CHEM 342. Spring 2002. Problem Set #1. Mortimer Chapters 14, 15.
For the first three problems, please circle the correct answer.
Compton Effect
1. The Compton Effect was first observed by studying the scattering of X-rays by a
graphite target. Although the incident X-rays were monochromatic, the scattered X-rays
contained an additional component of shorter, same, longer wavelength.
Photoelectric Effect
2. If the frequency of incident light is above the threshold frequency, then as the intensity
of light increases, the kinetic energy of ejected electrons decreases, remains constant, increases
and the number of electrons decreases, remains constant, increases.
3. If the frequency of incident light is above the threshold frequency, then as the
frequency of light increases, the kinetic energy of ejected electrons decreases, remains constant,
increases and the number of electrons decreases, remains constant, increases.
4. What is the effect of incident light striking a metal surface if the frequency of the light
is below the threshold frequency for this metal?
5. Define in a maximum of 20 words for each
(a) Correspondence Principle
(b) Compton Effect
(c) Photoelectric Effect
6. The work function for metallic cesium is 3.43  1019 J. Calculate the kinetic energy
and the speed of the electrons ejected by light of 300 nm wavelength. [Hint: Planck's constant,
h,is 6.626  1034 J s; the speed of light in a vacuum, c, is 3.00  108 m/s; the mass of an
electron, me, is 9.109  1031 kg]
Blackbody Radiation
7. The peak of the Sun's emission occurs at about 480 nm. Estimate the temperature on its
c
surface. Hint: The Wien displacement law reduces to T max  2 , where the constant
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2
c 2  1.44 10 m
Bohr Atom: Spectral Lines
8. Calculate the wavelength of light emitted when an electron falls from the n = 100 to
the n = 99 orbit of the hydrogen atom. [Hint: Rydberg's constant, R, is 1.097  107 m1]
DeBroglie Waves
9. Electrons are accelerated by a 1000 V potential drop. Calculate the de Broglie
wavelength. Also calculate the wavelength of the X-rays that would be produced when these
electrons strike a solid. [Hint:The electron charge is 1.602  1019 C; the mass of an electron, me,
is 9.109  1031 kg; Planck's constant, h,is 6.626  1034 J s.]
Well-Behaved Wave Functions
10. List the characteristics of a well-behaved wave function.
11. Which of the following functions are well-behaved? For those functions that are not
well-behaved, explain why not.
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CHEM 342. Spring 2002. Problem Set #1. Mortimer Chapters 14, 15.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
f(x) = x for x  0, and f(x) = 0 for x < 0
f(x) = x2
f(x) = e x
f(x) = e x
f(x) = cos x
f(x) = sin x 
f(x) = 1 x2 for 1 ≤ x ≤ 1, and f(x) = 0 for x < 1 and for x > 1
12. A particle can move only along the x-axis and has a wave function   e ikx . Give
the expression for
(a)  * , the complex conjugate of  (express answer in terms of k and x)
(b) P, the probability density (express answer in terms of  and  * )
(c) the probability that the particle is between x1 and x2 (in terms of  and  * ).
Hint: You only need to set up the appropriate integral.
For any normalized  , what is the probability that the particle is between  and +?
[Hint: this question has a numerical answer.]
Harmonic Oscillators: Hermite Polynomials
13. Calculate the zero-point energy of a harmonic oscillator consisting of a particle of
mass 2.33  1026 kg and force constant 155 N/m. [Hint: Planck's constant, h,is 6.626  1034 J
s.]
14. For the harmonic oscillator, substitute the wave function for the ground state into the
 2 d 2 1 2
ˆ
Schrodinger equation H  
 kz   E and derive the expression for the ground
2m dz 2 2
state energy (also known as the zero-point energy). Hint: The wave function for the ground state
1/ 4
2
km
a
is  0    e  az / 2 where a 
. The expression for the ground state energy is


1
E   hν where  is the frequency.
2
15. In the vibrational motion of HI, the iodine atom essentially remains stationary
because of its large mass. Assuming that the hydrogen atom undergoes harmonic motion and that
the force constant k is 317 N/m, what is the fundamental vibration frequency 0. [Hint: The mass
of a proton is 1.67  1027 kg.]
PLEASE NOTE
 The work you hand in should be neat and well organized, and it should show the strategy and
steps you used in solving the problems, as well as the bottom-line answers (or solutions). In
grading the problems, both your work-up and your final answers/solutions will be examined
and evaluated.
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CHEM 342. Spring 2002. Problem Set #1. Mortimer Chapters 14, 15.

The work handed in for grading must carry a pledge that the work is entirely yours and was
done without any collaboration with other persons (except for the course instructor and
TA's). You are encouraged to work with others in doing the exercises and problems found in
the textbook, but all work handed in for grading should be done independently.
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