Download Introduction to Quantum Physics

Introduction to Quantum Physics
Multiple Choice
1.
Your temperature is 98.6°F. Assuming your skin is a perfect radiator (ε = 1),
determine the wavelength corresponding to the largest intensity (in µm).
a.
b.
c.
d.
e.
2.
The threshold wavelength for photoelectric emission of a particular substance is
500 nm. What is the work function (in eV)?
a.
b.
c.
d.
e.
3.
4.2
4.0 × 10–19
4.0 × 10–10
2.5 × 10–19
2.5
What is the maximum velocity (in km/s) of a photoelectron emitted from a
surface whose work function is 5 .0 eV when illuminated by a light whose
wavelength is 200 nm?
a.
b.
c.
d.
e.
4.
8.0
9.3
3.0
5.7
29.4
460
650
420
550
1480
A stopping potential of 3.2 V is needed for radiation whose wavelength is
200 nm. What is the work function (in eV) of the material?
a.
b.
c.
d.
e.
4.0
3.0
5.0
6.0
2.0
321
5.
What is the maximum kinetic energy (in eV) of a photoelectron emitted from a
surface whose work function is 5.0 eV when illuminated by a light whose
wavelength is 200 nm?
a.
b.
c.
d.
e.
6.
What is the maximum kinetic energy (in eV) of a photoelectron when a surface,
whose work function is 5.0 eV, is illuminated by photons whose wavelength is
400 nm?
a.
b.
c.
d.
e.
7.
4
2
2
3
16
The light intensity incident on a metallic surface with a work function of 3 eV
produces photoelectrons with a maximum kinetic energy of 2 eV. The frequency
of the light is doubled. Determine the maximum kinetic energy (in eV).
a.
b.
c.
d.
e.
9.
3.1
–1.9
1.9
0
1.2
The light intensity incident on a metallic surface produces photoelectrons with a
maximum kinetic energy of 2 eV. The light intensity is doubled. Determine the
maximum kinetic energy of the photoelectrons (in eV).
a.
b.
c.
d.
e.
8.
1.9
1.2
3.1
zero
6.2
3
2
2
4
7
A photon whose energy is 8.00 × 10–15 J is scattered off an electron at a 90° angle.
What is the wavelength of the scattered wave?
a.
b.
c.
d.
e.
2.73 × 10–11 m
2.25 × 10–11 m
2.50 × 10–11 m
2.40 × 10–12 m
2.48 × 10–11 m
Introduction to Quantum Physics
10.
A photon whose wavelength is = 5.0 × 10–11 m is scattered straight backward.
What is the wavelength of the scattered wave?
a.
b.
c.
d.
e.
11.
A photon collides with an electron. After the collision the wavelength of the
scattered wave is
a.
b.
c.
d.
e.
12.
1.0 × 10–38 J
6.6 × 10–30 J
4.2 × 10–29 J
3.1 × 10–30 J
13.1 × 10–29 J
How much energy is in an 89.7 MHz photon of FM-radiation?
a.
b.
c.
d.
e.
14.
greater than or equal to the initial wavelength.
equal to the initial wavelength.
less than or equal to the initial wavelength.
greater than the initial wavelength.
less or greater depending on the scattering angle.
How much energy is in a 63 kHz photon of AM-radiation?
a.
b.
c.
d.
e.
13.
5.0 × 10–11 m
4.5 × 10–11 m
5.5 × 10–11 m
6.0 × 10–11 m
6.5 × 10–11 m
2.2 × 10–33 J
9.5 × 10–27 J
7.4 × 10–42 J
5.9 × 10–26 J
3.7 × 10–25 J
Assume electrons are accelerated through a potential difference of 25,000 V
inside a TV picture tube. What is the minimum wavelength that could be
produced when the electrons strike the phosphor? (1 Å = 10–10 m)
a.
b.
c.
d.
e.
0.5 Å
1.0 Å
10 Å
100 Å
0.25 Å
323
15.
A solid state pulsed laser has an energy of 400 mJ per pulse. If its wavelength is
1.06 × 10–6 m, how many photons are in each pulse?
a.
b.
c.
d.
e.
16.
A helium-neon laser emits red light having a wavelength of 6.4 × 10–7 m and a
power of 0.5 mW. How many photons are emitted each second?
a.
b.
c.
d.
e.
17.
3.4 × 103
2.8 × 103
3.9 × 103
2.6 × 103
1.7 × 103
A neutron has a mass of 1.67 × 10–27 kg. Its de Broglie wavelength is 1.4 × 10–10 m.
What is its kinetic energy (in eV)?
a.
b.
c.
d.
e.
19.
6.4 × 1038
1.6 × 1021
3.2 × 1025
2.6 × 1018
1.6 × 1015
A neutron has a mass of 1.67 × 10–27 kg. The de Broglie wavelength is
1.4 × 10–10 m. How fast is the neutron going? (in m/s)
a.
b.
c.
d.
e.
18.
2 × 1025
2 × 1021
3 × 1018
6 × 1038
2 × 1018
4
0.4
0.04
40
0.08
A neutron has a mass of 1.67 × 10–27 kg. Its de Broglie wavelength is 1.4 × 10–10 m.
What temperature would it correspond to if we had a monatomic gas having the
same average kinetic energy (in °C)?
a.
b.
c.
d.
e.
273
25
36
309
51
Introduction to Quantum Physics
20.
An electron is accelerated through a potential difference of 25 000 V. What is the
de Broglie wavelength of the electron (in m)?
a.
b.
c.
d.
e.
21.
3
4
5
6
14
In an experiment different wavelengths of light, all able to eject photoelectrons,
shine on a freshly prepared (oxide-free) zinc surface. Which statement is true?
a.
b.
c.
d.
e.
23.
5.9 × 10–12
6.8 × 10–12
6.5 × 10–12
7.8 × 10–12
5.5 × 10–12
Microscopes are inherently limited by the wavelength of the light used. How
much smaller (in order of magnitude) can we “see” using an electron microscope
whose electrons have been accelerated through a potential difference of 50 000 V
than using red light (500 nm)?
a.
b.
c.
d.
e.
22.
325
The number of photoelectrons emitted per second is independent of the
intensity of the light for all the different wavelengths.
The number of photoelectrons emitted per second is directly proportional to
the frequency for all the different wavelengths.
The maximum kinetic energy of the photoelectrons emitted is directly
proportional to the frequency for each wavelength present.
The maximum kinetic energy of the photoelectrons has a linear relationship
with the frequency for each wavelength present.
The maximum kinetic energy of the photoelectrons is proportional to the
intensity of the light and independent of the frequency.
When a photon collides with a free electron at rest and the direction of motion of
the photon changes,
a.
b.
c.
d.
e.
the magnitude of the momentum of the photon does not change.
the momentum of the electron does not change.
the kinetic energy of the electron does not change.
the total energy of the photon does not change.
both the magnitude of the momentum and the total energy of the photon
decrease.
24.
Find the uncertainty in the momentum (in kg · m/s) of an electron if the
uncertainty in its position is equal to 3.4 × 10–10 m, the circumference of the first
Bohr orbit.
a.
b.
c.
d.
e.
25.
Because the factor h on the right side of the Heisenberg uncertainty principle has
units of Joule-seconds, it suggests that the energy of a system also has
uncertainty. The uncertainty in energy depends on the length of the time interval
during which a system exists. ∆E∆t ≥ h/2π. Suppose an unstable mass is
produced during a high-energy collision such that the uncertainty in its mass is
me/100. (me = 9.11 × 10–31 kg.) How long will this particle exist?
a.
b.
c.
d.
e.
26.
1.3 × 10–19 s
2.3 × 10–23 s
1.0 × 1015 s
1.2 × 1013 s
8.1 × 10–19 s
Assume we can determine the position of a particle within an uncertainty of
0.5 nm. What will be the resulting uncertainty in the particle’s momentum (in
kg · m/s)?
a.
b.
c.
d.
e.
27.
6.2 × 10–25
3.1 × 10–25
15.5 × 10–25
19.4 × 10–25
2.0 × 10–24
1.9 × 10–25
4.2 × 10–25
2.1 × 10–25
1.3 × 10–24
6.6 × 10–25
Assume the Heisenberg uncertainty principle can take the form ∆E∆t ≥ h. How
accurate can the position of an electron be made if its speed is 5 × 106 m/s and if
the uncertainty in its energy is 10 eV?
a.
b.
c.
d.
e.
7.7 × 10–18 m
1.3 × 10–23 m
6.2 × 10–15 m
3.3 × 10–10 m
1.2 × 10–9 m
Introduction to Quantum Physics
28.
An electron has been accelerated by a potential difference of 100 V. If its position
is known to have an uncertainty of 1 nm, what is the percent uncertainty
(∆p/p × 100) of the electron?
a.
b.
c.
d.
e.
29.
<<1%
1%
2%
5%
10%
Film behind a double slit is exposed to light in the following way: First one slit is
opened and light is allowed to go through that slit for time ∆t. Then it is closed
and the other slit is opened and light is allowed to go through that slit for the
same time ∆t. When the film is developed the pattern will be
a.
b.
c.
d.
e.
31.
1%
2%
10%
>>10%
5%
A baseball (1 kg) has an energy of 100 joules. If its uncertainty in position is 1 m,
what is the percentage uncertainty (∆p/p × 100) in the momentum of the
baseball?
a.
b.
c.
d.
e.
30.
327
one single slit pattern.
two superimposed single slit patterns, their centers displaced from each
other by the distance between the two slits.
one double slit pattern.
two double slit patterns, their centers displaced from each other by the
distance between the two slits.
random darkening of the film. (no pattern at all)
Bohr’s Principle of Complementarity states that the wave and particle aspects of
either matter or radiation complement each other. This means that:
a.
b.
c.
d.
e.
the wavelength of the wave and the position of the particle or photon can be
measured simultaneously.
either the wavelength of the wave or the position of the particle or photon
can be measured in a single experiment.
either the wavelength of the wave or the position of the particle or photon
can be measured in experiments, but only one of the two and not the other
can ever be measured for particular particles or radiation.
the wavelength of the wave and the position of the particle or photon can
always be measured simultaneously for free particles and radiation.
the wavelength of the wave and the position of the particles or radiation can
be measured simultaneously for systems confined to atomic dimensions.
32.
A quantum particle
a.
b.
c.
d.
e.
33.
In electron diffraction, an electron moving at speed v << c acts like
a.
b.
c.
d.
e.
34.
can be localized in space.
can be represented by an infinitely long wave having a single frequency.
can be represented by a wave packet.
travels at the phase speed of the infinitely long wave having the highest
frequency.
has the highest probability of being present in those regions of space where
its component waves interfere destructively.
a particle with momentum mv.
a particle with position coordinate v/t.
a wave with wavelength v/t.
a wave with wavelength h/mv.
both a particle with position coordinate v/t and a wave with wavelength v/t.
If the position of an electron ( m = 9.11× 10−31 kg ) could be measured to within
10−30 m, the uncertainty in the magnitude of its speed could be as much as
a.
b.
c.
d.
e.
35.
The number of photons per second passing a plane perpendicular to a collimated
monochromatic (one frequency) beam of light transporting power P is directly
proportional to
a.
b.
c.
d.
e.
36.
6 × 10−34 m/s.
6× 1025 m/s.
6× 1030 m/s.
1031 m/s.
1061 m/s.
the wavelength of the light.
the frequency of the light.
the power of the beam.
all of the above.
only a and c above.
The wavelength of a 45 kg teenager moving at 5 m/s on a skateboard is about
a.
b.
c.
d.
e.
5× 10−37 m .
3× 10−36 m .
7 × 10−34 m .
0.1 m.
5 m.
Introduction to Quantum Physics
37.
Photoelectrons are ejected when monochromatic light shines on a freshlyprepared (oxide-free) sodium surface. In order to obtain the maximum increase
in the number of electrons ejected per second, the experimenter needs to
a.
b.
c.
d.
e.
38.
e.
all photons have the same energy.
photons all have frequencies greater than 1.0 Hz.
the only possible lower limit to the wavelength of a photon is about 10 26 m .
the change in energy of a photon interacting with matter always has the
same magnitude.
all photons travel at the speed of light.
The experimental observation(s) below that require(s) a quantum explanation for
the photoelectric effect
a.
b.
c.
d.
e.
40.
increase the frequency of the light.
increase the intensity of the light.
increase the area illuminated by the light.
do all of the above.
do only (b) and (c) above.
Celia says that because Planck’s constant h is finite, there is a lower limit of
6.6 × 10 −34 J to the energy of photons. She is wrong because
a.
b.
c.
d.
39.
329
is that more photoelectrons are emitted when the light frequency increases.
is that the maximum kinetic energy of the photoelectrons is related linearly
to the frequency of the light.
is that every metal surface has a work function, a minimum amount of
energy needed to free electrons.
is that the stopping potential measures the kinetic energy of the
photoelectrons.
are all of the above.
m
has a 0.500 kg bob and a 4.00 Hz
s2
oscillation frequency. If it is released from a point 0.150 m above the lowest point
it reaches, the number of quanta in this oscillation is
A pendulum located where g = 9.80
a.
b.
c.
d.
e.
2.77 × 1032 .
1.11 × 1033 .
4.87 × 10−34 .
0.184.
4.00.
41.
A wave packet can represent a quantum particle because
a.
b.
c.
d.
e.
42.
Because of Heisenberg’s Uncertainty Principle, the velocity of a particle is known
least precisely when the length of the wave packet representing the particle is
a.
b.
c.
d.
e.
43.
it has the localized nature of a particle.
the group velocity is identical to the speed of the particle.
the waves that compose the packet can show interference and diffraction.
of all of the above.
of only (a) and (b) above.
< 10−15 m .
< 10−10 m .
of the order of 1.00 m.
>10 m.
the length of a plane wave (inifinite.)
Cosmic rays are attacking Earth! Some 1.00 × 10−26 kg particles start at a distance
m
. If we ignore the
s
Earth’s motion in its orbit, the motion of the Sun and the motion of the Galaxy,
the uncertainty in their position when they reach Earth is about
of 3.00 × 1013 m and approach at a speed of 3.00 × 105
a.
b.
c.
d.
e.
10−34 m .
10−15 m .
1m.
10+15 m .
10+34 m .
Introduction to Quantum Physics
331
Open-Ended Problems
44.
If a rubidium surface is irradiated with blue light of wavelength 450.0 nm, what
is the kinetic energy of the electrons emitted? (The work function for rubidium is
φ = 2.09 eV.)
45.
What is the shortest x-ray wavelength that can be produced in a 12-keV x-ray
machine?
46.
What is the energy in eV of a photon of yellow light? λ = 500 nm.
47.
On a bright and sunny day, the intensity of solar radiation on the Earth’s surface
is 1000 W/m2. If the average wavelength of the sunlight is 500 nm, how many
photons are incident on a square meter of the Earth’s surface per second?
48.
The “seeing ability” or resolution of radiation is determined by its wavelength. If
an atom is approximately 10–10 m in diameter, how fast must an electron travel to
have a wavelength smaller than the size of an atom?
49.
An electron is sitting on a pinpoint having a diameter of 2.5 µm. What is the
minimum uncertainty in the speed of the electron?
50.
Suppose we use optical radiation (λ = 500 nm) to determine the position of the
electron to within the wavelength of the light. What will be the resulting
uncertainty in the electron’s velocity?
Introduction to Quantum Physics
1.
b
26.
c
2.
e
27.
d
3.
b
28.
b
4.
b
29.
a
5.
b
30.
b
6.
d
31.
b
7.
b
32.
c
8.
e
33.
d
9.
a
34.
b
10.
c
35.
e
11.
a
36.
b
12.
c
37.
e
13.
d
38.
c
14.
a
39.
b
15.
e
40.
a
16.
e
41.
d
17.
b
42.
a
18.
c
43.
c
19.
e
44.
0.67 eV
20.
d
45.
10–10 m
21.
c
46.
2.48 eV
22.
d
47.
2.51 × 1021 photons/s
23.
e
48.
7.3 × 106 m/s
24.
b
49.
46.3 m/s
25.
a
50.
1.5 km/s
Introduction to Quantum Physics
333