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