Physics 123 Homework Problems, Spring 2010

Physics 123HW #1, Due Fri, Apr 30

Follow the instructions printed in the syllabus. Review sections 14.1–14.3 of the text.

1-1. In 1983, the United States began making pennies using copper-clad zinc rather than pure

copper. The new and old coins have the same volume. If the mass of the old copper

penny is 3.083 g while that of the new penny is 2.517 g, calculate the percent of zinc (by

volume) in the new penny. The density of copper is 8.960 g/cm3, and that of zinc is

7.133 g/cm3.

1-2. What must be the contact area between a suction cup with [01] atm inside

and the ceiling in order to support a 127-lb student? Please note the handy conversion

table inside the back cover of your textbook.

1-3. If a certain nuclear weapon explodes at ground level, the peak over-pressure (that is, the

pressure increase above normal atmospheric pressure) is [02] atm at a

distance of 6.0 km. What force due to such an explosion will be exerted on the side of a

house with dimensions 4.5 m× 22 m? Give the answer in tons (1 ton = 2000 lb).

1-4. (a) What is the height of a fluid column in a barometer that uses water as its fluid in

[03] atm of air pressure? The density of water is 1000 kg/m3. Neglect the

vapor pressure above the column. Use g = 9.80 m/s2.

(b) What is the height if the fluid is mercury? The specific gravity (ratio of density to

that of water) of mercury is 13.6.

1-5. In a pressure test chamber, a person starts acting strange when the gauge pressure

exceeds [04] lb/in2. (Gauge pressure is the pressure in excess of atmospheric

pressure.) This is a well-known effect that limits the depth at which scuba divers should

breathe pure air. In sea water, which has a density of 1.03 g/cm3, to what depth should

a diver be limited?

In-Class Quiz• Read section 14.4 of edition 6 of the text. If you have edition 5, see alternative readingschedule at course website.• A large ice cube floats in a glass of water. The glass is filled with water to the brim, andthe ice cube protrudes well above the top of the glass. As the ice melts, the water levelA. goes down.B. remains unchanged.C. goes up and therefore spills out of the glass.

Physics 123HW #2, Due Fri, Apr 30

2-1. A geological sample weighs 10.3 lb in air and [01] lb under water. What is its

density in g/cm3?

2-2. A balloon is filled with [02] m3 of helium.

(a) How big a payload can the balloon lift? Include the balloon structure itself in the

payload (not including the helium). The density of air is 1.29 kg/m3, and the density of

helium is 0.18 kg/m3.

(b) How much additional mass can be lifted if the gas is changed to hydrogen? The

density of hydrogen is 0.09 kg/m3.

2-3. When a large beaker filled with water is placed on a scale, it reads 31.9 N. A

[03] kg mass of aluminum (density 2.70 g/cm3) is suspended on a string and

completely submerged in the water without touching the sides or bottom of the beaker.

(a) What is the new reading on the scale?

(b) What is the change in tension in the string as the aluminum is lowered into the

water? Be sure to include a minus sign in the answer if the change is negative (i.e., if the

final tension is less than the initial tension).

2-4. A block of wood with density 0.615 g/cm3 floats in water with only [04] % of

its volume above the surface because an aluminum mass is attached to its top side. Find

the percentage of the wood submerged when the block turns over so that the aluminum

is completely submerged. The density of aluminum is 2.70 g/cm3.

In-Class Quiz• Read sections 14.5–14.6.• A fluid moves faster as it passes through a narrowed section of a pipe. The pressure inthis section of pipe isA. lower.B. the same.C. higher.

Physics 123HW #3, Due Mon, May 3

3-1. What gauge pressure must a pump generate to get a jet of water to leave its nozzle with

a speed of 5.2 m/s at a height of [01] m above the pump? Assume that the

area of the nozzle is very small compared to that of the pipe near the pump.

3-2. Your parents’ basement (floor area 126 m2) has been flooded to a depth of 10 cm. You

have a garden hose with a diameter of 2 cm and you use it to siphon the water to a part

of the yard that is [02] m below the basement floor. How long will it take to

empty the basement? Neglect the pressure due to the 10-cm depth in the basement.

3-3. Water is pumped from the Colorado River to Grand Canyon Village through a

15.0-cm-diameter pipe. The river is at 564 m elevation, and the village is at 2096 m.

[03] m3 of water is pumped per day at a constant flow rate.

(a) What is the gauge pressure in the pipe near the pump assuming zero pressure at the

top as the water flows into a tank?

(b) What is the power delivered by the pump? HINT: Neglect the power necessary to

establish the kinetic energy of the water flow since it is small compared to the power

required to lift the water.

3-4. Examine the figure shown. A pilot tube is a device

used to determine the velocity of airflow (density

1.25 kg/m3) by measuring the difference in pressure

between two holes on the tube, one exposed to air

which comes to rest with respect to the tube (point A)

and the other exposed to air rushing past (the hole on

the top). The two holes are connected only through a

U-tube filled with mercury (density 13.6 g/cm3). A

difference in pressure causes the mercury column on

either side of the U-tube to be different in height by

∆h =[04] cm. Find the speed of the airflow.

In-Class Quiz• Skim chapter 16 and study sections 16.2, 16.5. Also note Eq. 16.18.• A sinusoidal wave is generated by continuously wiggling up and down one end of a longhorizontal cord. Energy is transported from the wiggled end to the far end where it isabsorbed completely. The amplitude of oscillations is doubled at the same frequency andtension.A. Transmitted power remains unchanged.B. Transmitted power doubles.C. Transmitted power quadruples.

Physics 123HW #4, Due Mon, May 3

4-1. A wave has the form, y(x, t) = A sin(kx− ωt− φ), where A = 10.0 cm,

k =[01] cm−1, ω =[02] s−1, and φ = 1.00 rad.

(a) What is the amplitude?

(b) What is the wavelength?

(c) What is the period?

(d) What is the magnitude of the velocity?

(e) What is the direction of the velocity?

(f) Draw y(x) at time zero and at a time one period later on the same graph. Do not

turn in this part, but be ready to refer to your drawing during an in-class quiz.

4-2. At position x = 0, a water wave varies in time as shown in the figure. (The curve is at

the 10-cm mark at both edges of the figure.) If the wave moves in the positive x direction

with a speed of [03] cm/s, write the equation for the wave in the form,

y(x, t) = A sin(kx− ωt− φ).

Give the values of (a) A, (b) ω, (c) k, and (d) φ. (Give the value of φ between 0 and 2π

rad.) HINT: When taking an inverse sine to find φ, you must be careful to use the right

quadrant. Your calculator by default will use the 1st and 4th quadrants. Check your

final answer to make sure that it actually fits the curve everywhere. To change

quadrants, use sin−1 x→ π − sin−1 x.

4-3. A 25.8-ft piece of elastic tubing weighs [04] lb and is stretched with a tension

of 18.6 lb. What is the speed (in ft/s) of a wave on the stretched tubing?

4-4. Transverse waves are being generated on a rope. By what factor does the required power

change (i.e., increases when the factor is greater than 1) if

(a) the wavelength is doubled at constant frequency?

(b) the frequency is doubled at constant tension?

(c) the amplitude is doubled and the tension is halved at constant frequency?

In-Class Quiz• Read sections 17.1–17.3.• The distance from a sound source is tripled. The amplitude of the pressure wave willA. decrease by 9.B. decrease by 3.C. remain unchanged.

Physics 123HW #5, Due Wed, May 5

5-1. When Sir Isaac Newton first derived the speed of sound in air, the laws of

thermodynamics were not yet understood. He did not take into account heating and

cooling effects due to compression and expansion in the gas. Instead, Newton concocted

arguments involving water vapor among other things to explain why his derivation of the

speed of sound disagreed with measurement. The correct formula for the speed of sound

is√γP/ρ, where γ was the part missing from Newton’s derivation and is equal to 7/5 for

a diatomic gas such as air. You will learn about γ later in the course (Chap. 21).

Calculate the speed of sound in air when P = 1.00 atm and ρ = 1.29 kg/m3.

5-2. Use the speed of sound (v = 5010 m/s) and the density from Table 15.1 to calculate

Young’s modulus for copper. Young’s modulus describes how rigid or flexible a material

is.

5-3. The sound intensity at some rock concerts reaches the pain threshold of 120 dB. Normal

conversation has an intensity of near [01] dB. What is the ratio of the power

delivered to the ear at a very loud rock concert compared to that delivered by typical

conversation?

5-4. A source emits sound uniformly in all directions and is placed between two observers that

are 110 m apart, along the line connecting them. Observer 1 records an intensity level of

[02] dB and observer 2 records an intensity level of 83 dB.

(a) How far is observer 1 from the source?

(b) What is the total average power output from the source?

5-5. An explosive charge is detonated at a height of 4.21 km above the ground. At a distance

of [03] m from the explosion, the acoustic over-pressure reaches a maximum

of 6.10 Pa. What will be the sound level (in dB) from the explosion when it reaches the

ground? You must consider the fact that sound is absorbed in air at a rate of

approximately 7.0 dB/km. Ignore the variations in air pressure with altitude. Use

1.29 kg/m3 for the density of air and 343 m/s for the speed of sound in air.

In-Class Quiz• Read section 17.4.• A stationary observer hears a pitch from a source that moves toward him at a largefraction of the speed of sound. If instead the observer moves at the same speed towardthe source (now stationary), the observed frequency will be:A. lower than before.B. the same as before.C. higher than before.

Physics 123HW #6, Due Wed, May 5

6-1. As a vehicle approaches, you hear a pitch of [01] Hz. As it recedes after

passing, you measure a pitch of 829 Hz. You are at rest and it is a calm day. The speed

of sound is 343 m/s.

(a) What is the speed of the vehicle?

(b) What is the at-rest frequency of the sound emitter?

6-2. Two horn players in the Cougar marching band perform in a half-time show at the

stadium. Both players face the press box and attempt to play the same note for an

extended duration. One player is positioned in front of the other, and they both march

steadily at 1.00 m/s toward each other, one moving forward and the other backward.

The rear player plays a frequency of [02] Hz (in his own reference frame). The

front player plays a frequency that matches what he hears from the rear player. The

speed of sound is 343 m/s. Please give all answers to this problem to 4 significant figures.

(a) What frequency does the front player play (in his own frame of reference)?

(b) What frequency does the audience near the press box hear from the front player?

(c) What frequency does the audience near the press box hear from the rear player?

6-3. On a very quiet morning, you drop a tuning fork vibrating at 512 Hz from a tall bridge.

How long until you will hear a frequency of [03] Hz? Take the speed of sound

in air to be 343 m/s and the acceleration of gravity to be 9.80 m/s2. HINT: Don’t forget

to include the time it takes for the sound to return to the point of release.

6-4. You notice a supersonic jet flying horizontally overhead before the sonic boom arrives.

As the jet recedes from view, you judge that its position makes a [04] -degree

angle with the horizon when you finally hear the sonic boom. What is the Mach number

(i.e., the speed of the plane divided by the speed of sound)?

In-Class Quiz• Read sections 18.1, 18.2, 18.7.• Two speakers emit sound waves with identical frequency. The power emitted from eachspeaker is the same. The sound waves interfere in a region of space. Some locationsexperience destructive interference resulting in no sound. Other regions experienceconstructive interference.A. Energy is not conserved because of the missing energy in the destructive regions.B. The constructive regions have approximately double the intensity from one speakeralone.C The constructive regions have approximately four times the intensity from one speakeralone.

Physics 123HW #7, Due Fri, May 7

7-1. Two speakers emitting [01] Hz are separated by a distance of 2.0 m. A

student is positioned directly in front of the first speaker and along a path 90◦ from the

line that joins the two speakers. As she walks directly toward the first speaker she

notices minima in the sound level.

(a) How many minima does she experience if she begins from far away?

(b) How far is she from the speaker for the first minimum she encounters? Use 343 m/s

for the speed of sound.

7-2. A student holds a tuning fork oscillating at 440 Hz and walks toward a wall at constant

speed [02] m/s. She observes beats between the source and its echo

(wa-wa-wa). The speed of sound is 343 m/s.

(a) What is the beat frequency (number of wa’s heard per second)?

(b) How fast must she move away from the wall to hear a beat frequency of

[03] Hz?

HINT: If you approach the problem using the Doppler shift (both source and observer

moving), spatial interferences will be included automatically so that you can consider it

as a problem of interference in time.

7-3. While tuning a C note (523.0 Hz) on a piano string, the tuner notices a beat frequency of

[04] Hz between a reference oscillator and the string.

(a) If the string is oscillating at a frequency higher than the oscillator, what is the

frequency of the string? Please give 4 significant figures on part (a).

(b) By what percentage should the tension be changed to bring the note into tune? You

may assume that the wavelength in a piano string equals 2L, where L is the length of the

string. HINT: Be sure to include a minus sign in the answer if the tension decreases.

7-4. A wave traveling to the right has the form y = y0 sin(kx− ωt) and another wave traveling

to the left has the form y = y0 sin(kx+ ωt). The two waves are superimposed.

(a) Using trigonometric identities, show that together they form a standing wave which

can be written as y = 2y0 sin kx cosωt.

(b) Make a sketch of the standing wave for several arbitrary times superimposed on one

another. Take the amplitude y0 to be 10 cm and the wavelength to be 1 m.

Turn in this problem on paper using the 10 lower bins near our classroom. Use the

bin that corresponds to the first digit of your class ID number.

In-Class Quiz• Read sections 18.3–18.5.• A musician plays a song on an acoustic guitar. He then steps into a room filled withhelium and plays the same song.A. The frequency of the notes will be lower.B. The frequency of the notes will remain the same.C. The frequency of the notes will be higher.

Physics 123HW #8, Due Fri, May 7

8-1. A standing wave is established in a [01] -cm string fixed at both ends. The

string vibrates in four segments when driven at 120 Hz.

(a) Determine the wavelength.

(b) What is the wave velocity in the string?

8-2. A violin string has a length of 0.350 m and is tuned to concert G (392 Hz).

(a) Where must the violinist place her finger to play [02] Hz? (How far from

the nearby end of the string?)

(b) When playing this frequency, suppose that the finger is mis-positioned by one half

the finger’s width (i.e., 0.6 cm) so that the frequency played is a little lower than it

should be. What percentage change in tension (with the finger positioned correctly)

would correspond to the same error? Be sure to include a minus sign in the answer if the

tension decreases.

8-3. If an organ pipe is to resonate at [03] Hz, what is the required length if it is

(a) open at both ends?

(b) open at one end? The speed of sound in air is 343 m/s.

8-4. A piccolo has a length of [04] cm and resonates as a pipe that is open on both

ends. What is the frequency of the lowest note it can play?

8-5. By opening holes on the side of a piccolo, the pipe is effectively shortened. Suppose the

highest note a piccolo can sound is [05] Hz. What is the distance between

resonant nodes for this mode of vibration?

8-6. Suppose that your shower stall is 2.4 m tall. As you sing in the shower, which frequencies

will resonate? Consider only frequencies between 200 Hz and 1500 Hz. Ignore side-to-side

sound waves and take the shower stall to be closed at both ends. HINT: To economize

effort, set up your answer as a frequency times an integer and give ranges for the integer.

Turn this problem in on paper using the 10 lower bins near our classroom. Use the

bin that corresponds to the first digit of your class ID number.

In-Class Quiz• Read and think about each problem on Practice Exam I.• Complete at least two of the problems. (Do not turn in your work.)

Physics 123HW #9, Due Mon, May 10

9-1. A tire is filled to [01] psi (gauge pressure) on an unusually hot day in autumn

(90◦F). What will be the pressure on an unusually cold morning in December (−20◦F)?

HINT: Don’t forget to include the 14.5 psi of atmospheric pressure before computing the

change. Then convert back to gauge pressure.

9-2. The mass of a hot-air balloon and its cargo (not including the air inside) is

[02] kg. The air outside is 10.2◦C and 1.00 Atm. The volume of the balloon is

623 m3. To what temperature must the air in the balloon be heated before the balloon

will lift off? Take the density of air at 10.2◦C to be 1.25 kg/m3.

9-3. A steel guitar string with a diameter of [03] mm is stretched between

supports 80.0 cm apart when the temperature is 25.0◦C.

(a) What is the tension in the string if it is tuned to 440 Hz? The density of steel is

7860 kg/m3.

(b) The guitar is then taken outside where the temperature is [04] ◦C. At

what new frequency will the string resonate if we neglect contraction of the wood support

structure? Please give 4 significant figures.

HINT: The string obeys Hooke’s law where the change in tension is k∆L and k is the

spring constant. In terms of Young’s modulus, the spring constant is k = AY/L, where A

is the cross sectional area, and L is the length. For steel, Y = 20× 1010 N/m2.

9-4. A mercury thermometer is constructed with a spherical bulb of diameter

[05] mm connected to a capillary tube of diameter 0.040 mm. The amount of

fluid in the capillary varies with temperature as the fluid in the bulb expands or

contracts. Find the change in height of the mercury for a temperature change of 40◦C.

Neglect the expansion or contraction of the glass housing.

In-Class Quiz• Read sections 20.1–20.3.• True or False: Given two different objects, the one with the higher temperaturecontains more heat.

Physics 123HW #10, Due Wed, May 12

10-1. An overweight person who has eaten a large dessert ([01] kcal) hopes to work

it off by hiking up a mountain. At the very least, he knows that he will burn as many

calories as are associated with the increase in vertical potential energy. How high must

he hike to accomplish this if he has a mass of 90 kg? (Unfortunately, he will have to stay

at the top for fear of gaining the potential energy back. Right? Note that 1 food calorie

is a kcal.)

10-2. A 3000-lb car moving at [02] mi/h quickly comes to rest without skidding the

tires. The kinetic energy is converted into heat in each of the four 15-lb iron rotors. By

how much will the temperature rise in the rotors?

10-3. An insulated container holds 400 ml of water at 20◦C. A [03] -g sample of

silver at a temperature of 100◦C is placed into the water. What is the final temperature

if the specific heat of silver is 0.056 cal/g · ◦C?

10-4. (a) 25 g of ice at 0◦C are added to a calorimeter containing [04] ml of water

initially at 30◦C. What is the final temperature of the system?

(b) What is the final temperature if instead 250 g of ice at 0◦C are added?

In-Class Quiz• Read section 20.7. Note: In table 20.3, the entry for diamond should be 151.• Two rods of the same length and made of the same material are connected in parallelbetween a high-temperature heat reservoir and a low-temperature reservoir. One rod hastwice the diameter of the other. The cold reservoir is removed and the temperature ismonitored on the end of each rod where the cold reservoir used to be. Assume perfectinsulation everywhere except when and where connected to a reservoir. The temperatureon the end of the larger rodA. increases more slowly than the temperature on the end of the smaller rod.B. increases at the same rate as the temperature on the end of the smaller rod.C. increases more rapidly than the temperature on the end of the smaller rod.

Physics 123HW #11, Due Wed, May 12

11-1. A container has a flat bottom made of aluminum that is [01] -cm thick. The

walls are insulated with thick styrofoam. The exterior bottom of the container is in

continual contact with boiling water. Inside the container, ethyl alcohol is boiling. How

long until the alcohol completely boils away if initially it has a depth of 5 cm? You will

want to consult Tables 15.1, 20.1, 20.2, and 20.3.

11-2. A sheet of copper and a sheet of aluminum with equal thickness are placed together so

that their flat surfaces are in contact. The copper is in thermal contact with a reservoir

at [02] ◦C, and the aluminum is in contact with a reservoir at 0◦C. What is

the temperature at the interface between the metals?

11-3. Your un-skirted trailer home has combined exterior surface area of [03] ft2

(excluding windows but including floor and ceiling). Suppose that all of these surfaces are

insulated with an R value of 7 (units implied). In addition, the combined window surface

area is 75 ft2, and the windows have a U value of 0.7 (note: U = 1/R). (Please neglect

effects of stagnant air layers.) You have an air conditioner that provides 10,000 BTU/h.

On a hot day of 104◦F, what is the temperature inside the trailer assuming a uniform

temperature throughout the interior and continuous running of the air conditioner?

Please ignore the effects of direct sunlight—perhaps the trailer is shaded by a big tree.

11-4. A 1-cm-radius spherical ball of polished gold hangs suspended inside an evacuated

chamber that is at room temperature (20◦C). There is no pathway for thermal

conduction to the chamber wall.

(a) If the gold is at a temperature of [04] ◦C, what is the initial rate of

temperature loss? The emissivity for polished gold is 0.02.

(b) What is the initial rate of temperature loss if the ball is coated with flat black paint,

which has emissivity 0.95? (Are you surprised?)

In-Class Quiz• Read sections 20.4–20.6.• The PV diagram represents a constant-temperature expansion ofan ideal gas from V1 to V2. The area under the curve represents thework accomplished (say, on a piston that allows the expansion; inthis case, the piston does negative work). Now consider gas confinedto a volume V1 behind a membrane which suddenly bursts so thatthe gas freely expands into vacuum to achieve the same final volumeof V2. Is work accomplished in this case?

Physics 123HW #12, Due Fri, May 15

12-1. Four grams of O2 gas (molecular weight 32 g/mol) is compressed from an initial state of

Pi = 1.30× 105Pa, Vi = 4.50 L to a final state of Pf = 1.10× 105 Pa,

Vf =[01] L along a path that forms a straight line on a PV diagram.

(a) What is the final temperature?

(b) What is the work done on the gas?

12-2. A sample of gas is taken through a single cycle as shown in the

figure, where P =[02] atm.

(a) How much work must be done on the gas during the cycle?

(b) How much heat is transferred out of the gas during the

cycle?

HINT: The ratio of the area of an ellipse to the area of the

rectangle containing it is π/4.

12-3. A cylindrical container with a sliding piston holds 0.20 moles of an ideal gas at a constant

pressure. If the temperature is increased from 20◦C to [03] ◦C, how much work

is done by the piston? HINT: A negative answer means the gas did work on the piston.

12-4. One mole of an ideal gas does [04] J of work on a piston as it expands to a

final volume of 25 L and a pressure of 1.00 atm. (NOTE: In this problem, the piston does

negative work.) The temperature is held constant during the process.

(a) What is the initial volume?

(b) What is the initial pressure?

In-Class Quiz• Read sections 21.1, 21.5.• A piston moves inward at 10 m/s and a gas molecule travels toward the piston. Afterbouncing elastically from the piston, the speed of the molecule will beA. the same as before.B. 10 m/s faster than before.C. 20 m/s faster than before.HINT: Change your perspective and consider the elastic bounce in the rest frame of thepiston. Then change your perspective back to the frame where the piston is moving.

Physics 123HW #13, Due Fri, May 14

13-1. Suppose that Moses consumed on average [01] liters of water per day during

his lifetime of 120 yrs. If this water is now thoroughly mixed with the Earth’s

hydrosphere (1.32× 1021 kg), how many of the same water molecules are found today in

your 1-liter bottle of water?

13-2. (a) How many atoms are required to fill a spherical helium balloon to a diameter of

30.0 cm at a temperature of [02] ◦C? Take the pressure to be 1.00 atm.

(b) What is the average kinetic energy of individual helium atoms?

(c) What is the root-mean-square speed of the atoms?

(d) What is the average speed of the atoms?

13-3. A container holds 1000 oxygen molecules at a temperature of 500 K.

(a) Make a graph of the Maxwell speed distribution versus speed (see Fig. 21.11 in the

textbook). Mark the horizontal axis at speed intervals of 100 m/s. HINT: The job of

graphing will be easier if you first manipulate Eq. (21.24) into the form,

Nv = (4.4 s/m)(

v

510 m/s

)2

exp

{−(

v

510 m/s

)2}.

(b) Compute the root-mean-square and average speeds and label them on the graph.

(c) Estimate the number of molecules with speeds between 300 m/s and 400 m/s.

HINT: The integral is hard, so approximate, using∫ v2

v1

Nv dv ≈ Nv(v2 − v1).

Note: Nv has units of number per velocity.

Turn in this problem on paper.

13-4. With specialized equipment, it is routine to achieve vacuums with pressures below

10−10 torr (1 torr = 1 mm of Hg = 133 Pa). However, special care must be taken in

cleaning and baking the walls of the stainless steel chamber, or “outgassing” of

contaminants will seriously increase the pressure (by orders of magnitude). If the

pressure is 1.00× 10−10 torr and the temperature is [03] ◦C, calculate the

number of molecules in a volume of 1.00 m3.

In-Class Quiz• Read sections 21.2–21.4.• Two gases in separate containers have equal volumes, equal numbers of molecules, andthe same internal energy Eint. One gas is monatomic and the other is diatomic. Thepressure of the diatomic gas isA. less than that of the monatomic gas.B. the same as that of the monatomic gas.C. greater than that of the monatomic gas.

Physics 123HW #14, Due Mon, May 17

14-1. What are the number of degrees of freedom for

(a) helium at room temperature?

(b) oxygen at room temperature?

(c) water vapor at 200◦C?

(d) hydrogen at a few thousand Kelvin?

14-2. A mole of air occupies 5.0 L at [01] ◦C in a cylinder with a piston that exerts

constant force. 4.4 kJ of heat is added. Air molecules are mostly diatomic. Use the

values of CV and CP for an ideal gas rather than values from Table 21.2. Determine the

(a) new volume, and (b) change in internal energy. If the piston is instead held in place

at 5.0 L, determine the (c) new pressure.

14-3. Warm air is able to hold more water vapor than cool air. It may seem surprising then

that thunderstorms often appear during the hottest part of summer days. As air is

heated, it expands and the resulting buoyant force propels large volumes of air upward.

In the upper atmosphere the warm gas expands further, owing to reduced pressure. The

expanding gas pushes the surrounding air out of the way, which accomplishes work. Since

the volumes involved are enormous, there is often insufficient time for heat transfer or

mixing with the upper atmosphere. Therefore, the process can be viewed as adiabatic.

Assuming that the pressure drops to [02] % as the air rises many kilometers,

what will be the final temperature (in Fahrenheit) if the mass of air begins its journey at

100◦F? Ignore the latent heat of water condensation, which in actuality plays a strong

role in temperature. Take air molecules to be diatomic.

14-4. One mole of a monatomic ideal gas is compressed adiabatically from an initial pressure

and volume of 2.00 atm and 10.0 L to a final volume of [03] L.

(a) Using W = −∫ V2

V1

P dV , find the work done on the gas. Be sure to include the sign if

negative.

(b) Find the final pressure.

(c) Find the final temperature.

(d) Use the first law together with the knowledge of the initial and final temperatures to

find the work done on the gas. HINT: Your answer should agree with part (a).

In-Class Quiz• Read sections 22.1, 22.3, 22.4.• Consider an arbitrary engine whose work output isconnected to a Carnot engine running in reverse as arefrigerator. The Carnot engine is special in that itdoes not violate the second law when a movie of itrunning is shown backward.

A. It is possible for the engine in the diagram to extract less heat from the hot reservoirthan is deposited by the Carnot refrigerator.B. It is possible for the engine in the diagram to deposit less heat into the cold reservoirthan is extracted by the Carnot refrigerator.C. Both A and B are possible.D. The Carnot refrigerator cannot deposit more heat into the hot reservoir than isextracted by the engine.

Physics 123HW #15, Due Mon, May 17

15-1. One of the most efficient engines ever constructed absorbs 140 kJ of thermal energy per

second from a reservoir at a temperature of 1870◦C and expels unconverted heat into a

cold reservoir.

(a) If the engine expels [01] kJ of thermal energy per second into the cold

reservoir, what is the efficiency of the engine?

(b) If the theoretical limit of efficiency is [02] %, what is the temperature of

the cold reservoir?

15-2. A sample of a monatomic gas is taken through the Carnot cycle ABCDA. For your

convenience, the cycle is drawn with the mathematical relationships of each part shown.

Complete the table for the cycle.

P V T

A 1400 kPa 10.0 L 720 K

B

C 24.0 L

D 15.0 L

Avoid rounding intermediate steps so that errors do not accumulate. You may find it

beneficial to solve for the unknowns in the order requested below.

First determine the number of moles from the date in row A.

(a) Find PD.

(b) Find the value of TD and TC , which are equal.

(c) Find PC .

(d) Find TB .

(e) Find VB .

You should then be able to find that PB = 875 kPa (provided here as a check).

15-3. For the parameters in Problem 15-2, complete the table below.

Q W ∆Eint

AB

BC

CD

DA

(a) What is the value of QAB?

(b) What is the value of WBC?

(c) What is the value of WCD?

(d) What is the value of ∆EintDA?

HINT: Curves AB and CD are constant temperature, meaning that the internal energy is

constant on the curves. Curves BC and DA are adiabatic, meaning that no heat flows

into or out of the gas.

15-4. (a) From the data in Problem 15-2, compute the efficiency of the given Carnot engine.

HINT: Eq. (22.4). Give the answer as a percent.

(b) From the data in Problem 15-3, compute the efficiency of the given Carnot engine.

HINT: Eq. (22.2). Give the answer as a percent.

In-Class Quiz• Read sections 22.2 and 22.5.• The door of an operating kitchen refrigerator is left open for a long time in a wellinsulated room. The temperature inside the room willA. decrease.B. remain the same.C. increase.

Physics 123HW #16, Due Wed, May 19

16-1. (a) Show that the efficiency for an engine working in the Sterling cycle represented below

is

e =W

Qin=

R(TH − TC) ln(VB/VA)RTH ln(VB/VA) + CV (TH − TC)

.

Qin includes heat injected along AB and DA.

Sterling cycle: The gas expands along AB at constant

temperature TH and is cooled at constant volume along BC.

The gas is then compressed along CD at constant

temperature TC , whereupon the pressure is increased at

constant volume along DA. Turn in this part on paper.

(b) Suppose that a diatomic gas is used and VB/VA = 3.5. If

TH = [01] K and TC = 400 K, what is the ratio of

the efficiency to that of the Carnot cycle?

16-2. Show that the efficiency for an engine working in the Diesel cycle represented ideally

below is

e = 1− 1γ

TD − TATC − TB

.

Turn in this problem on paper.

Diesel cycle: Adiabatic compression AB heats the gas

until ignition at B when fuel is introduced (no spark

plug needed). A constant pressure expansion BC takes

place as combustion adds heat. Adiabatic expansion CD

accomplishes additional work before the exhaust is

exchanged for new air during what can be thought of as

a constant volume cooling DA.

16-3. The definition of the coefficient of performance (COP) for a refrigerator is the heat

extracted from the cold reservoir compared to the work introduced. Suppose that a

Carnot engine runs in reverse to make a refrigerator.

(a) Prove that the coefficient of performance is

COP =QCWcycle

=TC

TH − TC.

Turn in this part of the problem on paper.

(b) If the Carnot engine has an efficiency of [02] %, what is the COP when it

is used as a refrigerator?

16-4. The definition of the coefficient of performance (COP) for a heat pump is the heat

deposited into a hot reservoir compared to the work introduced. Suppose that a Carnot

engine runs in reverse to make a heat pump. Suppose that a house continuously loses

[03] kW of heat per time through the exterior surfaces when the inside

temperature is 22◦C and the outside temperature is −5◦C. To keep up with this loss, an

electrical heater uses the same amount of power. How much power will be consumed if

instead an ideal heat pump delivers the required amount of heat per time while operating

between the temperatures given?

In-Class Quiz• Read sections 22.6–22.8.• The entropy in a cylinder of gas changes by −10 J/K. Choose the correct statement:A. The environment must be at a higher temperature.B. The process may have been adiabatic.C. The entropy of the environment does not increase by more than 10 J/K.D. None of the above.

Physics 123HW #17, Due Wed, May 19

17-1. (a) A container holds 1 mol of an ideal monatomic gas. A piston allows the gas to

expand gradually at constant temperature until the volume is [01] times

larger. What is the change in entropy for the gas?

(b) What is the change in entropy for the gas if the same increase in volume is

accomplished by a reversible adiabatic expansion followed by heating to the original

temperature?

(c) What is the change in entropy for the gas if the same increase in volume is

accomplished by suddenly removing a partition, which allows the gas to expand freely

into vacuum?

17-2. One mole of nitrogen is held at a constant pressure. What is the change of entropy as the

gas is heated from 0◦C to [02] ◦C?

17-3. Two 1.00-kg pieces of silver are brought into thermal contact while insulated from the

environment. If initially one piece is at [03] ◦C and the other at 0◦C, what is

the change in entropy for the system?

17-4. Assume that our classroom has a volume of [04] m3 which is filled with air at

1.00 atm and 25◦C.

(a) Calculate the probability that all of the air molecules will be found in the forward

half of the room. Represent this remote possibility as 1 part in 10x, where x is some large

number. Give the value of x. NOTE: 2N = 10N log 2.

(b) How much more entropy is present when the air is distributed throughout the room

rather than confined to the front half only?

In-Class Quiz• Read and think about each problem on Practice Exam II.• Complete at least two of the problems. (Do not turn in your work.)

Physics 123HW #18, Due Fri, May 21

18-1. On the fourth floor of the Eyring Science Center we occasionally set up a laser to shine

down a long corridor to hit a mirror and return. We have used this to measure the speed

of light by first bouncing the beam from a mirror which rotates at [01] Hz. In

the time it takes for the light to make the round trip, the mirror rotates through a small

angle so that the reflected beam does not return to its source. By how many millimeters

is the beam displaced to the side of its source if the distance from the source to the

rotating mirror is 2.00 m and the distance from the rotating mirror to the reflecting

mirror is 100 m? The speed of light is 3.00× 108 m/s. HINT: Notice that as the mirror

rotates through an angle δ, the reflected beam deviates by an angle 2δ.

18-2. A laser has a wavelength of [02] nm in air.

(a) What is the frequency in air?

(b) What is its speed in glass with n = 1.52?

(c) What is its frequency in glass?

(d) What is its wavelength in glass?

18-3. A beam of light containing multiple colors is incident

upon a prism with an angle of θ1 = 60.0◦. The apex of the

prism has an angle of φ =[03] ◦. If the prism is

made of flint glass which has an index of n = 1.66 for

violet light and an index of 1.62 for red light, what is the

angle separating those two colors after emerging from the

prism (i.e., θ4(violet)− θ4(red))?

18-4. You are a fish in deep, dark water with index 1.33. As you look up from

[04] m below the smooth surface, you see a bright circle through which light

enters from the outside world.

(a) What is the radius of the circle?

(b) Will you be able to see a fisherman 2.00 m tall standing at the water’s edge 4.00 m

away?

In-Class Quiz• Read section 38.6 to the top of page 1096. Read sections 36.1–36.2.• When an electromagnetic wave encounters atoms,electrons are stimulated to oscillate along the direction ofthe E-field polarization. (The figure depicts only one kindof polarization; the E-field can also point in and out of thepage.) These oscillations cause atoms to radiate like dipoleantennas, which is responsible for reflections. Antennasradiate energy out their sides, not out their ends, as shown.When light is incident upon a material interface atBrewster’s angle,A. only one polarization can transmit into the material.B. both polarizations transmit, but more of one than theother.

Dipoles aligned thisway cannot radiatein the reflecteddirection.

Physics 123HW #19, Due Mon, May 24

19-1. You wish to attenuate a polarized laser beam by inserting two polarizers. The second

polarizer is oriented to match the original polarization of the beam to ensure that the

final polarization remains unchanged. The first polarizer is then rotated through various

angles to control the intensity. Through what angle should the first polarizer be rotated

to reduce the final intensity by a factor of [01] ?

19-2. A prism is inserted into a polarized laser beam. The apex

angle φ is chosen so that the beam enters and leaves close to

Brewster’s angle. If the index of refraction is

n =[02] , what should be the apex angle φ?

19-3. A concave mirror has a radius of curvature of 60.0 cm. If the object is placed at

[03] cm, calculate (a) the image position and (b) the magnification. (c) Draw

a ray diagram.

Turn in part (c) on paper.

19-4. If the object is placed at [04] cm in front of the mirror in problem 19-3,

calculate (a) the image position and (b) the magnification. (c) Draw a ray diagram.

Turn in part (c).

HINT: Your diagrams for problems 19-3 and 19-4 should look similar to those shown

below. Consider two rays that leave the same point on the object. A ray traveling

parallel to the axis will pass through the focus after reflection, and a ray passing through

the focus will travel parallel to the axis after reflection. The two rays cross at the image.

Magnification is the ratio of the height of the image to that of the object (negative if

upside down).

19-5. A large concave mirror in the foyer of the Eyring Science Center images a dollar bill with

magnification M = −1. (If you have not seen it before, I recommend that you visit the

display.) The dollar bill is placed 170 cm from the mirror.

(a) Calculate the radius of curvature of the mirror.

(b) Draw a ray diagram for the setup. Turn in this part on paper.

In-Class Quiz• Read sections 36.3–36.4.• This question is not associated with the current reading assignment. An object islocated in front of a concave mirror. The image formed can occurA. at the same location as the object with it any desired magnification.B. behind the mirror, but only if it is upright.C. in front of the mirror and be virtual.D. in front of the mirror and be upright.

Physics 123HW #20, Due Mon, May 24

20-1. An object placed 30.0 cm in front of a convex mirror produces a virtual image

[01] cm behind the mirror.

(a) What is the radius of curvature for the mirror?

(b) What is the magnification?

(c) Draw a ray diagram using different colors for the real and virtual rays. Turn in this

part on paper.

20-2. A concave mirror has a focal length of f = 40.0 cm.

(a) Find the position of the object that gives an image that is upright and

[02] times larger.

(b) Draw a ray diagram using different colors for the real and virtual rays.

(c) Repeat part (a) for a convex mirror with focal length f = −40.0 cm.

(d) Draw a ray diagram for part (c).

Turn in parts (b) and (d) on paper.

20-3. You are trapped in the wilderness and must spear fish in order to survive. While looking

into the water from directly above, a fish appears to be [03] cm below the

surface.

(a) How far below the surface is it in actuality?

(b) Draw a ray diagram. Turn in this part on paper.

20-4. A thin lens with index of refraction n is immersed in a fluid with index n′. Prove that

the focal length in this situation is given by

1f

=( nn′− 1)( 1

R1− 1R2

).

Turn in this problem on paper.

In-Class Quiz• Read sections 36.5–36.7.• True or False: A near-sighted person has an advantage over a person with 20/20 visionwhen looking at tiny objects up close.

Physics 123HW #21, Due Wed, May 26

21-1. A converging lens has a focal length of 20.0 cm. If the object is at [01] cm,

(a) draw a ray diagram and find the (b) image distance and (c) magnification.

Turn in part (a) on paper.

HINT: The ray diagram will be similar to that shown below.

21-2. If the object in problem 21-1 is at [02] cm, (a) draw a ray diagram and find

the (b) image distance and (c) magnification.

Turn in part (a) on paper.

21-3. If the object in problem 21-1 is at [03] cm, (a) draw a ray diagram and find

the (b) image distance and (c) magnification.

Turn in part (a) on paper.

21-4. An object is located [04] cm to the left of a diverging lens having focal length

f = −32.0 cm.

(a) Find the location of the image.

(b) What is the magnification?

(c) Draw a ray diagram. Turn in this part on paper.

21-5. The eyes of an elderly person with 20/20 vision are only able to accommodate to a near

point of [05] cm.

(a) For such a person to be able to read a book at a distance of 30 cm, what must the

focal length of the corrective lens be?

(b) Give the power of the lens in diopters.

21-6. A near-sighted person has near and far points of 12 cm and [06] cm,

respectively. This defines the range over which the eye can accommodate.

(a) Find the the focal length of the lens that will move the far point to infinity.

(b) Find the power of the lens in diopters.

(c) With the lens in place, where is the new near point?

In-Class Quiz• Read sections 36.8–36.10.• This question is not associated with the current reading assignment. To correct thevision of a near-sighted person, a lens should be chosen which hasA. a negative focal length with magnitude equal to the distance to the near point.B. a negative focal length with magnitude equal to the distance to the far point.C. a positive focal length with magnitude equal to the distance to the near point.D. a positive focal length with magnitude equal to the distance to the far point.

Physics 123HW #22, Due Wed, May 26

22-1. A thin lens with focal length [01] cm is used as a simple magnifier by holding

it close to the eye.

(a) Suppose that a person would like to relax the eye during viewing (focusing at ∞).

Where should an object be placed for viewing?

(b) What is the angular magnification (that is, the angular size of the image compared to

the case of holding the object at 25 cm with no lens)?

22-2. A microscope has an objective with focal length 3.00 mm and an eyepiece with focal

length [02] mm. The microscope is adjusted so that the eye is relaxed while

viewing.

(a) If the object is positioned 3.20 mm from the objective lens, how far apart should the

two lenses by separated? Please don’t assume L� fe as is done for Eq. 36.20.

(b) What is the angular magnification?

22-3. A Keplerian telescope uses an objective lens with positive focal length

fo = [03] cm and an eyepiece with positive focal length

fe = [04] cm. The first lens forms an image, which becomes the intermediate

image/object to be viewed through the second lens.

(a) When the telescope is used for looking at far-away objects, what is the value for qofor the intermediate image/object?

(b) The eyepiece is positioned such that the final image occurs far away to be viewed

with a relaxed eye. What should be the value for pe to achieve this?

(c) Let h be the height of the intermediate object/image. Through the use of similar

triangles, the angular size of the original object θo is seen to be the same as h/qo, and the

angular size of the final image θe is seen to be the same as h/pe. What is the angular

magnification mθ of the telescope? Note |mθ| = θe/θo, where mθ is negative if the final

image is upside down. The small angles are greatly exaggerated in the figure.

22-4. A Galilean telescope is formed with an objective of focal length fo and an eyepiece of

focal length fe = −fo/3. In the diagram, the distance from point A to the objective lens

is fo. The distances from the objective lens to point B, from point B to the eyepiece lens,

and from the eyepiece lens to point C are all equal to fo/3.

(a) What is the angular magnification when the telescope is used to observe distant

objects?

(b) Is the final image upside down? (Note: the rays drawn are for convenience in problem

22-5.)

22-5. (a) Even though the telescope in problem 22-4 is designed to look at far-away objects, for

some strange reason you decide to look at an object 10 cm tall, which is located 2fo in

front of the objective lens. Complete the ray diagram below showing the relevant rays

and the position of the final image observed when looking through the eyepiece. Turn in

this part of the problem on paper.

(b) Now suppose that the objective lens has focal length fo =[05] cm. At

what position relative to the eyepiece does the final image occur? (Enter a negative

number if on the left.)

(c) What is its height?

In-Class Quiz• Read sections 37.1–37.4 and 38.4.• Monochromatic light is sent through a Young’s double-slit setup. The slit separation isincreased. The fringe pattern on a distance screenA. narrows.B. remains the same.C. broadens.

Physics 123HW #23, Due Fri, May 28

23-1. Suppose that you wish to determine the wavelength of monochromatic light using a

double slit with a separation of [01] mm. After the slit, the light travels

3.48 m to a screen. To obtain better accuracy, you measure the distance across 16

maxima (8 on each side of the center maximum) to be 16.8 cm. Find the wavelength.

23-2. A double slit is illuminated with light having a wavelength λ =[02] nm. When

you place a thin transparent membrane over one of the slits you notice that the maxima

and minima on a distant screen exchange places. If the membrane material has a

refractive index of n = 1.50, what is its minimum possible thickness?

23-3. Two narrow slits separated by 0.85 mm are illuminated with [03] -nm light.

The peak intensity on a screen 2.80 m away is 0.1 W/cm2. What is the intensity at a

distance 2.50 mm from the center of the central peak?

23-4. The diagram depicts a standard spectrometer setup. A lens (or concave mirror) following

a slit creates collimated light that strikes the grating (usually a reflective grating rather

than a transmission grating as shown). Suppose that the grating has

[04] lines/mm. Also suppose that you observe light from a sodium lamp

which has two strong emission lines at λ1 = 589.0 nm and λ2 = 589.6 nm.

(a) In the first diffraction order, what is the difference between the diffraction angles of

the two wavelengths (ignore the second lens)? HINT: See Eq. (38.7) where m = 1. Don’t

use the small angle approximation.

(b) To observe the two wavelengths well separated spatially, it is necessary to let the

light travel to a faraway screen. Because this can require very large distances, it is

convenient to image what would have appeared on the faraway screen to a closer screen

using a lens. The image appears at the focus of the lens, and the angular separation is

preserved, referenced from the position of the lens. If the final lens has a 30-cm focal

length, how far apart on the detector screen are the two sodium wavelengths?

In-Class Quiz• Read sections 37.5–37.7.• An oil film on water reflects different colors more or less brightly owing to interference,which depends on the thickness of the film. In an outer region where the film is thinnest(thin compared to visible wavelengths), all colors reflect brightly. From this information,we can tell that the index of refraction of the oil isA. less than that of water.B. the same as that of water.C. greater than that of water.

Physics 123HW #24, Due Fri, May 28

24-1. It is desired to apply a single-layer coating to a glass optical component (n = 1.50) such

that the transmission of 600-nm light is maximized while the transmission of 450-nm

light is simultaneously minimized. What is the minimum coating thickness that will

accomplish this if magnesium fluoride is used which has an index of n = 1.38?

24-2. A wedged air space is created between two plates of glass, and a sample of hair is

inserted at one edge. The plates are illuminated from above with [01] -nm

light and reflections from the air wedge are observed.

(a) Will the fringe near where the plates touch be bright or dark?

(b) If a total of 25 dark fringes are observed (including the one in part (a) if it is dark),

what is the diameter of the hair?

24-3. A Michelson interferometer is used to carefully measure the wavelength of a single

spectral line from a source. A computer connected to a scanning motor and a detector

records [02] fringes as the motor causes the mirror to move by 1.000 mm.

What is the wavelength? Please give 4 significant figures on this problem.

24-4. Review Problem: A lens of focal length f1 = 10.0 cm is placed a distance

x =[03] cm before a lens of focal length f2 = −10.0 cm. An object is

positioned 15.0 cm before the positive lens.

(a) Make a ray diagram for the system. There will be an intermediate image and a final

image. Turn in this part of the problem on paper.

(b) At what position relative to the location of the negative lens does the final image

occur? (Enter a negative number if on the left.)

(c) Calculate the overall magnification Moverall = hfinal image/hobject.

In-Class Quiz• Read sections 38.1–38.3.• Consider the central peak in a diffraction pattern that appears on a far-away screen.Which has the widest width?A. The pattern formed by two narrow slits separated by spacing d.B. The pattern formed by a single slit with width d.C. The pattern formed by a circular hole with diameter d.D. They all have the same widths.

Physics 123HW #25, Due Wed, June 2

25-1. You wish to measure the width of a single narrow slit by observing the diffraction of

[01] -nm light on a screen 3.00 m away.

(a) What is the ratio of the width of the central peak to the width of individual side

peaks?

(b) With a ruler you measure 15.5 cm for the distance from the fourth dark fringe on one

side of the central maximum to the fourth dark fringe on the other side. What is the

width of the slit?

25-2. Coherent light with wavelength λ passes through a round hole and propagates to a

faraway screen.

(a) Draw a picture of the setup and resulting pattern.

(b) If the lens is placed after the hole, where will the diffraction pattern appear? Draw a

second picture. HINT: Consider the pattern that would have appeared on the distant

screen as an object, and find where its image will be.

(c) How does the angular width of the pattern change when the lens is inserted?

HINT: Please consider similar triangles on the ray diagram of part (b) to see that the

angular width is the same.

Turn in this problem on paper.

25-3. On the night of April 18, 1775, a signal was sent from the Old North Church steeple to

Paul Revere who was 1.8 miles away: “One if by land, two if by sea.” If in the dark,

Paul’s pupils had [02] -mm diameters, what is the minimum possible

separation between the two lanterns that would allow him to correctly interpret the

signal? Assume that the predominant wavelength of the lanterns was 580 nm.

NOTE: Although the wavelength is modified by the refractive index within the eye, the

angles between incident rays are also modified by a similar amount. The two effects

cancel each other, so you need not worry about it.

25-4. Grote Reber, a pioneer in radio astronomy, constructed a radio telescope with a 10-m

diameter receiving dish. What was the telescope’s angular resolution when observing

[03] -m radio waves?

25-5. The Hubble telescope has a primary objective with approximately 1-m diameter. What is

the angular resolution when observing visible light with wavelength [04] nm?

25-6. A HeNe laser as a wavelength of 633 nm. If the collimated beam has a diameter of

0.50 cm, estimate the radius of the beam after it travels [05] km.

In-Class Quiz• Read and think about each problem on Practice Exam III.• Complete at least two of the problems. (Do not turn in your work.)

Physics 123HW #26, Due Fri, June 4

26-1. A clock is composed of a light bulb that sends a

new flash each time it senses its own flash reflected

from a mirror positioned above at a distance d. Let

the period of the clock in its own frame of reference

be ∆tp = 2d/c. The clock moves with speed v to

the right. An observer at rest sees the light

traveling along a triangular path as shown in the

figure with a period of ∆t. Use the principle of

relativity to derive a formula for time dilation (i.e.,

∆t = f(v)∆tp). Do not simply copy the proof from

the book. Please learn it and do it on your own.

Turn in this problem on paper.

26-2. In a laboratory, a muon is found to have an expected lifetime of 2.2 µs before it decays.

Suppose that a muon is created by a cosmic ray [01] km above the Earth.

What fraction of the speed of light must the muon travel if it is to reach the ground in its

expected lifetime? Express your answer as a number times c. Give your answer to 6

significant figures.

26-3. Astronauts travel at 0.950c from Earth to a star which is [02] ly away.

(a) How long does it take them to reach the star as observed by people on Earth?

(Earthlings know how much time it takes for a signal to reach them from the star, and

they do not include it as part of the travel time for the astronauts.)

(b) How long does the trip take from the perspective of the astronauts?

(c) How far apart are Earth and the star from the perspective of the astronauts as they

travel?

26-4. At Stanford Linear Accelerator, my former Ph.D. advisor was involved in experiments

where a high-intensity laser is aimed at electrons which approach almost straight-on with

a velocity of v = (1− 3× 10−10)c. In the lab frame, the time interval necessary for an

electron to cross sequential wavecrests of the light wave is Tlab = λlab/(c+ v), as you

would expect. Show that in the rest frame of the electron, that time interval is

Te =λlab

c

√1− v/c1 + v/c

,

and hence the wavelength experienced by the electron is

λe = λlab

√1− v/c1 + v/c

.

This formula describes the Doppler shift for light, where v is the relative motion between

the source and observer. HINT: 1− v2/c2 = (1 + v/c)(1− v/c). Turn in this problem

on paper.

26-5. For problem 26-4, if the wavelength of the laser in the laboratory frame is

λLab =[03] µm, what is the wavelength of the laser in the rest frame of the

electrons?

In-Class Quiz• Read sections 39.5–39.6.• Harry Potter and Draco Malfoy pass each other on broomsticks with relative speed v.Harry observes that Draco’s broom seems shorter according to the length contractionformula L = Lp

√1− v2/c2. Draco observes that Harry’s broom seems shorter, by the

same formula.A. This is truly a paradox, and is the reason that Special Relativity is called a “theory.”B. Actually, when used correctly, the formula shows that Draco’s broom must appear tobe lengthened when observed by Harry.C. The issue is resolved because simultaneous events in one frame are not simultaneousin another.

Physics 123HW #27, Due Fri, June 4

27-1. Suppose our Sun is about to explode and we escape in a spaceship toward the star Tau

Ceti. When we reach the midpoint of our journey, which takes place at

v =[1] c, we see our Sun explode and, unfortunately, we see Tau Ceti explode

as well (we observe the light arriving from each explosion).

(a) In the rest frame of the Sun and Tau Ceti, which are 12 lightyears apart, did the

explosions occur simultaneously?

(b) In the spaceship frame of reference, did the explosions occur simultaneously?

(c) In the spaceship frame of reference, how long before we saw the Sun explode did it

actually explode? (Enter a positive value for times in the past.)

(d) In the spaceship frame of reference, how long before we saw Tau Ceta explode did it

actually explode? (Enter a positive value for times in the past.)

27-2. Two spaceships having rest length 100 m pass each other traveling opposite directions

with a relative speed of [02] c. As the front of the spaceships just cross, each

pilot sets off a small flare at the back of her own ship, synchronized to the same instant

(t = 0 in her own frame).

(a) To each pilot, when does the flare of the back of the other ship occur (negative if in

the past)?

(b) To each pilot, how far in front does the flare of the back of the other ship occur?

27-3. In the laboratory frame, two particles produced by an accelerator travel in opposite

directions, one with a speed of [03] c and the other with speed 0.9980c. In the

rest frame of either particle, what is the relative speed as a number times c? Give your

answer to 6 significant figures.

27-4. In an accelerator, an electron experiences a constant electric field of E = 1.00 MV/m.

What is its speed (a number times c) after [04] ns assuming it starts from

rest? HINT: The force on the electron is F = qE, where q = 1.60× 10−19 C is the

electron charge. Note that a megavolt per meter is the same as 106 N/C. Eq. (39.20) is

trivially integrated since F is constant.

In-Class Quiz• Read sections 39.8–39.10.• A decade after his development of what we now call “Special Relativity,” Einsteindeveloped “General Relativity” which allows one to deal with accelerating frames ofreference. He ingeniously asserted thatA. there is energy in mass according to E = mc2 and this led to general relativity.B. there is no physical difference between a gravitational force and a force caused by theacceleration of a frame of reference.C. light from a distant star will bend as it passes near the Sun on its way to the Earth(viewed during an eclipse) because of the bright light emitted by the Sun.

Physics 123HW #28, Due Mon, June 7

28-1. It was known before Einstein’s time that light carries momentum,

which is connected to the transported energy through p = E/c.

Consider an enclosed box of mass M on a frictionless surface (or

in deep space). Inside the box, a flash of light with energy E is

emitted from one wall and is absorbed at the opposite wall.

Construct a short proof to show that in order for the center of

mass of the isolated system (the box) to remain unchanged, the

light must move a mass m from one wall to the other according

to the relation E = mc2. Be sure that you can do this proof by

heart. Turn in this problem on paper.

28-2. Consider an electron which has been accelerated to a total energy of [01] GeV.

(a) What fraction of the electron’s energy is due to its rest mass (i.e., the ratio of rest

energy to total energy)?

What is the momentum (b) in kg ·m/s and (c) in GeV/c?

(d) The speed of the electron can be written in the form v = (1− δ)c? Find the value

of δ. HINT:√

1 + x ≈ 1 + x/2 when x is small.

28-3. A pion particle with rest energy 138 MeV decays into a muon (rest energy 105 MeV) and

an antineutrino (negligible rest energy). Use conservation of energy and momentum to

find

(a) the energy of the antineutrino and

(b) the speed of the muon (a number times c).

28-4. A photon collides with an electron that is at rest. The photon imparts momentum to the

electron, and a new photon recoils in the opposite direction (exactly backward relative to

the incoming photon). Show that the momentum of the recoiling photon p′photon is

related to the momentum of the incident photon pphoton through

1p′photon

− 1pphoton

=2mec

.

Turn in this problem on paper.

In-Class Quiz• Read sections 40.1, 40.2.• One of the earliest clues of quantum physics came when scientists tried to understandthe nature of thermal radiation (which you studied briefly in section 20.7). Scientiststried to explain the light emitted from hot objects by requiring the material to be inthermal equilibrium with the surrounding light field. The attempt failed miserably whenusing classical mechanics. Planck guessed a formula that fit the experimental data, andthen notices that he could derive the formula only ifA. there is no light above a cutoff frequency given by the work function.B. he made a mistake in the algebra.C. the light field at a given frequency f can accommodate any amount of energy.D. the light field at a given frequency f takes on discrete values for energy, separatedby hf , where h is an experimentally determined constant.

Physics 123HW #29, Due Mon, June 7

29-1. What is the energy of a photon

(a) broadcast by a radio station at [01] kHz?

(b) in the infrared with wavelength [02] µm?

(c) of visible light with wavelength [03] nm?

29-2. (a) What is the energy of an x-ray photon with wave wavelength [04] nm?

(b) What is the wavelength of a gamma ray with energy [05] MeV?

29-3. A perfect black body is an object which does not reflect or scatter light but absorbs and

re-emits light of any wavelength. The temperature of the object determines the

wavelengths at which it radiates. Use Eq. (40.3) to derive Wien’s displacement law

(Eq. (40.1)) which specifies the wavelength where the maximum amount of radiation

takes place. HINT: Find the wavelength where Eq. (40.3) is maximum. When setting the

derivative to zero, you will get an equation of the form (5− x)ex = 5, which is satisfied

when x = 4.965. Turn in this problem on paper.

29-4. A star can be considered a black body radiator. A particular star similar to our Sun

most strongly radiates at a visible wavelength of [06] nm. What is its surface

temperature?

29-5. Use Eq. (40.3) to derive Stefan’s law (Eq. (20.18)) which you already used in Chap. 20 to

calculate the effects of thermal radiation for heat flow. Assume a perfect black body

which has emissivity of e = 1. Turn in this problem on paper.

HINT: Eq. (40.3) gives intensity per wavelength, so to find the total intensity for all

wavelengths, one must integrate

Itotal =∫ ∞

0

Iλ dλ.

The following integral formula is handy:∫ ∞0

dx

x5(ea/x − 1)=

π4

15a4.

Also, remember that intensity is power per area.

29-6. If a star similar to our Sun has a radius of R = 6.96× 108 m and its surface temperature

is [07] K, find the total power that it radiates.

29-7. A certain metal has a work function of [08] eV.

Find (a) the cutoff wavelength and (b) the threshold frequency for the photoelectric

effect.

(c) Calculate the stopping potential if the incident light has a wavelength of 480 nm.

In-Class Quiz• Read sections 40.3, 42.1–42.3.• Why were Rutherford’s alpha particle scattering results so surprising?A. Rutherford’s results suggested that the positive charge in an atom is spread over alarge volume with embedded electrons like “seeds-in-a-water-melon.”B. Classical physics suggests that electrons in orbit around a nucleus will radiate energyand quickly spiral into the nucleus.C. Bohr’s model of the atom contradicts Rutherford’s scattering experiment.

Physics 123HW #30, Due Wed, June 9

30-1. X rays having energy 300 keV undergo Compton scattering from a target. If the

scattered x rays are detected at [01] ◦ relative to the incident rays, find

(a) the Compton wavelength shift.

(b) the energy of the scattered x rays.

(c) the kinetic energy of the recoiling electrons for this angle.

30-2. A photon with wavelength [02] nm collides with an electron in a Compton

scattering event. The recoiling photon emerges at θ = 90◦ with respect to the direction of

the incident photon. What angle does the recoiling electron make with respect to the

direction of the incident photon?

30-3. A hydrogen atom is excited to the n = 6 state. It then undergoes a transition to the

n = 2 state and a photon is emitted.

(a) What is the energy of the photon?

(b) What is the wavelength of the photon?

30-4. A hydrogen atom is in the n = 2 state. Using the Bohr theory of the atom, calculate

(a) the radius of the orbit.

(b) the kinetic energy of the electron.

(c) the potential energy of the electron (negative).

(d) the total (or binding) energy of the electron (negative).

In-Class Quiz• Read sections 40.5–40.8.• De Broglie’s hypothesisA. confirmed that photons have no rest mass.B. gave justification for the quantization rule in the Bohr model ofthe atom.C. explained the photoelectric effect.

HINT: On a test, you should be able to give a short mathematicalderivation in support of your answer. Think of the de Brogliewavelength as needing to fit neatly around an orbital circle, to form astanding wave pattern.

Physics 123HW #31, Due Wed, June 9

31-1. An electron microscope is used to probe tiny structures. The microscope takes into

account the fact that electrons have wave characteristics similar to light. The resolution

of the microscope is limited to about a wavelength: diffraction prevents you from seeing

objects with dimensions smaller than a wavelength. Electrons are much less energetic

than photons with the same wavelength. Thus, if you want to resolve small objects while

minimizing damage, say to a biological sample such as a cell, there is an advantage to

using electrons instead of photons.

(a) What is the minimum kinetic energy of electrons necessary to resolve structures of

the size [01] nm. (Assume that the wavelength of the electron must be equal

to this size.) HINT: Relativistic kinematics is not necessary.

(b) What is the minimum energy of photons necessary to resolve the same structures?

31-2. An oscilloscope is modified to perform an electron interference experiment. Electrons are

incident on a pair of narrow slits 0.060 µm apart. The electrons are accelerated through

[02] V before they arrive at the slits. How far apart will adjacent bright

bands in the interference pattern be separated if the screen is 20 cm from the slits?

HINT: The classical expression for momentum is okay since the voltage is far below

511 kV, which would provide energy equivalent to the electron rest energy.

31-3. A very intense laser pulse has photons with energy [03] eV. Helium has a

binding energy (or work function) of 24 eV. Because the laser photon energy is far below

the work function, it would seem that the laser should not be able to ionize helium, yet

because of the extreme intensities involved, it can. The explanation lies in the

uncertainty principle: ∆E∆t ≥ h̄/2.

(a) How many photons are required to provide enough energy for ionization? (Round up

to an integer number of photons.)

(b) In what period ∆t must the photons arrive at the atom to force the uncertainty in

energy to be this great?

(c) What laser intensity is necessary (in units of W/cm2) assuming that the effective

absorbing area of the atom is a circle with the Bohr radius? HINT: Recall that intensity

is energy per time deposited on a given area (i.e., I = (∆E/∆t)/A).

31-4. An electron is captured and held by a nucleus of diameter 5.0× 10−15 m.

(a) Use the uncertainty principle to determine whether the electron motion is relativistic

or nonrelativistic.

(b) Are the motions of neutrons or protons in the nucleus relativistic or nonrelativistic?

31-5. A sample of atoms excited to a particular state emit photons having an energy spread of

[04] eV as the atoms make the transition to a lower state. What is the

lifetime for the transition?

In-Class Quiz• Read sections 44.1, 44.3–44.5. Note: In Table 44.1, the mass of the nucleus plus themass of two electrons is equal to the mass of the 4

2He atom given in Table A.3 ofAppendix A.• Iron has the most stable nucleus from the point of view that its constituents are boundwith the highest energy per nucleon. Fusion, the joining of nuclei to form larger ones,without the net input of external energy tends to be possible forA. elements which are lighter than iron.B. iron.C. elements which are heavier than iron.

Physics 123HW #32, Due Fri, June 11

32-1. (a) Calculate the binding energy per nucleon for 2H. HINT: Please refer to Table A.3 in

Appendix A. Be aware that the table includes the mass of the electrons in orbit about

the nuclei. Before using Eq. (44.4), you will need to remove this excess mass.

I recommend that you do it by replacing mp in Eq. (44.4) with m1H. Then the electron

masses will be canceled automatically.

(b) Repeat for 4He.

32-2. 56Fe is located at the peak of the stability curve. Show that 56Fe has a higher binding

energy per nucleon than its neighbors, 55Mn and 59Co. Turn in this problem on

paper.

32-3. (a) Can the decay process 23892 U→ 234

90 Th + 42He occur spontaneously without the need for

external energy? HINT: If the resulting nuclei are bound with more energy (negative),

then energy is released in the process.

(b) Can the process 9844Ru→ 94

42Mo + 42He occur spontaneously?

32-4. Cosmic rays continuously generate 146 C in the upper atmosphere. This effect causes the

ratio of 146 C to 12

6 C in the carbon dioxide of the atmosphere to remain roughly constant

at about 1 part in 7.7× 1011 even though 146 C decays with a half-life of 5730 y. Tissues of

living organisms interact directly or indirectly with the atmosphere, so the ratio of 146 C to

126 C tends to be the same in organisms. However, upon death the exchange of carbon

with the atmosphere ceases and the number of 146 C atoms decays. The skeleton of a

mammoth is found to have [01] % as much 146 C as the atmosphere. Assuming

that the concentration of 146 C in the atmosphere has remained constant, how long ago did

the mammoth live?

32-5. (a) The half life of iodine-131 is 8 days. How many micrograms of iodine-131 are required

to produce a sample with an activity of [02] Ci? You may use 132 g for the

molar mass of iodine-131.

(b) How long until the activity decreases to 90%?

(c) What is the activity after 32 days?

In-Class Quiz• Read sections 44.6, 44.7. Browse Chapter 45.• Radon (222Rn) is an inert noble gas, which comes up through the Earth’s crust and canenter people’s houses. Radon is dangerous to breathe because it has a half-life of about4 days.A. If a home has a radon gas problem, it is only necessary to wait for a period muchlonger than 4 days and the problem will go away.B. Radon gas in people’s homes is a problem because of the mining of fissionablematerials.C. Radon gas is very corrosive chemically.D. None of the above.

Physics 123HW #33, Due Fri, June 11

33-1. Identify the missing nuclide or particle (X):

(a) 21584 Po→ X + 4

2He.

(b) X → 5526Fe + β+ + ν.

(c) 42He + 14

7 N→ 178 O +X.

(d) 10948 Cd +X → 109

47 Ag + ν.

For parts (a) through (c) type the chemical symbol followed by the mass number (no

spaces). For example Na23, not Na 23 or na23 or NA23. Part (d) is multiple choice.

Hint: The missing nuclides may or may not be present in Table 44.2. You will probably

need to consult a periodic table of the elements, such as the one on p. 1240.

33-2. 8035Br is one of the few nuclides that can decay via any of the three β decay processes:

electron emission, electron capture, and positron emission. Calculate the energy released

(Q) by each of the interactions. You will need M8035Br = 79.918528 u,

M8036Br = 79.916376 u, and M80

34Se = 79.916521 u.

(a) 8035Br→ 80

36Kr + e− + ν̄. CAUTION: The mass of 8035Br given above includes

35 electrons, and the mass of 8036Kr includes 36 electrons. You can think of the emitted

electron as becoming the 36th electron for the krypton.

(b) 8035Br + e− → 80

34Se + ν. CAUTION: The mass of 8035Br includes the electron which gets

captures by the nucleus.

(c) 8035Br→ 80

34Se + e+ + ν. CAUTION: The mass of 8034Se does not include the positron,

nor does it include an outer electron of bromine that wanders away after the positron.

33-3. Calculate the energy released in the D-T fusion reaction, 21H + 3

1H→ 42He + n.

33-4. (a) How much energy is required to overcome the Coulomb repulsion to allow D-T

fusion? Assume that the strong force “turns on” when the particles get within

1.0× 10−14 m. HINT: Check your work with Example 45.3.

(b) Estimate the temperature required if the energy is shared equally by the two particles

and in each case is equal to 32kBT .

33-5. The yield of a nuclear weapon is expressed in terms of the energy released by a megaton

of TNT, where 1.00 megaton of TNT = 4.3× 1015 J. How many kilograms of 23592 U are

required to make a 1-megaton bomb? Assume that each uranium atom releases 200 MeV

of energy as it fragments into a host of smaller nuclides.

33-6. The movie, “Armageddon” depicts an asteroid the size of Texas heading toward Earth.

A team of “experts” plants a nuclear warhead in the asteroid’s interior. The detonation

splits the asteroid into two halves and imparts enough momentum so that each fragment

misses the Earth by passing to either side one day later. Take the mass of the asteroid to

be ma = me/203, since Texas is about 120 the diameter of Earth. The velocity imparted

to each fragment is at least one Earth radius per day (ignoring energy required to

overcome gravity). How many 20-megaton bombs are associated with the combined

kinetic energy given to both fragments? (I don’t recommend the movie.)

In-Class Quiz• Read and think about each problem on Practice Exam IV.• Complete at least two of the problems. (Do not turn in your work.)

Answers to Homework Problems, Physics 123, Spring Term, 2010

1-1. 60.0, 95.0%1-2. 90, 140 cm2

1-3. 150, 400 tons1-4a. 7.0, 10.0 m1-4b. 500, 800 mm1-5. 10, 30 m2-1. 3.50, 6.00 g/cm3

2-2a. 300, 600 kg2-2b. 25, 50 kg2-3a. 35.0, 40.0 N2-3b. −3.5, −7.5 N2-4. 60.0, 80.0%3-1. 1.00× 105, 2.20× 105 Pa3-2. 90, 130 min3-3a. 1.00× 107, 2.00× 107 Pa3-3b. 690, 870 kW3-4. 90, 120 m/s4-1a. 5.0, 15.0 cm4-1b. 300, 600 cm4-1c. 10.0, 16.0 s4-1d. 20.0, 60.0 cm/s4-2a. 10, 30 cm4-2b. 1.0, 3.0 s−1

4-2c. 0.010, 0.025 cm−1

4-2d. 3.0, 4.0 rad4-3. 70, 110 ft/s5-1. 300, 360 m/s5-2a. 2.00× 1011, 3.00× 1011 N/m3

5-3. 1.0× 105, 10.0× 105 ± 0.1× 105

5-4a. 90, 110 m5-4c. 0.040, 0.400 W5-5. 50, 70 dB6-1a. 40.0, 70.0 m/s6-1b. 920, 990 Hz6-2a. 800.0, 910.0 Hz6-2b. 800.0, 910.0 Hz6-2c. 800.0, 910.0 Hz6-3. 1.50, 5.50 s6-4. 1.3, 3.07-1b. 3.00, 4.50 m7-2a. 2.0, 6.0 Hz7-2b. 1.00, 2.50 m/s

7-3a. 520.0, 530.0 Hz7-3b. −0.5, −2.0 %8-1a. 50.0, 70.0 cm8-1b. 60.0, 90.0 m/s8-2a. 2.0, 7.0 cm8-2b. −3.0, −5.0%8-3a. 6.0, 12.0 m8-3b. 3.0, 6.0 m8-4. 450, 700 Hz8-5. 4.0, 6.0 cm9-1. 20.0, 30.0 psi9-2. 100, 200 ◦C9-3a. 700, 1500± 10 N9-3b. 440.0, 445.0 Hz9-4. 20, 90 mm10-1. 1.5, 3.0 km10-2. 40, 70◦C10-3. 20.0, 30.0◦C10-4a. 15.0, 25.0 ◦C10-4b. 0, 0◦C11-1. 50, 80 s11-2. 30, 100◦C11-3. 70, 90◦F11-4a. 0.010, 0.050◦C/s11-4b. 0.5, 2.5◦C/s12-1a. 150, 270 K12-1b. 150, 450 J12-2a. 900, 1600± 10 J12-2b. 900, 1600± 10 J12-3. −250, −650 J12-4a. 5.0, 12.0 L12-4b. 2.00, 5.00 atm13-1. 1.50× 109, 3.00× 109 molecules13-2a. 2.50× 1023, 4.00× 1023

13-2b. 5.50× 10−21, 7.50× 10−21 J13-2c. 1200, 1500± 10 m/s13-2d. 1200, 1500± 10 m/s13-4. 1.5× 1012, 3.5× 1012

14-2a. 6.0, 7.0 L14-2b. 3.0, 5.0 kJ14-2c. 1.10× 106, 1.50× 106 Pa14-3. 20, 60◦F

14-4a. 5.0, 12.0 kJ14-4b. 3.0× 106, 9.5× 106 Pa14-4c. 700, 1200± 10 K14-4d. 5.0, 12.0 kJ15-1a. 30, 50%15-1b. 300, 600◦C15-2a. 100, 999 kPa15-2b. 100, 999 K15-2c. 100, 999 kPa15-2d. 100, 999 K15-2e. 10.0, 99.9 L15-3a. 1000, 9990± 10 J15-3b. −1000, −9990± 10 J15-3c. 1000, 9990± 10 J15-3d. 1000, 9990± 10 J15-4a. 20, 30%15-4b. 20, 30%16-1b. 0.450, 0.55016-3b. 1.50, 2.5016-4. 350, 550 W17-1a. 6.0, 11.0 J/K17-1b. 6.0, 11.0 J/K17-1c. 6.0, 11.0 J/K17-2. 8.0, 13.0 J/K17-3. 4.0, 12.0 J/K17-4a. 1.5× 1027, 3.0× 1027

17-4b. 4.5× 104, 9.5× 104 J/K18-1. 6.0, 11.0 mm18-2a. 4.00× 1014, 5.00× 1014 Hz18-2b. 1.50× 108, 2.50× 108 m/s18-2c. 4.00× 1014, 5.00× 1014 Hz18-2d. 350, 500 nm18-3. 1.5, 4.0◦

18-4a. 1.00, 2.00 m19-1. 30, 50◦

19-2. 60.0, 70.0◦

19-3a. 40, 60 cm19-3b. −0.40, −0.8019-4a. −10, −60 cm19-4b. 1.5, 3.019-5a. 50, 400 cm20-1a. −30.0, −60.0 cm

20-1b. 0.30, 0.5020-2a. 25.0, 35.0 cm20-2c. −25.0, −35.0 cm20-3. 50, 80 cm21-1b. 25.0, 40.0 cm21-1c. −0.40, −0.8021-2b. 40.0, 100.0 cm21-2c. −1.20, −4.0021-3b. −6.0, −60.0 cm21-3c. 1.20, 4.0021-4a. −10.0, −15.0 cm21-4b. 0.50, 0.7021-5a. 40, 80 cm21-5b. 1.0, 2.5 diopters21-6a. −20, −30 cm21-6b. −3.0, −5.0 diopters21-6c. 20, 30 cm22-1a. 4.0, 7.0 cm22-1b. 4.0, 7.022-2a. 60.0, 80.0 mm22-2b. −100, −20022-3a. 120, 160 cm22-3b. 9.0, 13.0 cm22-3c. −20.0, +20.022-4a. 3.00, 3.0022-5b. −10.0, −25.0 cm22-5c. 3.00, 6.00 cm23-1. 600, 800 nm23-2. 500, 600 nm23-3. 0.000, 0.100 W/cm2

23-4a. 0.040, 0.120◦

23-4b. 200, 600± 10 µm24-1. 100, 900 nm24-2b. 6.0, 9.0 µm24-3. 500.0, 700.0 nm24-4b. −20.0, −30.0 cm24-4c. 2.0, 4.025-1b. 70, 110 µm25-3. 0.1, 1.0 m25-4a. 5, 30◦

25-5a. 3.5× 10−5, 5.0× 10−5 degrees25-6a. 0.5, 2.5 m

26-2. 0.999850c, 0.999950c26-3a. 6.00, 9.50 y26-3b. 1.50, 3.50 y26-3c. 1.50, 3.50 ly26-5. 0.010, 0.070 nm27-1c. 1.5, 25.0 y27-1d. 1.5, 25.0 y27-2a. −0.60, −1.10 µs27-2b. 200, 350± 10 m27-3. 0.999940c, 0.999980c27-4. 0.940c, 0.995c28-2a. 1.0× 10−5, 3.0× 10−5

28-2b. 1.0× 10−17, 3.0× 10−17 kg ·m/s28-2c. 20, 50 GeV/c28-2d.0.5× 10−10, 4.0× 10−10 ± 0.2× 10−10

28-3a. 20, 50 MeV28-3b. 0.10, 0.50c29-1a. 4.0× 10−9, 7.0× 10−9 eV29-1b. 0.050, 0.090 eV29-1c. 1.50, 3.00 eV29-2a. 800, 2500± 10 eV29-2b. 0.00050, 0.00150 nm29-4. 4000, 6000± 10 K29-6. 2.00× 1026, 5.00× 1026 W29-7a. 600, 900 nm29-7b. 3.00× 1014, 5.00× 1014 Hz29-7c. 0.50, 1.10 V30-1a. 3.00× 10−13, 9.00× 10−13 m30-1b. 200, 300 keV30-1c. 20, 60 keV30-2. 30.0, 40.0◦

30-3a. 1.00, 5.00 eV30-3b. 400, 500 nm30-4a. 0.200, 0.300 nm30-4b. 3.00, 4.00 eV30-4c. −5.00, −8.00 eV30-4d. −3.00, −4.00 eV31-1a. 0.1, 2.0 eV31-1b. 300, 1500± 100 eV31-2. 0.20, 0.60 mm31-3a. 10, 3031-3b. 1.0× 10−17, 2.0× 10−17 s

31-3c. 3.0× 1015, 4.0× 1015 W/cm2

31-5. 1.0× 10−11, 4.0× 10−11 s32-1a. 1.00, 2.00 MeV32-1b. 5.00. 8.00 MeV32-4. 10000, 20000± 100 y32-5a. 5, 50 µg32-5b. 0.5, 2.0 days32-5c. 0.05, 0.40 Ci33-2a. 0.50, 2.50 MeV33-2b. 0.50, 2.50 MeV33-2c. 0.50, 2.50 MeV33-3. 10.0, 20.0 MeV33-4a. 100, 200± 10 keV33-4b. 3.0× 108, 7.0× 108 K33-5. 30, 90 kg33-6. 1.0× 107, 3.0× 107