Introduction To Quantum Mechanics
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 HCl should consist of closely spaced doublets, with a splitting given by Δv=7.51×104v.

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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. If your calculator is unable to do this calculation try the web site https://www.wolframalpha.com 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,…
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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.
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