1. Fundamentals of Physics, 9e
1. In a double-slit arrangement the slits are separated by a
distance equal to 110 times the wavelength of the light passing
through the slits.
(a) What is the angular separation between the central maximum
and an adjacent maximum?
(b) What is the distance between these maxima on a screen 52.4
cm from the slits?
2. A double-slit arrangement produces interference fringes that
have an angular separation of 3.32 x 10-3 rad for light with a
wavelength of λ = 418 nm. For what wavelength would the
angular separation be 9.93% greater?
3. Monochromatic light of wavelength 555 nm illuminates two
parallel narrow slits 6.07 μm apart. Calculate the angular
deviation of the third-order (for m = 3) bright fringe? Units
4. We wish to coat flat glass (n = 1.50) with a transparent
material (n = 1.27) so that reflection of light at wavelength 689
nm is eliminated by interference. What minimum thickness can
the coating have to do this? (in nm)
5. A 660-nm-thick soap film (n = 1.43) in air is illuminated with
white light in a direction perpendicular to the film. For how
many different wavelengths in the 300 to 700 nm range is there
a. (a) fully constructive interference (__units)
b. (b) Fully destructive interference in the reflected light?
(__units)
6. The rhinestones in costume jewelry are glass with index of
refraction 1.50. To make them more reflective, they are often
coated with a layer of silicon monoxide of index of refraction
2.00. What is the minimum coating thickness needed to ensure
that light of wavelength 471 nm and of perpendicular incidence
will be reflected from the two surfaces of the coating with fully
constructive interference? ____nm
7. Monochromatic light of wavelength 577 nm is incident on a
narrow slit. On a screen 1.51 m away, the distance between the

2. second diffraction minimum and the central maximum is 1.73
cm.
a. (a) Calculate the angle of diffraction θ of the second
minimum. (____units)
b. (b) Find the width of the slit in nanometers.(____units)
8. Light of wavelength 547 nm is incident on a narrow slit. The
angle between the first diffraction minimum on one side of the
central maximum and the first minimum on the other side is
1.34°. What is the width of the slit? (____units)
9. (a) How far from grains of red sand must you be to position
yourself just at the limit of resolving the grains if your pupil
diameter is 1.7 mm, the grains are spherical with radius 54 μm,
and the light from the grains has wavelength 660 nm? (
_____units) (b) If the grains were blue and the light from them
had wavelength 430 nm, would the answer to (a) be larger
(show 1) or smaller (show 0)?
10. The radar system of a navy cruiser transmits at a wavelength
of 1.5 cm, from a circular antenna with a diameter of 1.9 m. At
a range of 8.3 km, what is the smallest distance in meters that
two speedboats can be from each other and still be resolved as
two separate objects by the radar system? (_____units)
11. A diffraction grating 23.3 mm wide has 8210 rulings. Light
of wavelength 700 nm is incident perpendicularly on the
grating. What are the (a) largest, (b) second largest, and (c)
third largest values of θ at which maxima appear on a distant
viewing screen?
a. _____degrees
b. _____degrees
c. _____degrees
12. A grating has 420 lines/mm. How many orders of the visible
wavelength 524 nm can it produce in addition to the m = 0
order? (_____units)
13. The mean lifetime of certain subatomic particles is
measured to be 1.7511 μs when they are stationary. However,
the mean lifetime of fast-moving particles of the same kind
observed in a burst of cosmic rays is measured to be 18.596 μs.

3. What is the speed parameter β of these cosmic-ray particles
relative to Earth? (_____units)
14. You wish to make a round trip from Earth in a spaceship,
traveling at constant speed in a straight line for exactly 3
months (as you measure the time interval) and then returning at
the same constant speed. You wish further, on your return, to
find Earth as it will be exactly 1000 years in the future.
a. (a) To eight significant figures, at what speed parameter must
you travel? (____units)
b. (b) Does it matter whether you travel in a straight line on
your journey? (Yes/ No)
15. An unstable high-energy particle enters a detector and
leaves a track 1.37 mm long before it decays. Its speed relative
to the detector was 0.931c. What is its proper lifetime in
seconds? That is, how long would the particle have lasted
before decay had it been at rest with respect to the detector?
(____units)
16. An electron of β = 0.999 995 moves along the axis of an
evacuated tube that has a length of 2.32 m as measured by a
laboratory observer S at rest relative to the tube. An observer S'
at rest relative to the electron, however, would see this tube
moving with speed v (=βc). What length would observer S'
measure for the tube? (____units)
17. A meter stick in frame S' makes an angle of 42° with the x'
axis. If that frame moves parallel to the x axis of frame S with
speed 0.97c relative to frame S, what is the length of the stick
as measured from S? (____units)
18. Observer S reports that an event occurred on the x axis of
his reference frame at x = 2.51 x 108 m at time t = 1.89 s.
Observer S' and her frame are moving in the positive direction
of the x axis at a speed of 0.475c. Further, x = x' = 0 at t = t' =
0. What are the (a) spatial and (b) temporal coordinate of the
event according to S'? If S' were, instead, moving in the
negative direction of the x axis, what would be the (c) spatial
and (d) temporal coordinate of the event according to S'?
a. _____units

4. b. _____units
c. _____units
d. _____units
19. The origins of two frames coincide at t = t' = 0 and the
relative speed is 0.998c. Two micrometeorites collide at
coordinates x = 114 km and t = 282 μs according to an observer
in frame S. What are the (a) spatial and (b) temporal coordinate
of the collision according to an observer in frame S'?
a. _____units
b. _____mus
20. An experimenter arranges to trigger two flashbulbs
simultaneously, producing a big flash located at the origin of
his reference frame and a small flash at x = 32.8 km. An
observer, moving at a speed of 0.372c in the positive direction
of x, also views the flashes. What is the time interval in seconds
between them according to her? (____units)
21. A particle moves along the x' axis of frame S' with velocity
0.21c. Frame S' moves with velocity 0.68c with respect to frame
S. What is the speed of the particle with respect to frame S?
(____units)
22. Galaxy A is reported to be receding from us with a speed of
0.51c. Galaxy B, located in precisely the opposite direction, is
also found to be receding from us at this same speed. What
multiple of c gives the recessional speed an observer on Galaxy
A would find for (a) our galaxy and (b) Galaxy B?
a. ______
b. ______
23. A spaceship, moving away from Earth at a speed of 0.974c,
reports back by transmitting at a frequency (measured in the
spaceship frame) of 81.3 MHz. To what frequency must Earth
receivers be tuned to receive the report? (_____MHz)
24. How fast would you have to be moving for the 659 nm
wavelength of a light source to appear as 588 nm to you,
assuming that a relativistic calculation is not needed?
(_____units)
25. How much work (in terms of MeV) must be done to increase

5. the speed of an electron from rest to (a) 0.462c, (b) 0.981c, and
(c) 0.9959c?
a. ______MeV
b. ______ MeV
c. ______ MeV
26. The mass of an electron is 9.109 381 88 x 10-31kg. Find (a)
γ and (b) β for an electron with kinetic energy 23.5659 MeV.
a. ______units
b. ______ units
27. How much work (in terms of keV) must be done to increase
the speed of an electron from (a) 0.26c to 0.28c and (b) from
0.92c to 0.94c? Note that the speed increase is 0.02c in both
cases.
a. _____keV
b. _____keV
28. What is the nuclear mass density <ρm of (a) the fairly low-
mass nuclide 56Fe and (b) the fairly high-mass nuclide 210At?
Compare the two answers, with an explanation.What is the
nuclear charge density ρq of (c)56Fe and (d)210At? Compare
the two answers, with an explanation.
a. ______units
b. ______ units
c. _____ units
d. _____ units
29. What is the mass excess Δ1 of 1H (whose actual mass is
1.007825 u) in (a) atomic mass units and (b) MeV/c2?
What is the mass excess Δn of a neutron (actual mass is
1.008665 u) in (c) atomic mass units and (d) MeV/c2?
What is the mass excess Δ120 of 120Sn (actual mass is
119.902197 u) in (e) atomic mass units and (f) MeV/c2?
a. _______units
b. _______ MeV/c2
c. _______units
d. _______ MeV/c2
e. _______units
f. _______ MeV/c2

6. 30. What is the binding energy per nucleon of the americium
isotope
31. Cancer cells are more vulnerable to x and gamma radiation
than are healthy cells. In the past, the standard source for
radiation therapy was radioactive 60Co, which decays, with a
half-life of 5.27 y, into an excited nuclear state of 60Ni. That
nickel isotope then immediately emits two gamma-ray photons,
each with an approximate energy of 1.2 MeV. How many
radioactive 60Co nuclei are present in a 7000 Ci source of the
type used in hospitals? (Energetic particles from linear
accelerators are now used in radiation therapy.) ______units
32. The half-life of a radioactive isotope is 120 d. How many
days would it take for the decay rate of a sample of this isotope
to fall to 0.58 of its initial rate? (______units)
33. A radioactive nuclide has a half-life of 24.1 y. What
fraction of an initially pure sample of this nuclide will remain
undecayed at the end of 78.8 y? _____
34. A certain radioactive nuclide decays with a disintegration
constant of 0.0143 h-1. (a) Calculate the half-life (in terms of
hours) of this nuclide. What fraction of a sample will remain at
the end of (b) 4.64 half-lives and (c) 7.69 days?
a. ______units
b. ______
c. ______
35. Plutonium isotope 239Pu decays by alpha decay with a half-
life of 24100 y. How many milligrams of helium are produced
by an initially pure 13.5 g sample of 239Pu at the end of 19610
y? (Consider only the helium produced directly by the
plutonium and not by any by-products of the decay process.)
_____units
36. The cesium isotope 137Cs is present in the fallout from
aboveground detonations of nuclear bombs. Because it decays
with a slow (30.2 y) half-life into 137Ba, releasing considerable
energy in the process, it is of environmental concern. The
atomic masses of the Cs and Ba are 136.9071 and 136.9058 u,
respectively; calculate the total energy released in such a decay.

7. (_____MeV)
37. The isotope 238U decays to 206Pb with a half-life of 4.47 x
109 y. Although the decay occurs in many individual steps, the
first step has by far the longest half-life; therefore, one can
often consider the decay to go directly to lead. That is,
238U → 206Pb + various decay products
A rock is found to contain 4.17 mg of 238U and 2.760 mg of
206Pb. Assume that the rock contained no lead at formation, so
all the lead now present arose from the decay of uranium. How
many atoms of (a) 238U and (b) 206Pb does the rock now
contain? (c) How many atoms of 238U did the rock contain at
formation? (d) What is the age of the rock?
a. _______
b. _______
c. _______
d. _______years
38. A radiation detector records 77 x 102 counts in 1.0 min.
Assuming that the detector records all decays, what is the
activity of the radiation source in (a) becquerels and (b)
nanocuries?
a. _______units
b. _______units
39. A 83 kg person receives a whole-body radiation dose of 2.3
x 10-4 Gy, delivered by alpha particles for which the RBE
factor is 12. Calculate (a) the absorbed energy (in terms of mJ)
and (b) the dose equivalent.
a. _____MJ
b. _____units
40. During the Cold War, the Premier of the Soviet Union
threatened the United States with 4.0 megaton 239Pu warheads.
(Each would have yielded the equivalent of an explosion of 4.0
megatons of TNT, where 1 megaton of TNT releases 2.6 × 1028
MeV.) If the plutonium that actually fissioned had been 9.61%
of the total mass of the plutonium in such a warhead, what was

8. that total mass? (______kg)
41. An electron cannot decay into two neutrinos. Which of the
following conservation laws would be violated if it did: (a)
energy, (b) angular momentum, (c) charge, (d) lepton number,
(e) linear momentum, (f) baryon number? (Several choices may
be correct.)_____
42. A proton cannot decay into a neutron and a neutrino. Which
of the following conservation laws would be violated if it did:
(a) energy (assume the proton is stationary), (b) angular
momentum, (c) charge, (d) lepton number, (e) linear momentum,
(f) baryon number? (Several choices may be correct.) _______
43. Which conservation laws are violated in the proposed
decay? Assume that the initial particle is stationary and the
decay products have zero orbital angular momentum.
44. In the laboratory, one of the lines of sodium is emitted at a
wavelength of 590.0 nm. In light from a particular galaxy,
however, this line is seen at a wavelength of 614.3 nm.
Calculate the distance (in ly) to the galaxy, assuming that
Hubble's law holds and that the Doppler shift of Eq. 37-36
applies. (______units)
45. What is the observed wavelength of the 656.3 nm (first
Balmer) line of hydrogen emitted by a galaxy at a distance of
1.94 x 108 ly? Assume that the Doppler shift of Eq. 37-36 and
Hubble's law apply. (______nm)
46. If Hubble's law can be extrapolated to very large distances,
at what distance would the apparent recessional speed become
equal to the speed of light? (_____ly)
47. At what rate does a star emit photons? For simplicity,
assume that the star's entire emission at the rate of 4.9 x 1026
W is at the single wavelength of 550 nm. (______nm)
48. The meter was once defined as 1 650 763.73 wavelengths of
the orange light emitted by a source containing krypton-86
atoms. What is the photon energy of that light? (______eV)
49. Light from a certain lamp is brightest at a wavelength of
603 nm. What is the photon energy (in eV) for light at that
wavelength? (______units)

9. 50. Light strikes a metal surface, causing photoelectric
emission. The stopping potential for the ejected electrons is 6.3
V, and the work function of the metal is 2.5 eV. What is the
wavelength of the incident light (in terms of nm)? (_______nm)
51. The work function of tungsten is 4.50 eV. Calculate the
speed of the fastest electrons ejected from a tungsten surface
when light whose photon energy is 5.62 eV shines on the
surface. (______Km/s)
52. The wavelength associated with the cutoff frequency for
silver is 325 nm. Find the maximum kinetic energy of electrons
ejected from a silver surface by ultraviolet light of wavelength
253 nm. (_______eV)
53. Light of wavelength 5.46 pm is directed onto a target
containing free electrons. Find the wavelength of light scattered
at 101° from the incident direction. The electron Compton
wavelength is 2.43 x 10-12 m. (_______pm)
54. What (a) frequency, (b) photon energy, and (c) photon
momentum magnitude are associated with x rays having
wavelength 34.5 pm?
a. _______Hz
b. _______units
c. _______units
55. In an old-fashioned television set, electrons are accelerated
through a potential difference of 24.1 kV. What is the de
Broglie wavelength of such electrons? (Relativity is not
needed.) (_______pm)
56. Singly charged sodium atoms are accelerated through a
potential difference of 238 V. (a) What is the momentum
acquired by such an ion? (b) What is its de Broglie wavelength
(in pm)? The mass of a sodium ion is 3.819 x 10-26 kg.
a. _______units
b. _______pm
57. The wavelength of the yellow spectral emission line of
sodium is 590 nm. At what kinetic energy would an electron
have that wavelength as its de Broglie wavelength?
_______microeV

10. 58. What is the wavelength of (a) a photon with energy 9.0 eV
(in nm), (b) an electron with energy 9.0 eV (in nm), (c) a
photon of energy 9.0 GeV (in fm), and (d) an electron with
energy 9.0 GeV (in fm)?
a. ______nm
b. _______nm
c. _______units
d. _______units
59. A particle of mass 3.1 x 10-27 kg has a potential energy of
7.5 x 10-15 J, independently of its position. If its energy is 12 x
10-15 J, what is its angular wave number? (_____units)
60. An electron in a one-dimensional infinite potential well of
length L has ground-state energy E1. The length is changed to
L' so that the new ground-state energy is E1' = 0.660E1. What is
the ratio L'/L? ______
61. The ground-state energy of an electron trapped in a one-
dimensional infinite potential well is 3.0 eV. What will this
quantity be if the width of the potential well is multiplied by 7?
_______eV
62. What must be the width (in nm) of a one-dimensional
infinite potential well if an electron trapped in it in the n = 1
state is to have an energy of 6.1 eV? _______nm
63. An electron is trapped in a one-dimensional infinite
potential well. For what (a) higher quantum number and (b)
lower quantum number is the corresponding energy difference
equal to the energy difference 7E43 between the levels n4 and
n3? (c) Can a pair of adjacent levels have an energy difference
equal to 2E43? If no, then enter 0. If yes, then enter 1.
a. _______units
b. _______units
c. _______units
64. An electron is trapped in a one-dimensional infinite
potential well that is 330 pm wide; the electron is in its ground
state. What is the probability that you can detect the electron in
an interval of width δx = 5.0 pm centered at x = 310 pm? (Hint:
The interval δx is so narrow that you can take the probability

11. density to be constant within it.) (_____units)
65. What is the ratio of wavelength #4 of the Balmer series to
wavelength #4 of the Lyman series? (______units)
66. An atom (not a hydrogen atom) absorbs a photon whose
associated wavelength is 235 nm and immediately emits a
photon whose associated wavelength is 590 nm. How much net
energy (in terms of eV) is absorbed by the atom in this process?
(______eV)
67. What are the (a) energy (in eV), (b) magnitude of the
momentum, and (c) wavelength (in nm) of the photon emitted
when a hydrogen atom undergoes a transition from a state with
n = 5 to a state with n = 3?
a. _______nm
b. _______units
c. ______nm
68. An atom (not a hydrogen atom) absorbs a photon whose
associated frequency is 6.9 x 1014 Hz. By what amount does the
energy (in terms of eV) of the atom increase? (_____eV)
69. What is the intensity of a traveling plane electromagnetic
wave if Bm is 1.1 x 10-5 T?_____ W/m^2
70. Assume (unrealistically) that a TV station acts as a point
source broadcasting isotropically at 1.2 MW. What is the
intensity of the transmitted signal reaching a nearby star that is
18 ly away. (An alien civilization at that distance might be able
to watch X Files.) A light-year (ly) is the distance light travels
in one year. _______ W/m^2
71. A plane electromagnetic wave has a maximum electric field
of magnitude 2.98 x 10-6 V/m. Find the maximum magnetic
field amplitude. ______T
72. In a plane radio wave the maximum value of the electric
field component is 6.83 V/m. Calculate (a) the maximum value
of the magnetic field component and (b) the wave intensity.
a. ______T
b. ______ W/m^2
73. The maximum electric field 10 m from a point light source
is 1.6 V/m. What are (a) the maximum value of the magnetic

12. field and (b) the average intensity of the light there? (c) What is
the power of the source?
a. ______T
b. ______ W/m^2
c. ______units
74. High-power lasers are used to compress a plasma (a gas of
charged particles) by radiation pressure. A laser generating
radiation pulses with peak power 2200 MW is focused onto 0.99
mm2 of high-electron-density plasma. Find the pressure exerted
on the plasma if the plasma reflects all the light beams directly
back along their paths. _______units
75. It has been proposed that a spaceship might be propelled in
the solar system by radiation pressure, using a large sail made
of foil. How large must the surface area (in m2) of the sail be if
the radiation force is to be equal in magnitude to the Sun's
gravitational attraction? Assume that the mass of the ship + sail
is 1400 kg, that the sail is perfectly reflecting, and that the sail
is oriented perpendicular to the Sun's rays. (With a larger sail,
the ship is continuously driven away from the Sun.) The rate at
which the Sun emits energy is 3.90 × 1026 W. The Sun's mass is
1.99 × 1030 kg. Gravitational constant is 6.67 × 10-11
N•m2/kg2. _______units
76. When the rectangular metal tank in the figure is filled to the
top with an unknown liquid, observer O, with eyes level with
the top of the tank, can just see corner E. A ray that refracts
toward O at the top surface of the liquid is shown. If D = 93.4
cm and L = 2.30 m, what is the index of refraction of the liquid?
______units
77. Light in vacuum is incident on the surface of a slab of
transparent material. In the vacuum the beam makes an angle of
37.8° with the normal to the surface, while in the slab it makes
an angle of 22.7° with the normal. What is the index of
refraction of the transparent material? _______units
78. The figure shows light reflecting from two perpendicular
reflecting surfaces A and B. Find the angle (in o) between the

13. incoming ray i and the outgoing ray r'. ______units
79. In the figure, light is incident at angle θ1 = 42.0˚ on a
boundary between two transparent materials. Some of the light
travels down through the next three layers of transparent
materials, while some of it reflects upward and then escapes
into the air. If n1 = 1.28, n2 = 1.42, n3 = 1.30 and n4 = 1.43,
what is the value of (a)θ4 and (b)θ5?
a. _______units
b. _______units
80. A point source of light is 65.3 cm below the surface of a
body of water. Find the diameter of the circle at the surface
through which light emerges from the water. Water has an index
of refraction of 1.33.______cm
81. In the figure, a ray of light is perpendicular to the face ab of
a prism (n = 1.41). Find the largest value for the angle so that
the ray is totally reflected at face ac if the prism is immersed
(a) in air and (b) in water (n=1.33).
a. _______units
b. _______units
82. A lens is made of a transparent material having an index of
refraction of 1.5. One side of the lens is flat, and the other
convex with a radius of curvature of 25 cm. (a) Find the focal
length of the lens. (b) If an object is placed 110 cm in front of
the lens, where will the image be located?
a. _______cm
b. _______cm
83. A movie camera with a (single) lens of focal length 70 mm
takes a picture of a person standing 35 m away. If the person is
160 cm tall, what is the height of the image in millimeters on
the film? _______mm
84. You produce an image of the Sun on a screen using a thin
lens whose focal length is 17.3 cm. What is the diameter of the
image in millimeters? (Take the radius of the Sun to be 6.96 x
108 m and its distance to Earth to be 1.5 x 1011 m.)

14. ________mm
85. An illuminated slide is held 75 cm from a screen. How far
from the slide (between the slide and the screen) must a lens of
focal length 6.7 cm be placed to form an image of the slide's
picture on the screen? (Give the smaller of the two possible
answers.) _______cm
86. In the figure, a real inverted image I of an object O is
formed by a certain lens (not shown); the object-image
separation is d = 31.4 cm, measured along the central axis of the
lens. The image is just 1/2 the size of the object. (a) How far
from the object must the lens be placed? (b) What is the focal
length of the lens?
a. _______cm
b. _______cm
87. In a microscope of the type shown in the figure, the focal
length of the objective is 5.89 cm, and that of the eyepiece is
9.98 cm. The distance between the lenses is 25.1 cm. (a) What
is the tube length s? (b) If image I in the figure is to be just
inside focal point F'1, how far from the objective should the
object be? What then are (c) the lateral magnification m of the
objective, (d) the angular magnification mθ of the eyepiece, and
(e) the overall magnification M of the microscope?
a. ________units
b. ________units
c. ________units
d. ________units
e. ________units