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Physics for Scientists and Engineers, 6e
Chapter 40 - Introduction to Quantum Physics
This figure shows two stars in the constellation Orion.
Betelgeuse appears to glow red, while Rigel looks
blue in color. Which star has a higher surface
temperature?
1
1.
Betelgeuse
2.
Rigel
3.
They both have the same
surface temperature.
4.
Impossible to determine.
2
3
4
25% 25% 25% 25%
5
1
2
3
4
A very hot star will have its peak in the blackbody
intensity distribution curve at wavelengths shorter
than the visible. As a result, more blue light is
emitted than red light.
While standing outdoors one evening, you are exposed to the
following four types of electromagnetic radiation: yellow light
from a sodium street lamp, radio waves from an AM radio
station, radio waves from an FM radio station, and microwaves
from an antenna of a communications system. Rank these
types of waves in terms of increasing photon energy, lowest
first.
1
1.
sodium light, AM, FM,
microwave
2.
AM, FM, sodium light,
microwave
3.
AM, FM, microwave, sodium
light
4.
microwave, sodium light, AM,
FM
2
3
4
5
25% 25% 25% 25%
1
2
3
4
The order of photon energy will be the
same as the order of frequency. See Figure
34.12 for a pictorial representation of
electromagnetic radiation in order of
frequency.
Consider one of the curves shown in this figure.
Suppose the intensity of the incident light is held
fixed but its frequency is increased. The stopping
potential in the figure:
1
1.
remains fixed
2.
moves to the right
3.
moves to the left
2
3
4
5
33%
1
33%
2
33%
3
When the frequency is increased, the photons
each carry more energy, so a stopping potential
larger in magnitude is required for the current to
fall to zero.
Note that for any given scattering angle θ, Equation 40.11
(seen below) gives the same value for the Compton shift for
any wavelength. Keeping this in mind, for which of the following
types of radiation is the fractional shift in wavelength at a given
scattering angle the largest?
1
1.
radio waves
2.
microwaves
3.
visible light
4.
x-rays
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3
4
5
25% 25% 25% 25%
1
2
3
4
The shift Δλ is independent of λ. Thus, the
largest fractional shift will correspond to the
smallest wavelength.
We have discussed two wavelengths associated
with the electron—the Compton wavelength and the
de Broglie wavelength. Which is an actual physical
wavelength associated with the electron?
1
1.
the Compton wavelength
2.
the de Broglie wavelength
3.
both wavelengths
4.
neither wavelength
2
3
4
5
25% 25% 25% 25%
1
2
3
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The Compton wavelength (Section
40.3) is a combination of constants and
has no relation to the motion of the
electron. The de Broglie wavelength
(Eq. 40.15) is associated with the
motion of the electron through its
momentum.
As an analogy to wave packets, consider an “automobile
packet” that occurs near the scene of an accident on a
freeway. The phase speed is analogous to the speed of
individual automobiles as they move through the backup
caused by the accident. The group speed can be identified as
the speed of the leading edge of the packet of cars. For the
automobile packet,
33%
1
1.
the group speed is the same as
the phase speed.
2.
the group speed is less than
the phase speed.
3.
the group speed is greater than
the phase speed.
2
3
4
5
1
33%
2
33%
3
The group speed is zero because the leading
edge of the packet remains fixed at the location
of the accident.
As another analogy to wave packets, consider a “runner
packet” that occurs at the start of a footrace of length L. As the
runners begin the race, the packet of runners spreads in size
as the faster runners outpace the slower runners. The phase
speed is the speed of a single runner, while we can identify the
group speed vg as the speed with which the average position
of the entire packet of runners moves. The time interval for the
winning runner to run the race is
33%
1
1.
greater than L/vg.
2.
equal to L/vg.
3.
less than L/vg.
2
3
4
5
1
33%
2
33%
3
The phase speed of the winning runner is
larger than the average speed of all the
runners, so the time interval for the winning
runner is less than L/vg.
The location of a particle is measured and specified
as being exactly at x = 0, with zero uncertainty in
the x direction. How does this affect the uncertainty
of its velocity component in the y direction?
1
1.
It does not affect it.
2.
It makes it infinite.
3.
It makes it zero.
2
3
4
5
33%
1
33%
2
33%
3
The uncertainty principle relates uncertainty in
position and velocity along the same axis. The
zero uncertainty in position along the x axis
results in infinite uncertainty in its velocity
component in the x direction, but it is
unrelated to the y direction.
A quantum argument for the phenomenon of diffraction of light claims that
photons passing through a narrow slit have been localized to the width of the
slit. Because we have gained information about their position, they must have a
larger uncertainty in momentum along the plane of the screen in which the slit
is cut. Thus, the photons gain momentum perpendicular to their original
direction of propagation and spread out, forming on a screen a bright area that
is wider than the slit. Suppose we are observing diffraction of light and
suddenly Planck’s constant drops to half its previous value. This quantum
argument for diffraction would claim that
33%
1
1.
the bright area on the
screen is unchanged.
2.
the bright area on the
screen becomes wider.
3.
the bright area on the
screen becomes narrower.
2
3
4
5
1
33%
2
33%
3
According to the uncertainty principle, if Planck’s
constant is smaller, the uncertainty in momentum
can be smaller and the momentum perpendicular
to the original direction of propagation would be
smaller. Note that classical wave theory does not
include Planck’s constant, so it would predict no
effect.