Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 7, Problem 55E
For states where
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The Morse potential
The harmonic potential, V(x) = ½kx?, is useful start for modelling molecular vibrations, but it has
limitations. A realistic potential between to atoms should accurately represent the sharp
increase in the potential as two nuclei come in close proximity, and also have the ability for a
bond to break: that is, an asymptote V →0 as x →00.
One option, as shown in the figure, is the Morse potential:
V(r) = D(1 – e-«(r=re))2
15
10
10
15
20
The parameter D is the well depth (or binding energy) of the potential, re is the bond length,
and a is the anharmonicity constant.
A spin state of an electron in the vector form is given by
3i
X = A
4
%3D
(a) Determine the normalization constant A, assuming it to be real and positive.
(b) Write down the x using the X+ and X-. If z-component of the spin of the electron is
measured, what is the probability of finding the value in +ħ/2?
(c) Determine the expectation value and uncertainty of S? in terms of h when the electron
is in spin state x. Justify your answer.
(d) Determine the expectation value of the product S?S, in terms of h when the electron
is in spin state X.
There is a minimum energy of (.5[hbar][omega]) in any vibrating system; this energy is sometimes known as the zero-point motion. (a) Use an argument based on the uncertainty principle to explain why the vibrating system can never have E=0. (b) The hydrogen molecule H2 can be treated as a vibrating system, with an effective force constant k=3.5 x 103 eV/nm2. Compute the zero-point energy of one of the protons in H2. How does it compare with the molecular binding energy of 4.5 eV? (c) Compute the amplitude of the zero-point motion and compare with the atomic spacing of 0.074 nm
Chapter 7 Solutions
Modern Physics
Ch. 7 - Prob. 1CQCh. 7 - Prob. 2CQCh. 7 - Prob. 3CQCh. 7 - Prob. 4CQCh. 7 - Prob. 5CQCh. 7 - Prob. 6CQCh. 7 - Prob. 7CQCh. 7 - Prob. 8CQCh. 7 - Prob. 9CQCh. 7 - What are the dimensions of the spherical harmonics...
Ch. 7 - Prob. 11CQCh. 7 - Prob. 12CQCh. 7 - Prob. 13CQCh. 7 - Prob. 14CQCh. 7 - Prob. 15CQCh. 7 - Prob. 16CQCh. 7 - Prob. 17ECh. 7 - Prob. 18ECh. 7 - Prob. 19ECh. 7 - Prob. 20ECh. 7 - Prob. 21ECh. 7 - Prob. 22ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27ECh. 7 - Show that of hydrogen’s spectral seriesLyman,...Ch. 7 - Prob. 29ECh. 7 - Prob. 30ECh. 7 - Prob. 31ECh. 7 - Prob. 32ECh. 7 - Prob. 33ECh. 7 - Prob. 34ECh. 7 - Prob. 35ECh. 7 - Prob. 36ECh. 7 - Prob. 37ECh. 7 - A particle orbiting due to an attractive central...Ch. 7 - Prob. 39ECh. 7 - Prob. 40ECh. 7 - Prob. 41ECh. 7 - Prob. 42ECh. 7 - Prob. 43ECh. 7 - How many different 3d states are there? What...Ch. 7 - Prob. 45ECh. 7 - Prob. 46ECh. 7 - Prob. 47ECh. 7 - Prob. 48ECh. 7 - Prob. 49ECh. 7 - Prob. 50ECh. 7 - Prob. 51ECh. 7 - Prob. 52ECh. 7 - Prob. 53ECh. 7 - Prob. 54ECh. 7 - For states where l=n1 , the radial probability...Ch. 7 - Prob. 56ECh. 7 - Prob. 57ECh. 7 - Prob. 58ECh. 7 - Prob. 59ECh. 7 - Prob. 60ECh. 7 - Prob. 61ECh. 7 - Prob. 62ECh. 7 - Prob. 63ECh. 7 - Prob. 64ECh. 7 - Prob. 65ECh. 7 - Prob. 66ECh. 7 - Prob. 67ECh. 7 - Prob. 68ECh. 7 - Prob. 69ECh. 7 - Prob. 70ECh. 7 - Prob. 71ECh. 7 - Prob. 72ECh. 7 - Prob. 73ECh. 7 - Prob. 74ECh. 7 - Prob. 75ECh. 7 - Prob. 76ECh. 7 - Prob. 77ECh. 7 - Prob. 78ECh. 7 - Prob. 79CECh. 7 - Prob. 80CECh. 7 - Prob. 81CECh. 7 - Prob. 83CECh. 7 - Prob. 84CECh. 7 - Prob. 85CECh. 7 - Prob. 86CECh. 7 - Prob. 87CECh. 7 - Prob. 89CE
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