SPH4U –Modern Physics Problems Set
Quantum Mechanics
1. A 2.0-W laser emits a coherent light beam at a wavelength of 632.4 nm. Assuming
that all the power is radiated, how many photons leave the laser tube every
second?1
2. The human eye can respond to as little as 10-18 J of light energy. For a wavelength
at the peak of visual sensitivity (550 nm), how many photons lead to an
observable flash?2
3. a) Does a beam of infrared photons always have less energy than a beam of
ultraviolet electrons? Explain.
b) Does a single infrared photon always have less energy than a single ultraviolet
photon? Explain.3
4. A photon has a wavelength of 400 pm.
a) What is its frequency?
b) What is its momentum?
c) What is its mass equivalence? 4
5. An electric stove produces many infrared photons. If the peak wavelength of the
radiation coming from the stove element is 10μm, what is the momentum of the
released photons?5
6. An electron at rest is struck be an x-ray photon. If the scatter angle is 180° and the
final speed of the electron is 7.12×105 m/s, what was the wavelength of the
incident photon?6
7. If a photon with an incident wavelength of 18 pm loses 67% of its energy, what is
the corresponding change in the photon’s wavelength (i.e. Compton shift) as a
percentage?7
8. A 45-g golf ball is struck and leaves the club at a speed of 50 m/s. What is the de
Broglie wavelength associated with this ball?8
9. What is the de Broglie wavelength of an electron with a kinetic energy of 50 eV?9
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Physics Book Two, Irwin Publishing, Chapter 12 Problems, #22
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Physics 6 Edition, Giancoli, Chapter 27 Problems, #16
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Physics 6 Edition, Giancoli, Chapter 27 Questions, #26
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Physics Book Two, Irwin Publishing, Chapter 12 Problems, #30
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Physics Book Two, Irwin Publishing, Chapter 12 Problems, #32
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Physics Book Two, Irwin Publishing, Chapter 12 Problems, #34
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Physics Book Two, Irwin Publishing, Chapter 12 Problems, #35
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Physics Book Two, Irwin Publishing, Chapter 12 Problems, #36
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SPH3U1 - Waves Problems Set
10. In some scattering experiments, the speed of the particles is tuned so that their
de Broglie wavelength has a specific value. If a wavelength of 0.117 nm is
required, how fast must a neutron be travelling to achieve this wavelength?10
11. An electron has a de Broglie wavelength of 5.0×10-10 m.
a) What is its momentum?
b) What is its speed?
c) What voltage was needed to accelerate it to this speed?11
12. Is it possible for the de Broglie wavelength of a “particle” to be greater than the
dimensions of the particle? To be smaller? Is there any direct connection?12
13. Calculate the centripetal force required to maintain an electron in the first energy
level in an atom of hydrogen.13
14. An electron is in the ground state of a doubly ionized Lithium atom.
a) What is the kinetic energy of the electron?
b) What is the potential energy of the electron?
c) What is the ionization energy (escape energy) of the electron?
15. Calculate the wavelength of the emitted photon when an electron drops from the
4th energy state to the 2nd energy state in a Hydrogen atom. Is this photon visible?
If so, what is its colour?14
Special Relativity
16. If you were riding inside the closed cabin of a steadily moving luxury cruise ship
(no windows)m could you devise a simple physics experiment to see if you were
truly moving or not? Explain. 15
17. Light from your camera flash reflects off the mirror of a car moving towards you
with a speed v. What would you measure as the speed of this light? Explain. 16
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Physics Book Two, Irwin Publishing, Chapter 12 Problems, #39a
Physics Book Two, Irwin Publishing, Chapter 12 Problems, #37
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Physics 6 Edition, Giancoli, Chapter 27 Problems, #41
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Physics 6 Edition, Giancoli, Chapter 27 Questions, #20
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Physics Book Two, Irwin Publishing, Chapter 12 Problems, #43
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Physics Book Two, Irwin Publishing, Chapter 12 Problems, #40
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Physics Book Two, Irwin Publishing, Chapter 13 Conceptual Questions, #3
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Physics Book Two, Irwin Publishing, Chapter 13 Conceptual Questions, #20
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SPH3U1 - Waves Problems Set
18. If you travelled to a star that is 5 ca (light-years) away in a time of one year
according to your watch, have you travelled faster than the speed of light?
Explain. 17
19. Do time dilation and length contraction occur at ordinary speed, say 90 km/h?
Explain. 18
20. At what speed do the relativistic formulas time, length and mass formulas differ
from classical values by 1.00% (This is a reasonable way to estimate when to do
relativistic calculations rather than classical)? 19
21. A rod lying parallel to and moving parallel to the axis with a speed of 0.80c has a
proper length of 1.0 m. What is its length in the rest frame?20
22. A spaceship appears to be shortened to one-third of its proper length. What is its
relative speed? 21
23. Muons are produced from the decay of pions in the upper atmosphere. If the
pions have and average rest frame half-life of 2.6×10-8 s and travel at 0.998c,
calculate how far they travel into our atmosphere before decaying?22
24. Emily travels at a speed of 0.95c to a distant planet and immediately returns to
Earth. On landing, she finds that her twin brother is one year older! How far is it
from the Earth to the planet? 23
25. As an object speeds up, does its density dilate at the same rate as its mass?
Explain. 24
26. Find the radius, r, of the circular path of an electro with speed v = 0.8c, travelling
at right angles to a uniform magnetic field strength of 1.5 T. 25
27. An electron is limited to travel at speeds less than c. Does this put an upper limit
on the momentum of an electron? If so, what is this upper limit? If not, explain. 26
28. A particle of rest mass m0 travels at a speed of 0.20c. At what speed will its
momentum be doubled? 27
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Physics Book Two, Irwin Publishing, Chapter 13 Conceptual Questions, #11
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Physics 6 Edition, Giancoli, Chapter 26 Questions, #10
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Physics 6 Edition, Giancoli, Chapter 26 Problems, #10
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Physics Book Two, Irwin Publishing, Chapter 13 Problems, #30
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Physics Book Two, Irwin Publishing, Chapter 13 Problems, #31
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Physics Book Two, Irwin Publishing, Chapter 13 Problems, #33
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Physics Book Two, Irwin Publishing, Chapter 13 Problems, #44
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Physics Book Two, Irwin Publishing, Chapter 13 Conceptual Questions, #17
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Physics Book Two, Irwin Publishing, Chapter 13 Problems, #45
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Physics 6 Edition, Giancoli, Chapter 26 Questions, #15
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Physics 6 Edition, Giancoli, Chapter 26 Problems, #17
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SPH3U1 - Waves Problems Set
The Standard Model
29. Calculate the overall charge of the following hadrons, and state whether they are
baryons or mesons: 28
a)
̅
b)
c) ̅
d) ̅
30. Using only up or down quarks or antiquarks, find the combination for the π-meson (q = -1). 29
31. Is it possible for a particle to be both
a) a lepton and a baryon?
b) a baryon and a hadron?
c) a meson and a quark?
d) a hadron and a lepton? 30
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Physics Book Two, Irwin Publishing, Chapter 14 Problems, #87, 88
Physics Book Two, Irwin Publishing, Chapter 14 Problems, #91
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Physics 6 Edition, Giancoli, Chapter 32 Questions, #17
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SPH3U1 - Waves Problems Set
ANSWERS:
1. 6.36×1018 photons/s
2. 28 photons
4a) 7.5×1017 Hz
b) 1.66×10-24 N∙s
5. 6.63×10-29 N∙s
6. 2.04×10-9 m
7. 302 %
8. 2.9×10-34 m
9. 1.73×10-10 m
10. 3371 m/s
11a) 1.3×10-24 N∙s b) 1.5×106 m/s
13. 8.22×10-8 N
14a) 4.36×10-18 J b) -8.72×10-18 J
15. 4.34×10-7 m, visible, violet
20. 0.141c
21. 0.6 m
22. 2.83×108 m/s
23. 123 m
24. 0.691 ca
26. 1.52×10-3 m
28. 0.38c
29a) 0, baryon
b) +1, meson
30. ̅
c) 5.53×10-33 kg
c) 6.0 V
c) 4.36×10-18 J
c) 0, meson d) 0, meson