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Physics 106 Homework Problems, Winter 2007
Sec. 2, Stephanie Magleby
These problems are adapted from Serway and Faughn, College Physics, and are usedwith permission from Harcourt Brace College Publishers.
1-1. In the figure, q1 = 6.27 µC, q2 = [01] µC,
q3 = −2.38 µC, r1 = 3.49 cm, and r2 = 3.22 cm.
Calculate the magnitude and direction of the Coulomb
force on (a) q1, (b) q2, and (c) q3. Indicate a force to
the right with a + sign and a force to the left with a −sign.
1-2. A charge of 2.63 nC is placed at the origin, and a charge of [02] nC is placed
at x = 1.57 m. Locate the point between the two charges at which a charge of 3.38 nC
should be placed so that the net electric force on it is zero. (Give the value of x for that
point.)
1-3. An alpha particle (charge = +2e) is sent at high speed toward a gold nucleus
(charge = +79e). What is the electrical force acting on the alpha particle when it is
[03] m from the gold nucleus?
1-4. Three point charges are aligned along
the x axis, as shown in the figure. Find
the magnitude and direction of the
electric field at the position
x = [04] m, y = 0. Indicate a
field to the right with a + sign and a
field to the left with a − sign.
1-5. In the figure, determine the distance from the charge at
the left (other than infinity) at which the total electric
field is zero. In the figure, d = [05] m.
1-6. Three charges are arranged as shown in the figure. Find the
(a) magnitude and (b) direction (angle with the x axis) of the
electrostatic force on the 6.00-nC charge. In the figure,
q = [06] nC.
1-7. An electron with a speed of 3.19× 106 m/s moves into a uniform electric field of
[07] N/C. The field is parallel to the electron’s motion. How far does the
electron travel before it is brought to rest?
2-1. The difference in potential between the accelerating plates of a television set is 25200 V.
If the distance between these plates is [01] cm, find the magnitude of the
uniform electric field in this region.
2-2. An electron moves from one plate to another across which there is a potential difference
of [02] V. (a) Find the speed with which the electron strikes the positive
plate. (b) Repeat part (a) for a proton moving from the positive to the negative plate.
2-3. Two point charges are on the y axis. One charge of 3.18 nC is at the origin and a second
charge of 6.35 nC is at the point y = 29.2 cm. Calculate the potential at
y = [03] cm.
2-4. Find the electric potential at the upper right corner
(the corner without a charge) of the rectangle in the
figure if the width w of the rectangle is
[04] cm.
2-5. A parallel-plate capacitor has an area of 2.74 cm2, and the plates are separated by
[05] mm with air between them. How much charge does this capacitor store
when connected to a 6.00-V battery?
2-6. (a) Find the equivalent capacitance of the group of
capacitors in the figure if C = [06] µF. (b) Find
the potential difference across the 2.35 µF capacitor.
(c) Find the charge on the 2.35 µF capacitor.
2-7. A parallel-plate capacitor has 2.46-cm2 plates that are separated by [07] mm
with air between them. If a 12.0-V battery is connected to this capacitor, how much
energy does it store?
3-1. If a current of [01] mA exists in a metal wire, how many electrons flow past a
given cross section of the wire in 10.0 min?
3-2. If [02] kg of gold is deposited on the negative electrode of an electrolytic cell
in a period of 2.78 h, what is the current through the cell in this period? Assume that
the gold ions carry one elementary unit of positive charge.
3-3. A 283-km-long high-voltage transmission line 2.58 cm in diameter carries a steady current
of [03] A. If the conductor is copper with a free-charge density of 8.53× 1028
electrons/m3, how long does it take one electron to travel the full length of the cable?
3-4. A high-voltage transmission-line with a resistance of [04] Ω/km carries
1460 A, starting at 701 kV for a distance of 168 km. (a) What is the power loss due to
resistance in the line? (b) What percentage of the initial power does this loss represent?
3-5. An 18.3-Ω resistor and a [05] -Ω resistor are connected in series across an
18.0-V battery. Find (a) the current and (b) the voltage drop across the 18.3-Ω resistor.
3-6. Find the equivalent resistance of the circuit in the figure
if R = [06] Ω.
3-7. Extra credit activity: Connecting a light bulb to a battery. For this activity, you will
need (1) a 1.5-V battery (the kind which is in a flashlight or TV remote control), (2) a
small lightbulb (handed out in class, or, if you didn’t get one in class, remove one from a
flashlight), and (3) a wire about 6 inches long (or anything metallic, such as a paper clip
or strip of aluminum foil). Connect these three items together so that the lightbulb turns
on. When you submit your homework answers, select “yes” if you were able to turn on
the light bulb and select “no” if not. You must make this selection on the first try to
receive credit.
4-1. An uncharged capacitor and a resistor are connected in series to a source of emf. If
E = 9.00 V, C = [01] µF, and R = 127 Ω, find (a) the time constant of the
circuit, (b) the maximum charge on the capacitor, and (c) the charge on the capacitor
after one time constant.
4-2. A heating element in a stove is designed to dissipate [02] W when connected
to 240 V. (a) Assuming that the resistance is constant, calculate the current in this
element if it is connected to 120 V. (b) Calculate the power it dissipates at this voltage.
4-3. Find the equivalent resistance between points a and b
in the figure if R = [03] Ω.
4-4. Find the values of (a) I1, (b) I2, and (c) I3 for the
circuit in the figure if R = [04] Ω. The
algebra in this problem is challenging. Apply the loop
rule to the outer loop first and then to the left loop.
4-5. For the circuit in the figure, where
R = [05] Ω, calculate (a) the
equivalent resistance of the circuit and (b) the
power dissipated by the entire circuit. (c) Find
the current in the resistor R.
4-6. The figure shows a circuit diagram. If
R = [06] Ω, determine (a) the current,
(b) the potential of wire A relative to ground, and
(c) the voltage drop across the 1530-Ω resistor.
4-7. (Extra credit) Find (a) the equivalent resistance
of the circuit in the figure
(R = [07] Ω) and (b) the current I5.
5-1. Sodium ions (Na+) move at 0.851 m/s through a blood-stream in the arm of a person
standing near a large magnet. The magnetic field has a strength of [01] T and
makes an angle of 90 with the motion of the sodium ions. The arm contains 127 cm3 of
blood with 2.84× 1020 Na+ ions/cm3. If no other ions were present in the arm, what
would be the magnetic force on the arm? The charge of a sodium ion is equal to the
elementary charge e.
5-2. A proton travels with a speed of [02] m/s at an angle of 37 with the
direction of a magnetic field of 0.30 T in the +y direction. What are (a) the magnitude
of the magnetic force on the proton and (b) the proton’s acceleration?
5-3. A current I = 15 A is directed along the positive x axis and perpendicularly to a
magnetic field. The conductor experiences a magnetic force per unit length of
[03] N/m in the negative y direction. Calculate the (a) magnitude and
(b) direction of the magnetic field in the region through which the current passes.
5-4. A thin, horizontal copper rod is 1.29 m long and has a mass of 52.6 g. What is the
minimum current in the rod that can cause it to float in a horizontal magnetic field of
[04] T?
5-5. Two species of singly charged positive ions of masses 20.0× 10−27 kg and 23.4× 10−27 kg
enter a magnetic field at the same location with a speed of 1.12× 105 m/s. If the
strength of the field is [05] T, and the ions move perpendicularly to the field,
find their distance of separation after they complete one half of their circular path.
5-6. A 2.53-µC charged particle with a kinetic energy of 0.0929 J is fired into a uniform
magnetic field of magnitude 0.147 T. If the particle moves in a circular path of radius
[06] m, determine its mass.
5-7. At what distance from a long, straight wire carrying a current of [07] A is
the magnetic field due to the wire equal to the strength of the Earth’s field,
approximately 5.0× 10−5 T?
5-8. Two long parallel conductors are carrying currents in
the same direction, as in the figure. Conductor A
carries a current of 151 A and is held firmly in position;
conductor B carries current IB and is allowed to slide
freely up and down (parallel to A) between a set of
nonconducting guides. If the linear mass density of
conductor B is 0.138 g/cm, what value of current IB
will result in equilibrium when the distance between the
two conductors is [08] cm? Hint: Consider a
length L of these wires. At the end of the calculation,
L will cancel out and the answer will not depend on L.
6-1. A solenoid 4.29 cm in diameter and [01] cm long has 250 turns and carries a
current of 15.7 A. Calculate the magnetic field through the circular cross-sectional area of
the solenoid.
6-2. A circular loop of radius [02] cm is placed in an external magnetic field of
strength 0.246 T so that the plane of the loop is perpendicular to the field. The loop is
pulled out of the field in 0.308 s. Find the average induced emf during this interval.
6-3. A wire loop of radius 0.374 m lies so that an external magnetic field of strength +0.360 T
is perpendicular to the loop. The field changes to −0.218 T in [03] s. (The
plus and minus signs here refer to opposite directions through the loop.) Find the
magnitude of the average induced emf in the loop during this time.
6-4. A circular coil, enclosing an area of 113 cm2, is made of 200 turns of copper wire. The
wire making up the coil has a resistance of [04] Ω and the ends of the wire are
connected to form a closed loop. Initially, a 1.15 T uniform magnetic field points
perpendicularly upward through the plane of the coil. The direction of the field then
reverses so that the final magnetic field has a magnitude of 1.15 T and points downward
through the coil. If the time required for the field to reverse directions is 0.129 s, what
average current flows through the coil during this time?
6-5. Consider the arrangement shown in the figure.
Assume that R = 6.39 Ω and ` = 1.22 m, and that a
uniform [05] -T magnetic field is directed
into the page. At what speed should the bar be moved
to produce a current of 0.576 A in the resistor?
6-6. When the current in the long, straight wire in the figure
decreases rapidly to zero, a current is induced in the loop.
Which direction will this induced current flow through the
resistor? Answer to the right or to the left.
6-7. A solenoid of radius 2.52 cm has [06] turns and a length of 19.2 cm. Find
(a) its inductance and (b) the magnitude of the rate at which current must change
through it to produce an emf of 75.7 mV.
6-8. The switch in a series RL circuit in which R = [07] Ω, L = 3.31 H, and
E = 24.7 V is closed at t = 0. (a) What is the maximum current in the circuit? (b) What
is the current when t = τ = L/R?
7-1. A [01] -µF capacitor is connected across an alternating voltage with an rms
value of 9.28 V. The rms current in the capacitor is 25.2 mA. (a) What is the source
frequency? (b) If the capacitor is replaced by an ideal coil with an inductance of 0.167 H,
what is the rms current in the coil?
7-2. An RLC circuit is used to tune a radio to an FM station broadcasting at
[02] MHz. The resistance in the circuit is 11.8 Ω and the capacitance is
1.39 pF. What inductance should be placed in the circuit?
7-3. A series circuit contains a 3.17-H inductor, a [03] -µF capacitor, and a 28.7-Ω
resistor connected to a 115-V rms source of variable frequency. Find the power delivered
to the circuit when the frequency of the source is (a) the resonance frequency and (b) one
half the resonance frequency.
7-4. An ac power generator produces 45.2 A (rms) at 3630 V (rms). The voltage is stepped up
to [04] V (rms) by an ideal transformer, and the energy is transmitted
through a long-distance power line that has a resistance of 113 Ω. What percentage of
the power delivered by the generator is dissipated as heat in the power line?
7-5. What is the wavelength of (a) an AM radio station broadcasting at [05] kHz
and (b) an FM radio station broadcasting at [06] MHz?
7-6. (a) What capacitance will resonate with a one-turn loop of inductance 436 pH to give a
radar wave of wavelength [07] cm? (b) If the capacitor has square parallel
plates separated by 1.17 mm of air, what should the edge length of the plates be?
7-7. (Extra credit) An ac source with an rms voltage of
115 V and f = [08] Hz is connected
between points a and d in the figure. Calculate the
rms voltages between the points (a) a and b,
(b) b and c, (c) c and d, (d) b and d.
8-1. A flashlight on the bottom of a 4.17-m-deep swimming pool sends a ray upward and at
an angle so that the ray strikes the surface of the water [01] m from the point
directly above the flashlight. What angle (in air) does the emerging ray make with the
water’s surface? Use n = 1.333 for the index of refraction of water. Be careful: The
problem asks for the angle with the water’s surface. This is not the angle in Snell’s law.
8-2. A cylindrical cistern, constructed below ground level, is 2.78 m in diameter and 1.88 m
deep and is filled to the brim with a liquid whose index of refraction is [02] . A
small object rests on the bottom of the cistern at its center. How far from the edge of the
cistern can a girl whose eyes are 1.21 m from the ground stand and still see the object?
8-3. Two light pulses are emitted simultaneously from a source. The pulses take parallel paths
to a detector [03] m away, but one moves through air and the other through a
block of ice. Determine the difference in the pulses’ times of arrival at the detector.
8-4. A jewel thief hides a diamond by placing it on the
bottom of a public swimming pool. He places a
circular raft on the surface of the water directly
above and centered on the diamond, as shown in the
figure. If the surface of the water is calm and the
pool is h = [04] m deep, find the
minimum diameter d of the raft that would prevent
the diamond from being seen.
8-5. A transformer on a pole near a factory steps the voltage down from 3600 V to 120 V.
The transformer, which is 91.7% efficient, is to deliver [05] kW to the factory.
Find (a) the power delivered to the primary, (b) the current in the primary, and (c) the
current in the secondary.
8-6. The light beam in the figure strikes surface 2 at the critical
angle θ = [06] . Determine the angle of
incidence θi.
8-7. A plastic light pipe has an index of refraction of [07] . For total internal
reflection, what is the maximum angle of incidence to the wall of the pipe if the pipe is in
(a) air? (b) water? Be careful: The problem asks for the angle with the wall of the pipe.
This is not the angle in Snell’s law. Use n = 1.333 for the index of refraction of water.
9-1. A convex mirror has a focal length of [01] cm. (a) Determine the object’s
location for which the image will be one half as tall as the object. (b) Draw a ray
diagram on the next sheet in this packet and turn it into the homework bins.
9-2. A 2.31-cm-high object is placed 3.12 cm in front of a concave mirror. (a) If the image is
[02] cm high and virtual, what is the focal length of the mirror? (b) Draw a
ray diagram on the next sheet in this packet and turn it into the homework bins.
9-3. The nickel’s image in the figure has twice the diameter of the
nickel when the lens is [03] cm from the nickel.
(a) Determine the focal length of the lens. (b) Draw a ray
diagram on the next sheet in this packet and turn it into the
homework bins.
Physics 106 Identification numberHomework Set 9
Score: out of 6 points
Do the following homework problems on this sheet of paper and submit it through thePhysics 106 slots outside N357 ESC. This part of the assignment is due at class time onthe same day that the rest of the assignment is due. Late papers will receive half credit.
For each problem, draw a ray diagram to find the location and size of the image.(Construct three rays.) Use solid lines for the actual paths of the rays of light. Usedashed lines for all other lines drawn to guide the eye. Draw the image. Do your workaccurately and neatly, using a ruler.
9-1 (b). In the figure below, a convex mirror is shown. Indicate the position of the focalpoint on the diagram (each division on the diagram represents 1 cm). From the answeryou obtained in part (a), draw the object on the diagram. (It should be on the left sideof the mirror.) Represent the object as an arrow about 2 CM LONG . Then draw theray diagram and the image.
9-2 (b). In the figure below, a concave mirror and an object (represented as an arrow)are shown. From the answer you obtained in part (a), indicate the position of the focalpoint on the diagram (each division on the diagram represents 1 cm). Then draw the raydiagram and the image.
O
9-3 (b). A lens is shown in the figure below. From the data for the problem, draw theobject on the diagram (each division on the diagram represents 1 cm). Represent theobject as an arrow about 1.5 CM LONG and draw it on the left side of the lens. Fromthe answer you obtained in part (a), indicate the position of the focal points on thediagram. Then draw the ray diagram and the image.
9-4. We want to form an image 29.2 cm in front of a diverging lens with a focal length of
[04] cm. (The image is on the same side of the lens as the object.) (a) Where
must we place the object? (Give the distance between the object and the lens.)
(b) Determine the magnification.
9-5. The distance between an object and its upright image is 20.0 cm. If the magnification is
[05] , what is the focal length of the lens being used to form the image?
9-6. An object’s distance from a converging lens is [06] times the focal length. How
far is the image from the focal point? Express the answer as a fraction of the focal length.
10-1. Assume that a camera has a fixed focal length of 65.0 mm and is adjusted to properly
focus the image of a distant object. (a) How far and (b) in what direction must the lens
be moved to focus the image of an object that is [01] m away?
10-2. A retired bank president can easily read the fine print of the financial page when the
newspaper is held [02] cm from the eye. What should be the focal length of
an eyeglass lens that will allow her to read at the more comfortable distance of 24 cm?
10-3. An individual is nearsighted; his near point is 13.5 cm and his far point is
[03] cm. (a) What lens power is needed to correct his nearsightedness?
(b) When the lenses are in use, what is this person’s near point?
10-4. A lens having a focal length of [04] cm is used as a simple magnifier.
(a) What is the angular magnification obtained when the image is formed at the normal
near point (q = −25.0 cm)? (b) What is the angular magnification produced by this lens
when the eye is relaxed (image formed at infinity)?
10-5. The length of a microscope tube is 15.0 cm. The focal length of the objective is 1.00 cm,
and the focal length of the eyepiece is [05] cm. What is the magnification of
the microscope, assuming it is adjusted so that the eye is relaxed? Caution: Do not use
the approximate expression in Eq. [25.7]. Determine the values of p1 and q1 and calculate
the lateral magnification exactly, using M1 = −q1/p1.
10-6. An elderly sailor is shipwrecked on a desert island but manages to save his eyeglasses.
The lens for one eye has a power of +1.24 diopters, and the other lens has a power of
+[06] diopters. (a) what is the magnifying power of the telescope he can
construct with these lenses? (b) How far apart are the lenses when the telescope is
adjusted so that the eye is relaxed?
10-7. (Extra credit) The full Moon is photographed using a camera with a [07] -mm
focal length lens. Determine the diameter of the Moon’s image on the film. (Note: The
diameter of the Moon is 3.48× 106 m, and the Earth-Moon distance is 3.84× 108 m.)
10-8. (Extra credit) A laboratory (astronomical) telescope is used to view a scale that is 300
cm from the objective, which has a focal length of [08] cm. The eyepiece has
a focal length of 2.00 cm. Calculate the angular magnification when the telescope is
adjusted so that the eye is relaxed. (Note: The object is not at infinity, and so the simple
expression m = fo/fe is not sufficiently accurate for this problem. As in Fig. 25.8 in the
textbook, measure the angular size θ0 of the object from the position of the objective
lens.)
11-1. If the distance between two slits is [01] mm and the distance to a screen is
2.53 m, find the spacing between the first- and second-order bright fringes for yellow light
of 615 nm.
11-2. A Young’s interference experiment is performed with blue-green laser light. The
separation between the slits is [02] mm, and the interference pattern on a
screen 3.31 m away shows the first maximum 3.45 mm from the center of the pattern.
What is the wavelength of the laser light?
11-3. A light source emits two major spectral lines, an orange line of wavelength
[03] nm and a blue-green line of wavelength 478 nm. If the spectrum is
resolved by a diffraction grating having 5000 lines/cm and viewed on a screen 2.12 m
from the grating, what is the distance between the two spectral lines in the second-order
spectrum? Caution: Do not use the “small-angle approximation”.
11-4. A thin layer of liquid methylene iodide (n = 1.756) is sandwiched between two flat
parallel plates of glass (n = 1.518). What would be the minimum thickness of the liquid
layer if normally incident light with λ = [04] nm in air is to be strongly
reflected?
11-5. A thin layer of oil (n = 1.252) is floating on water. What is the minimum thickness of the
oil in the region that strongly reflects light with a wavelength of
[05] nm (in air)? Use n = 1.333 for the index of refraction of water. Be
careful about using Eqs. [24.9] and [24.10] in the textbook. Read the paragraph following
Eq. [24.10].
11-6. A light beam is incident on some transparent material (n = [06] ) at the
polarizing angle. Calculate the angle of refraction for the transmitted ray.
11-7. Two motorcycles, separated laterally by 2.3 m, are approaching an observer holding an
infrared detector that is sensitive to radiation of wavelength 885 nm. What aperture
diameter is required in the detector if the two headlights are to be resolved at a distance
of [07] km?
11-8. A spy satellite circles the Earth at an altitude of 212 km and carries out surveillance with
a special high-resolution telescopic camera having a lens diameter of [08] cm.
If the angular resolution of this camera is limited by diffraction, estimate the separation
of two small objects on the Earth’s surface that are just resolved in yellow-green light
(λ = 550 nm).
11-9. Light of wavelength [09] nm falls on a 0.427-mm-wide slit and forms a
diffraction pattern on a screen 1.46 m away. Find the distance on the screen from the
central maximum to the first dark band on either side of it.
11-10. Light of wavelength 587.5 nm illuminates a single [10] -mm-wide slit. At what
distance from the slit should a screen be placed if the first minimum in the diffraction
pattern is to be 0.851 mm from the central maximum?
11-11. (Extra credit) A diffraction grating is calibrated by using the 546.1-nm line of mercury
vapor. It is found that the first-order line is at an angle of [11] . Calculate
the number of lines/mm on this grating.
12-1. The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime)
is 26 ns. If the meson moves with a speed of [01] c, what is (a) its mean
lifetime as measured by an observer on Earth and (b) the average distance it travels
before decaying as measured by an observer on Earth? (c) What distance would it travel
if time dilation did not occur?
12-2. If astronauts could travel at v = [02] c, we on Earth would say it takes about
four years to reach Alpha Centauri, 4.21 lightyears away. The astronauts disagree.
(a) How much time passes on the astronaut’s clocks? (b) What is the distance to Alpha
Centauri as measured by the astronauts? Caution: Do not use four years as the time
interval measured on Earth. That is only approximate.
12-3. A friend in a spaceship travels past you at a high speed. He tells you that his ship is
20.23 m long and that the identical ship you are sitting in is [03] m long.
According to your observations, (a) how long is your ship, (b) how long is his ship, and
(c) what is the speed of your friend’s ship?
12-4. Observer A measures the length of two rods, one stationary, the other moving with a
speed of [04] c. She finds that the rods have the same length. A second
observer B travels along with the moving rod. What is the ratio of the length of A’s rod
to the length of B’s rod according to observer B? Caution: The two rods do not have the
same proper length. They have the same length only when B’s rod is moving and A’s rod
is at rest.
12-5. An electron moves to the right with a speed of 0.902c relative to the laboratory frame. A
proton moves to the left with a speed of [05] c relative to the electron. Find
the speed of the proton relative to the laboratory frame.
12-6. A space vehicle is moving at a speed of 0.754c with respect to an external observer. An
atomic particle is projected at [06] c in the same direction as the spaceship’s
velocity with respect to an observer inside the vehicle. What is the speed of the
projectile as seen by the external observer?
12-7. An unstable particle at rest breaks up into two fragments of unequal mass. The mass of
the lighter fragment is 2.50× 10−28 kg, and that of the heavier fragment is
1.67× 10−27 kg. If the lighter fragment has a speed of [07] c after the breakup,
what is the speed of the heavier fragment? Hint: Use conservation of relativistic
momentum. Since the initial momentum is zero (before the particle breaks up), the
momentum of the heavier fragment must be equal in magnitude and opposite in direction
to the momentum of the lighter fragment.
12-8. (Extra credit) Spaceship I, which contains students taking a physics exam, approaches
Earth with a speed of 0.658c, while spaceship II, which contains an instructor proctoring
the exam, moves away from Earth at [08] c as in the figure. If the instructor in
spaceship II stops the exam after 50.00 min have passed on his clock, how long does the
exam last as measured by the students? (This is simply the time dilation of the
instructor’s clock in the students’ reference frame.)
13-1. A proton moves with a speed of [01] c. Calculate its (a) kinetic energy and
(b) total energy.
13-2. A mass of [02] kg is converted completely into energy of other forms. (a) How
much energy of other forms is produced and (b) how long would this much energy keep a
100-W light bulb burning?
13-3. In a color television tube, electrons are accelerated through a potential difference of
[03] V. With what speed do the electrons strike the screen?
13-4. A quantum of electromagnetic radiation has an energy of [04] keV. What is
its wavelength?
13-5. The threshold of dark-adapted (scotopic) vision is 4.0× 10−11 W/m2 at a central
wavelength of 500 nm. If light with this intensity and wavelength enters the eye when the
pupil is open to a diameter of [05] mm, how many photons/s enter the eye?
13-6. Electrons are ejected from a metallic surface with speeds ranging up to
[06] m/s when light with a wavelength of λ = 625 nm is used. (a) What
is the the work function of the surface? (b) What is the cutoff frequency for this surface?
13-7. A monoenergetic beam of electrons is incident on a single slit of width
[07] nm. A diffraction pattern is formed on a screen 23.6 cm from the slit. If
the distance between successive minima of the diffraction pattern is 2.18 cm, what is the
kinetic energy of the incident electrons? Note: “Successive minima” means, for example,
the minima at m = 1 and m = 2 (see Eq. [24.11] in the textbook). Hint: you may use the
small-angle approximation: sin θ ≈ tan θ ≈ θ (θ in radians). Also, you may use 12mv2 for
the kinetic energy of the electron.
13-8. (Extra credit) Calculate the de Broglie wavelength of a proton moving (a) at
[08] m/s and (b) at [09] m/s. Note that in part (b) the
velocity is relativistic. You must use the relativistic momentum in calculating the de
Broglie wavelength.
13-9. (Extra credit) Determine the energy required to accelerate an electron from 0.500c to
[10] c.
14-1. The half-life of an isotope of phosphorus is 14.2 days. If a sample contains
[01] such nuclei, determine its activity.
14-2. A radioactive sample contains [02] µg of pure 116 C, which has a half-life of
20.4 min. (a) How many moles of 116 C are present initially? (The atomic mass of 11
6 C is in
Appendix B of the textbook.) (b) Determine the number of nuclei present initially. What
is the activity of the sample (c) initially and (d) after 8.23 h?
14-3. Suppose that you start with 1.000 mg of a pure radioactive substance and 2.09 h later
determine that only [03] mg of the substance remains. What is the half-life of
this substance?
14-4. Radon gas has a half-life of 3.83 days. If 3.23 g of radon gas is present at time t = 0,
what mass of radon will remain after [04] days have passed?
14-5. Identify X (chemical symbol and mass number) in each of the following decays:
(a) 125 B→ X + e− + ν
(b) 23490 Th→ 230
88 Ra + X
(c) X → 147 N + e− + ν
Type the chemical symbol followed by the mass number (no spaces). For example Na23,
not Na 23 or na23 or NA23.
14-6. What mass of 23592 U must undergo fission to operate a 1000-MW power plant for one day
if the conversion efficiency is [05] %? (Assume 208 MeV released per fission
event.)
Answers to Homework Problems, Physics 106, Winter Semester, 2007Sec. 2, Stephanie Magleby
1-1a. −10.0, −70.0 N1-1b. 60.0, 140.0 N1-1c. −50.0, −80.0 N1-2. 0.650, 0.770 m1-3. 30, 100 N1-4. 8.0, 30.0 N/C1-5. 1.40, 2.20 m1-6a. 3.50× 10−7, 5.00× 10−7 N1-6b. −10.0, −20.0
1-7. 1.00, 3.00 cm2-1. 1.20× 106, 2.60× 106 N/C2-2a. 2.30× 107, 3.30× 107 m/s2-2b. 5.00× 105, 8.00× 105 m/s2-3. 600, 900 V2-4. 2.50, 3.20 MV2-5. 5.50, 10.00 pC2-6a. 1.80, 2.40 µF2-6b. 3.60, 4.50 V2-6c. 8.50, 11.00 µC2-7. 2.60× 10−11, 5.30× 10−11 J3-1. 2.20× 1020, 3.40× 1020
3-2. 0.100, 0.300 A3-3. 70, 110 years3-4a. 70.0, 150.0 MW3-4b. 7.0, 14.0 %3-5a. 0.550, 0.650 A3-5b. 10.2, 11.6 V3-6. 15.40, 15.90 Ω4-1a. 1.90, 3.20 ms4-1b. 130, 230 µC4-1c. 80, 150 µC4-2a. 5.20, 7.30 A4-2b. 620, 880 W4-3. 7.60, 7.80 Ω4-4a. −0.100, +0.200 A4-4b. 0.350, 0.800 A4-4c. 0.450, 0.600 A4-5a. 10.0, 20.0 Ω4-5b. 40, 70 W4-5c. 1.50, 2.50 A4-6a. 2.90, 3.30 mA4-6b. −18.0, −20.0 V
4-6c. 4.5, 5.0 V4-7a. 10.0, 20.0 Ω4-7b. 0.150, 0.250 A5-1. 700, 1200 ±10 N5-2a. 2.0× 10−14, 9.0× 10−14 N5-2b. 1.0× 1013, 6.0× 1013 m/s2
5-3a. 2.0× 10−3, 8.0× 10−3 T5-4. 0.100, 0.500 A5-5. 2.00, 5.00 cm5-6. 4.50× 10−12, 9.50× 10−12 kg5-7. 1.0, 6.0 cm5-8. 40.0, 120.0 A6-1. 0.0180, 0.0330 T6-2. 25.0, 110.0 mV6-3. 120, 260 mV6-4. 2.60, 8.10 A6-5. 1.00, 1.60 m/s6-7a. 1.00, 3.30 mH6-7b. 23.0, 65.0 A/s6-8a. 3.50, 5.00 A6-8b. 2.00, 3.50 A7-1a. 140, 220 Hz7-1b. 40.0, 62.0 mA7-2. 1.80, 3.80 µH7-3a. 450, 470 W7-3b. 0.100, 0.220 W7-4. 0.040, 0.200 %7-5a. 180, 560 m7-5b. 2.70, 3.50 m7-6a. 0.40, 0.80 pF7-6b. 7.0, 11.0 mm7-7a. 70, 120 V7-7b. 140, 160 V7-7c. 60, 130 V7-7d. 20, 90 V8-1. 22.0, 55.0
8-2. 1.80, 3.80 m8-3. 4.00, 8.00 ns8-4. 3.00, 5.00 m8-5a. 1000, 2500± 10 kW8-5b. 300, 650 A8-5c. 8000, 20000± 100 A
8-6. 20.0, 50.0
8-7a. 44.0, 52.0
8-7b. 17.0, 34.0
9-1a. 3.00, 5.00 cm9-2a. 5.00, 7.50 cm9-3a. 4.00, 6.00 cm9-4a. 70, 110 cm9-4b. 0.270, 0.4209-5. 40, 160 cm9-6. 0.100, 0.15010-1a. 1.00, 5.00 mm10-2. 40, 60 cm10-3a. −1.60, −2.50 diopters10-3b. 17.0, 21.0 cm10-4a. 2.00, 3.0010-4b. 1.00, 2.0010-5. −90, −16010-6a. 5.60, 9.7010-6b. 0.80, 1.00 m10-7. 0.40, 1.10 mm10-8. 5.0, 20.011-1. 2.50, 4.00 cm11-2. 400, 650 nm11-3. 24.0, 66.0 cm11-4. 70.0, 100.0 nm11-5. 200, 240 nm11-6. 30.0, 33.0
11-7. 2.3, 7.0 mm11-8. 20, 95 cm11-9. 1.70, 2.40 mm11-10. 0.80, 1.30 m11-11. 470, 780 lines/mm12-1a. 100, 160 ns12-1b. 30.0, 45.0 m12-1c. 7.0, 8.0 m12-2a. 1.00, 1.60 years12-2b. 1.00, 1.50 light years12-3a. 20.00, 21.00 m12-3b. 18.00, 19.00 m12-3c. 0.34, 0.46c12-4. 0.050, 0.12012-5. 0.20, 0.60c
12-6. 0.970, 0.999c12-7. 0.230, 0.360c12-8. 54.00, 58.00 min13-1a. 1600, 3000 ±10 MeV13-1b. 2500, 4000 ±10 MeV13-2a. 1.8× 1016, 6.3× 1016 J13-2b. 5.0, 20.0 million years13-3. 0.230, 0.310c13-4. 0.50, 1.00 nm13-5. 4400, 6400 ±100 photons/s13-6a. 1.40, 1.90 eV13-6b. 3.40× 1014, 4.60× 1014 Hz13-7. 450, 1200± 10 eV13-8a. 1.50× 10−11, 2.70× 10−11 m13-8b. 0.80× 10−15, 2.30× 10−15 m13-9. 0.120, 0.270 MeV14-1. 0.30, 0.70 Ci14-2a. 2.20× 10−7, 4.10× 10−7 mol14-2b. 1.30× 1017, 2.50× 1017
14-2c. 7.0× 1013, 14.0× 1013 Bq14-2d. 4.0× 106, 8.0× 106 Bq14-3. 0.90, 1.20 h14-4. 1.80, 2.40 g14-6. 2.5, 4.5 kg