Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Question
Chapter 40, Problem 25P
(a)
To determine
To normalize the wave function for the ground state of a simple harmonic oscillator.
(b)
To determine
The probability of finding the oscillator in a narrow interval of
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A) An atom has two electronic levels of energy 0 and ɛ. Suppose the atom is in thermal
equilibrium with a heat bath at temperature T. What ensemble should be used for this atom?
Calculate the partition function Z, the average energy E, and the Helmholtz free energy F for
this atom in the canonical encapsulation. Find the probabilities of each microstate of the atom.
The Einstein's model makes the assumption that a solid can be treated a set of N identical, independent harmonic oscillators. Compute the heat capacity for such a system. Make the simplifying assumption that a single harmonic oscillator is described by the quantized energy levels: Ek=kℏω, where k=0,1,2,….
15
6x4 – 12Lx³ + 15 L²x? -
3,3
(-
L²r?
L3x
6r4 -
N2
2me
12La3
dx =
dx
2
2
2
Evaluate the integral in the numerator.
p*H@ dx = N²
40m
h² L³
e
40me
The denominator of the E expression from Step 1 is
6 _ 3Lx +
13 ,2 4
-L²x
4
Lx³ +
F8-3Lz' + 12rt - (%) Lz3 + +L교2
p dx = N²
dx
Evaluate the integral in the denominator.
1
1
φ φ αχx = N2
840
840
Step 3 of 6
Divide the numerator by the denominator (both from Step 2) and simplify. (Use the following as necessary: ħ, L, me, P, T, and x.)
21h?
E
L²m
21h?
L²me
e
Step 4 of 6
Calculate the energy for an electron in a 0.43-nm box using the formula from Step 3.
= 4.0 0.26 X
840 kJ•mol-1
φ
Step 5 of 6
Calculate the exact energy for an electron in the first excited state in a 0.43-nm box.
n2h2
Recall that for a particle in a one-dimensional box we can write En
we can therefore calculate an exact solution.
8mL2'
Eexact = 4.0 197
X kJ-mol-1
Submit
Chapter 40 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 40.1 - Prob. 40.1QQCh. 40.2 - Prob. 40.2QQCh. 40.2 - Prob. 40.3QQCh. 40.5 - Prob. 40.4QQCh. 40 - Prob. 1PCh. 40 - Prob. 2PCh. 40 - Prob. 3PCh. 40 - Prob. 4PCh. 40 - Prob. 5PCh. 40 - Prob. 6P
Ch. 40 - Prob. 7PCh. 40 - Prob. 9PCh. 40 - Prob. 10PCh. 40 - Prob. 11PCh. 40 - Prob. 12PCh. 40 - Prob. 13PCh. 40 - Prob. 14PCh. 40 - Prob. 15PCh. 40 - Prob. 16PCh. 40 - Prob. 17PCh. 40 - Prob. 18PCh. 40 - Prob. 19PCh. 40 - Prob. 20PCh. 40 - Prob. 21PCh. 40 - Prob. 23PCh. 40 - Prob. 24PCh. 40 - Prob. 25PCh. 40 - Prob. 26PCh. 40 - Prob. 27PCh. 40 - Prob. 28PCh. 40 - Prob. 29PCh. 40 - Two particles with masses m1 and m2 are joined by...Ch. 40 - Prob. 31APCh. 40 - Prob. 32APCh. 40 - Prob. 33APCh. 40 - Prob. 34APCh. 40 - Prob. 36APCh. 40 - Prob. 37APCh. 40 - Prob. 38APCh. 40 - Prob. 39APCh. 40 - Prob. 40APCh. 40 - Prob. 41APCh. 40 - Prob. 42APCh. 40 - Prob. 44CPCh. 40 - Prob. 46CPCh. 40 - Prob. 47CP
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