 5.2 - Prob. 5.15PCh. 5.2 - Prob. 5.16PCh. 5.2 - Prob. 5.17PCh. 5.2 - Prob. 5.18PCh. 5.2 - Prob. 5.19PCh. 5.3 - Prob. 5.20PCh. 5.3 - Prob. 5.21PCh. 5.3 - Prob. 5.22PCh. 5.3 - Prob. 5.23PCh. 5.3 - Prob. 5.24PCh. 5.3 - Prob. 5.25PCh. 5.3 - Prob. 5.26PCh. 5.3 - Prob. 5.27PCh. 5 - Prob. 5.29PCh. 5 - Prob. 5.30PCh. 5 - Prob. 5.31PCh. 5 - Prob. 5.32PCh. 5 - Prob. 5.33PCh. 5 - Prob. 5.34PCh. 5 - Prob. 5.35PCh. 5 - Prob. 5.36PCh. 5 - Prob. 5.38PCh. 5 - Prob. 5.39P
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