Chapter 13
Quantum Physics
F I G U R E 13.1 The opening to the
cavity inside a hollow object is a good
approximation of a black body. Light
entering the small opening strikes the
interior walls, where some is absorbed
and some is reflected at a random
angle. The cavity walls re-radiate at
wavelengths corresponding to their
temperature. Some of the energy
from these standing waves can leave
through the opening.
Intensity
4 000 K
3 000 K
2 000 K
0 1 2 3 4
Wavelength (µ m)
Figure 13.2
Intensity of blackbody radiation
versus wavelength at three
temperatures. Note that the amount
of radiation emitted (the area under
a curve) increases with increasing
temperature. The visible range of
wavelengths is between 0.4 m and
0.7 m. Therefore, the 4 000-K curve
has a peak that is near the visible
range and represents an object that
would glow with a yellowish-white
appearance. At about 6000 K, the
peak is in the center of the visible
wavelengths and the object appears
white.
Classical theory
Intensity Experimental
data
Wavelength
F I G U R E 13.3 Comparison
of the experimental results with
the curve predicted by classical
theory for the distribution of
blackbody radiation.
to n =
E n
4hf 4
3hf 3
2hf 2
ENERGY
hf 1
0 0
F I G U R E 13.4 Allowed energy
levels for an oscillator with a
natural frequency f. Allowed
transitions are indicated by the
double-headed arrows.
(Photodisc/Getty Images)
FIGURE 13.5 An ear
thermometer measures a patient’s
temperature by detecting the
intensity of infrared radiation
leaving the eardrum.
Photoelectrons
C E
Light
Variable power
supply
Figure 13.6
A circuit diagram for studying the photoelectric effect.
When light strikes the plate E (the emitter),
photoelectrons are ejected from the plate. Electrons
moving from plate E to plate C (the collector)
constitute a current in the circuit.
Current
High intensity
Low intensity
– Vs Applied voltage
Figure 13.7
Photoelectric current versus
applied potential difference for
two light intensities. The current
increases with intensity but
reaches a saturation level for
large values of V. At voltages
equal to or more negative than
2 Vs, where Vs is the stopping
potential, the current is zero.
Metal 1 Metal 2 Metal 3
K max
0
f
φ1
– φ2
φ3
Figure 13.8
A plot of results for Kmax of
photoelectrons versus frequency of
incident light in a typical
photoelectric effect experiment.
Photons with frequency less than the
cutoff frequency for a given metal do
not have sufficient energy to eject an
electron from the metal.
+200 V +600 V +1 000 V +1 400 V Vacuum
0V +400 V +800 V +1 200 V +1 600 V
Incoming Photocathode
photon Output
to counter
F I G U R E 13.9 The multiplicationof electronsin a photomultiplier tube.
Recoiling electron
θ
f0, 0
f ,λ
F I G U R E 13.10 The quantum model for x-ray scattering from
an electron. The collision of the photon with the electron displays
the particle-like nature of the photon.
Carbon
target
θ = 90 Rotating crystal
′
0
X-ray
source
Ionization
chamber
F I G U R E 13.11 Schematic diagram of Compton’s
apparatus. Photons are scattered through 90° from a
carbon target. The wavelength is measured with a rotating
crystal spectrometer using Bragg’s law (Section 12.9).
Intensity
θ=0
Primary beam
0
Intensity
θ = 45
θ = 90
Intensity
θ = 135
Intensity
F I G U R E 13.12 Scattered
x-ray intensity versus
wavelength for Compton
scattering at 0°, 45°, 90°,
and 135°.
F I G U R E 13.13 (a) Diagram of a transmission
Electron gun
electron microscope for viewing a thinly sectioned
Vacuum
Cathode sample. The “lenses” that control the electron beam
are magnetic deflection coils. (b) An electron
Anode microscope in use.
Electromagnetic Core
lens
Coil
Electromagnetic
condenser
lens Electron
beam
Specimen
goes
here
Specimen
(© David Parker/Photo Researchers, Inc.)
chamber
door
Screen
Projector
lens
Visual
transmission
Photo
chamber
(b)
(a)
x
0
(a)
Wave 1:
x
0
Wave 2:
x FIGURE 13.14 (a) An idealized
0
wave of an exact single frequency is
Superposition: the same throughout space and time.
(b) If two ideal waves with slightly
different frequencies are combined,
x beats result (Section 14.6 Vol. I). The
0 regions of space at which there is
constructive inter-ference are
different from those at which there is
destructive interfer-ence.
(b)
Figure 13.15
x
0 If a large number of waves are
combined, the result is a wave packet,
which represents a particle.
( )
2A cos ∆k x – ∆ ω t
2 2
x Figure 13.16
0
The beat pattern of Figure 13.14b,
with an envelope function (blue
curve) superimposed.
Number of electrons
detected per minute
Electrons x
θ
d θ
Electron
detector
F I G U R E 13.17 Electron interference. The slit separation d is much greater than the individual slit widths and much less
than the distance between the slit and the detector. The electron detector is movable along the y direction in the drawing and
so can detect electrons diffracted at different values of . The detector acts like the “viewing screen” of Young’s double-slit
experiment with light discussed in Chapter 12.
(a) After 28 electrons
(a – d, From C. Jönsson, Zeitschrift fur Physik 161:454, 1961; used with permission Springer Verlag)
(b) After 1000 electrons
(c) After 10000 electrons
(d) Two-slit electron pattern
Figure 13.18
(a, b, c) Computer-simulated
interference patterns for a beam of
electrons incident on a double slit.
(d) Photograph of a double-slit
interference pattern produced by
electrons.
2
F I G U R E 13.19 Results of the
two-slit electron diffraction
experiment with each slit closed
half the time (blue). The result
with both slits open is shown in
brown. Individual Accumulated
counts/min counts/min
2
ψ
x
a b
F I G U R E 13.20 The probability
of a particle being in the interval a
x b is the area under the
probability density curve from a to b.
L
v
m
(a)
x
0 L
(b)
F I G U R E 13.21 (a) A
particle of mass m and velocity :v,
confined to bouncing between
two impenetrable walls separated
by a distance L. (b) The potential
energy function for the system.
2
ψ3 ψ3
n=3 n=3
2
ψ2 ψ2
n=2 n=2
2
ψ1 ψ1
n=1 n=1
x x
0 L 0 L
(a) (b)
Figure 13.22
The first three allowed states for a particle confined to a one-dimensional box. The states are shown superimposed on the
2
potential energy function of Figure 13.22b. (a) The wave functions for n 1, 2, and 3. (b) The probability densities
for n 1, 2, and 3. The wave functions and probability densities are plotted vertically from separate axes that are offset
vertically for clarity. The positions of these axes on the potential energy function suggest the relative energies of the states,
but the positions are not shown to scale.
n
4 E4 = 16E1
3 E3 = 9E1
E2 = 4E1
ENERGY
1 E1
E=0
Ground-state energy > 0
Figure 13.23
Energy level diagram for a particle
confined to a one-dimensional box
of length L. The lowest allowed
energy is E1 h2/8mL2.
(IBM Research, Almaden Research Center. Unauthorized use prohibited)
FIGURE 13.24 This photograph is a
demonstration of a quantum corral consisting of
a ring of 48 iron atoms located on a copper
surface. The diameter of the ring is 143 nm, and
the photograph was obtained using a low-
temperature scanning tunneling microscope
(STM) as mentioned in Section 13.13. Corrals
and other structures are able to confine surface
electron waves. The study of such structures will
play an important role in determining the future
of small electronic devices.
U
ψI
ψ ψ II
ψ III
U
I II III
F I G U R E 13.25 Wave function for a
particle incident from the left on a barrier of height
U and width L. The wave function is sinusoidal in
regions I and III but exponentially decaying in
region II. The wave function is plotted vertically
from an axis positioned at the energy of the
particle.
(Alexandra Héder)
(a) (b)
Figure Q13.14
1.0
Relative intensity
0.8
0.6
0.4
0.2
0
400 500 600
Wavelength (nm)
Figure P13. 3
θ
Electron φ
beam Scattered
a electrons
Figure P13.21
Energy
L
U
E Electron
x
0
Figure P13.47 Problems 13.47 and 13.47.
Betelgeuse
(John Chumack/Photo Researchers, Inc.)
Rigel
F I G U R E 13.1 (Quick Quiz
13.1) Which star is hotter?
K max
High intensity
Low intensity (delayed)
f
Probability
density
0 L
