all assignments (2016)

8/15/2019 All Assignments (2016)

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EM Assignments: Electromagnetic Waves

Questions:

1. The figure at right shows the electric and magnetic fields of an electromagnetic wave at a certaininstant of time. In which direction is the wave traveling? (HRW10e 33.4Q)

2. If the magnetic field of a light wave oscillates parallel to the y-axis and is given by:

, (a) in what direction does the wave travel, and (b) parallelto which axis does the associated electric field oscillate? (HRW10e 33.1Q)

3. The figure at right shows four long horizontal layers A-D of different materials, with air above and below them. The index of refraction of each material is given. Rays of light aresent into the left end of each layer as shown. In which layer is there the possibility of totallytrapping the light in that layer so that, after many reflections, all the light reaches the right endof the layer? (HRW10e 33.9Q; see also 12Q)

4. If a light beam carried momentum, should a person who turns on a flashlight feel a recoil analogous to the recoil of arifle when it is fired? Why is this recoil not actually observed? (YF12e 32.11)

5. The figure at right shows light reaching a polarizing sheet whose polarizing directionis parallel to the y axis. We plan to rotate the sheet 40 o clockwise about the light’sindicated line of travel. During this rotation will the fraction of the initial light intensity

passed by the sheet increase, decrease, or remain the same if the light is (a) initially un- polarized, (b) initially polarized parallel to the x axis, and (c) initially polarized parallel tothe y axis? (HRW10e 33.3Q reworded)

Problems:

1. An electric heater emits 1.0 kW uniformly in all directions. How close would you have to stand to feel an intensity of

100 W/m 2 ? (HRW5e 34.21; see also HRW10e 33.8)

2. An electromagnetic wave has a frequency of 100 MHz and is traveling in a vacuum. The magnetic field is given by:B ( z , t ) = (10 -8 T) cos ( kz - ù t ) i . (a) Find the direction of propagation of the wave. (b) Find the electric vector E (z,t).(c) Give the Poynting vector and find the intensity of the wave. (T 29.28; see also HRW10e 33.11 & 13)

3. What is the radiation pressure 1.5 m away from a 500 W light bulb? Assume that the surface on which the pressure isexerted faces the bulb and is perfectly absorbing and that the bulb radiates uniformly in all directions. (HRW10e 33.21)

4. The earth (radius R = 6.4 x 10 6 m) orbits the sun at an average distance D = 1.5 x 10 11 m. (a) What fraction of theelectromagnetic radiation emitted by the sun is intercepted by the earth? (b) The intensity of sunlight striking the earth'supper atmosphere is known as the solar constant. What is the solar constant? (NOTE: The sun has power 3.83 x 10 26

W.) (c) Calculate the force on the earth due to this radiation if all of it is absorbed and none of it is reflected. (d) Whatis the ratio of the force of radiation on the earth to the gravitational force on the earth due to the Sun? ( D. Brown; seealso HRW10e 33.26, 29, & 30)

5. Small particles might be blown out of planetary systems around other stars by the radiation pressure of starlight.Assume spherical particles of radius r and density 1.0 g/cm 3 that absorb all the radiation in a cross-sectional area ð r 2 .Assume they are a distance D from a solar-type star which has power 3.83 × 10 26 W and mass 1.99 × 10 30 kg. How smallmust a particle be ( i.e. what is r ) for the radiation force of repulsion to exactly balance the gravitational attraction of thestar? (T 29.47; see also HRW10e 33.24)


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6. Two polarizing sheets have their transmission axes crossed so that no light gets through. A third sheet is inserted between the first two such that its transmission axis makes an angle è with that of the first sheet. Un-polarized light of intensity I o is incident on the first sheet. Find the intensity of the light transmitted through all three sheets if (a) è = 45

o

and (b) è = 30 o . (HRW10e 33.84 extended; see also HRW10e 33.43 & 44)

7. We have a stack of N+1 ideal polarizing sheets with each sheet rotated by an angle of ð /2N radians with respect tothe preceding sheet. A plane linearly polarized light wave of intensity I o is incident normally on the stack. The incidentlight is polarized along the transmission axis of the first sheet and therefore normal to the transmission axis of the lastsheet in the stack. (a) What is the transmitted intensity through the stack in general? (b) For 3 sheets (N=2), what is thetransmitted intensity? (c) For 101 sheets, what is the transmitted intensity? (d) What is the direction of polarization of the transmitted beam in each case? (T 30.39; see also HRW10e 33.37)

8. A bottom-weighted vertical pole extends 2.0 m above the bottom of a swimming pool and0.5 m above the water. Sunlight is incident at 45 o. What is the length of the shadow of the

pole on the bottom of the pool? (HRW10e 33.55 modified)

9. A ray of light is incident normally on the face ab of a glass prism (n = 1.52) as shown

in the figure at right. What is ö so that the ray is totally reflected at face ac if the prismis immersed in (a) air? (b) water? (HRW10e 33.59; see also 63 & 65)

10. A point source of light is located 5 m below the surface of a large pool of water. Find the area of the largest circle onthe pool's surface through which light coming directly from the source can emerge. (T30.25; see also HRW10e 33.62)

11. A signal rocket explodes at a height of 200 m above a ship on the surface of a smooth lake. The explosion sends outsound waves in all directions. Since the speed of sound in water (1500 m/s) is larger than the speed of sound in air (340m/s), a sound wave can suffer total reflection at a water surface if it strikes at a sufficiently large angle of incidence. At

what minimum distance from the ship will a sound wave from the explosion suffer total reflection? (OH 37.12)

12. The critical angle for total internal reflection for a substance is 45 o. What is the polarizing angle for this substance?(T 30.19; see also HRW10e 33.69)

Brief Answers to Questions:

1. into the page2. (a) + z direction (b) x-axis3. Layer B4. yes - it happens - but is too small to be noticed compared to the other forces that act on a person5. (a) same; (b) increase; (c) decrease


7/15

OP Assignments: Optics

Questions:

1. The figure at right shows a fish and a fish stalker in water. (a) Does the stalker see the fish inthe general region of point a or point b? (b) Does the fish see the (wild) eyes of the stalker inthe general region of point c or point d ? (HRW10e 34.1Q)

2. For what range of object positions does a concave spherical mirror form a real image? What about a convex sphericalmirror? (YF 12e Q34.6)

3. When a T. rex pursues a jeep in the movie Jurassic Park , we see a reflected image of the T. rex via a side-view mirror,on which is printed the (then darkly humorous) warning: “Objects in mirror are closer than they appear.” Is the mirror flat, convex, or concave? (HRW10e 34.5Q)

4. Can an image formed by one reflecting or refracting surface serve as an object for a second reflection or refraction?Does it matter whether the first image is real or virtual? Explain. (YF12e Q34.19)

5. The figure at right shows four thin lenses, all of the same material, with sides that either are flat or have a radius of curvature of magnitude 10 cm. Without written calculation, rank

the lenses according to the magnitude of the focal length, greatest first. (HRW10e 34.9Q)

Problems:

1. You are standing 5.0 m in front of a plane mirror. You see an object in the mirror. It is 5.0 m to your right and 1.0 mcloser to the mirror. For what distance must you focus a camera in order to photograph the object? (based on HR 44.2; seealso HRW10e 34.1)

2. An object is p centimeters in front of a concave mirror of focal length 20 cm. Where does the image form and what isit like (magnification? type - real or virtual? erect or inverted?) if: (a) p = +10 cm? (b) p = +30 cm? (HRW6e 35.10 a,c )

3. A virtual image forms 10 cm from a spherical mirror with radius of curvature r = - 40 cm. (a) What type of mirror isthis? (b) Where is the object? (HRW6e 35.10e)

4. An object is 10 cm from a thin lens with radii of curvature r 1 = +30 cm and r 2 = -30 cm. What type of lens is this?Where does the image form? What type of image is it (real - virtual - erect - inverted)? What is its magnification?Assume that the glass in the lens has index of refraction 1.5 . (HRW6e 35.24e; see also HRW10e 34.41 & 68)

5. Repeat problem # 4 with r 1 = -30 cm and r 2 = -60 cm. (HRW6e 35.24g)

6. An erect object is placed in front of a converging lens at a distance equal to twice the focal length f 1 of the lens. Onthe other side of the lens is a concave mirror of focal length f 2 separated from the lens by a distance 2( f 1 + f 2). (a) Findthe location, type, orientation, and lateral magnification of the final image, as seen by an eye looking toward the mirror through the lens and just past (to one side of) the object. (b) Draw a ray diagram to locate the image. (HRW6e 35.52;see also HRW10e 34.91 & 105 & 106)


1. (a) point a ; (b) point c2. Object distances p > f for a concave mirror. Never for a convex mirror.3. Convex; 4. Yes; No; 5. d (infinite) > a = b > c


8/15

IF Assignments: Interference

Questions:

1. If you move from one bright fringe in a two-slit interference pattern to the next one farther out, (a) does the pathlength difference Ä L increase or decrease and (b) by how much does it change, in wavelengths ë ? (HRW10e 35.2Q)

2. Does the spacing between fringes in a two-slit interference pattern increase, decrease, or stay the same if (a) theslit separation is increased, (b) the color of the light is switched from red to blue, and (c) the whole apparatus issubmerged in cooking sherry? (d) If the slits are illuminated with white light, then at any side maximum, does the

blue component or the red component peak closer to the central maximum? (HRW10e 35.1Q)

3. The figure at right ( Fig. 35-29 in HRW10e ) shows the transmission of light through athin film in air by a perpendicular beam (tilted in the figure for clarity). (a) Did ray r 3undergo a phase shift due to reflection? (b) In wavelengths, what is the reflection phaseshift for ray r 4 ? (c) If the film thickness is L, what is the path length difference betweenrays r 3 and r 4 ? (HRW10e 35.12Q)

4. Figure (a) at right ( Fig. 35-27 in HRW7e ) shows the cross section of a vertical thin filmwhose width increases downward because gravitation causes slumping. Figure (b) atright is a face-on view of the film, showing four bright (red) interference fringes thatresult when the film is illuminated with a perpendicular beam of red light. Points in thecross section corresponding to the bright fringes are labeled. In terms of the wavelengthof light inside the film, what is the difference in film thickness between (a) points a & band between points b & d ? (HRW10e 35.10Q)

5. A very thin soap film ( n = 1.33), whose thickness is much less than a wavelength of visible light, looks black; it appears to reflect no light at all. Why? By contrast, an equally thin layer of soapy water on glass (index 1.50) appears quite shiny. Why is there a difference? (YF12e 35.14Q)

Problems:

1. The wavelength of yellow sodium light in air is 589 nm. What is (a) its frequency, (b) its wavelength in glass,and (c) its velocity in glass? Assume an index of refraction of 1.52 for the glass. (HRW10e 35.6)

2. Two waves of light in air, of wavelength 600.0 nm, are initially in phase. They then travelthrough plastic layers with L 1 = 4.00 ì m, L 2 = 3.50 ì m, n1 = 1.40, and n 2 = 1.60. (a) In

wavelengths, what is their phase difference after they both have emerged from the layers? (b)If the waves later arrive at some common point, what type of interference do they undergo?(HRW10e 35.13)

3. In a lecture demonstration, laser light is used to illuminate two slits separated by 0.5 mm, and the interference pattern is observed on a screen 5 m away. The distance on the screen from the centerline to the thirty-seventh brightfringe is 25.7 cm. What is the wavelength of the light? (T33.15)


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4. A double-slit experiment uses a helium-neon laser with a wavelength of 633 nm and a slit separation of 0.12mm. When a thin sheet of plastic is placed in front of one of the slits, the interference pattern shifts by 5.5 fringes.When the experiment is repeated under water, the shift is 3.5 fringes. Calculate (a) the thickness of the plastic sheetand (b) the index of refraction of the plastic sheet. (T33.67; see also HRW10e 35.27)

5. In a double-slit arrangement the distance between slits is 5.0 mm and the slits are 1.0 m from the screen. Twointerference patterns can be seen on the screen, one due to light of 480 nm and the other 600 nm. What is theseparation on the screen between the third-order interference fringes of the two different patterns? (HRW10e 35.21;see also 26)

6. Two radio beacons emit waves of frequency 2.0 x 10 5 Hz. The beacons are on a north-south line, separated by adistance of 3.0 km. The southern beacon emits waves 1/4 of a cycle later than the northern beacon. Find theangular directions for constructive interference. Measure angles relative to the east-west line and assume that thedistance between the beacons and the point of observation is large. (OH38.22)

7. In the figure at right, A and B are identical radiators of waves that are in phase and of the same wavelength ë . The radiators are separated by distance d = 3.00 ë . Find thegreatest distance from A, along the x axis, for which fully destructive interference occurs.(HRW10e 35.25 modified)

8. A thin layer of a transparent material with an index of refraction of 1.30 is used as anonreflective coating on the surface of glass with an index of refraction of 1.50. Howthick should the material be in order for the glass to be nonreflecting for light of wavelength 600 nm (in a vacuum)?

(T33.7; see also HRW10e 35.35)

9. White light reflected at perpendicular incidence from a soap bubble has an interference maximum at 600 nmand a minimum at the violet end of the spectrum, with no other minimum in between. If n = 1.33 for the film,calculate its thickness, assumed uniform. (HRW10e 35.53 - modified; see also 36 & 40)

10. In the figure at right (top) a broad beam of light of wavelength 600 nm

is sent directly downward through a glass plate (n = 1.5) that, with a plastic plate (n = 1.2), forms a thin wedge of air which acts as a thin film. Anobserver looking down through the top plate sees the fringe pattern shownin the figure (bottom), with dark fringes centered on ends A and B. (a)What is the thickness of the wedge at B? (b) How many dark fringes willthe observer see if the air between the plates is replaced with water (n =1.33)? (HRW6e 36.61; see also HRW10e 35.71-74)


1. Ä L increases by one wavelength.

2. (a) decreases; (b) decreases; (c) decreases; (d) blue is closer.

3. (a) no; (b) zero; (c) 2 L

4. (a) half a wavelength; (b) one wavelength

5. Hint: Think about the phase changes for reflection .


10/15

DF Assignments: Diffraction

Questions:

1. The figure at right shows the bright fringes that lie within the centraldiffraction envelope in two double-slit diffraction experiments using the samewavelength of light. Are (a) the slit width a , (b) the slit separation d , and (c)

the ratio d /a in experiment B greater than, less than, or the same as those inexperiment A? (HRW10e 36.12Q)

2. The figure at the right shows a red line (left line) and a green line (rightline) of the same order in the pattern produced by a diffraction grating. If weincreased the number of rulings in the grating by removing tape that hadcovered the outer half of the rulings, would (a) the widths of the lines and (b)the separation of the lines increase, decrease, or stay the same? (c) Would the lines shift to the right, shift to the left,or remain in place? (HRW10e 36.9Q; see also 11)

3. Why can we readily observe diffraction effects for sound waves and water waves, but not for light? Is this

because light travels so much faster than these other waves? Explain. (YF12e Q36.1)

4. Light of wavelength ë and frequency f passes through a single slit of width a . The diffraction pattern is observedon a screen. Which of the following will decrease the width of the central maximum? (a) Decrease the slit width;(b) decrease the frequency f of the light; (c) decrease the wavelength ë of the light. (YF12e Q36.4 modified)

5. In a diffraction experiment with waves of wavelength ë , there will be no intensity minima (that is, no dark fringes) if the slit width is small enough. What is the maximum slit width for which this occurs? (YF12e Q36.5)

Problems:

1. In a single slit diffraction pattern, the distance between the first minimum on the right and the first minimum onthe left is 5.2 mm. The screen on which the pattern is displaced is 80 cm from the slit and the wavelength is 546nm. Calculate the slit width. (HR 46.3; see also HRW10e 36.7)

2. A plane wave of wavelength 590 nm is incident on a slit in a screen, where the aperture of the slit is a = 0.40mm. A thin converging lens of focal length +70 cm is placed between the slit and a second screen and focuses thelight on the screen, i.e. the separation between screens is 70 cm. (This gives the same single slit diffraction patternthat we would get without the lens & with a very large distance between the screens.) (a) How far is the screenfrom the lens? (b) What is the distance on the screen from the center of the diffraction pattern to the firstminimum? (HRW10e 36.3 reworded)

3. The telescope on Mount Palomar has a diameter of 200 inches. We want to use this telescope to resolve theimages of the two stars in a double star system that is 4 light-years distant from Earth. What minimum separationmust the two stars have? (Use ë = 500 nm.) (T 33.45; see also HRW10e 36.29 & 74)

4. The Impressionist painter Georges Seurat used a technique called "pointillism," in which his paintings arecomposed of small, closely spaced dots of pure color, each about 2-mm in diameter. The illusion of the colors

blending together smoothly is produced in the eye of the viewer by diffraction effects. Calculate the minimumviewing distance for this effect to work properly. Use the wavelength of visible light that requires the greatestdistance, so that you're sure the effect will work for all visible wavelengths. Assume that the pupil of the eye has adiameter of 5-mm. (T 33.57; see also HRW10e 36.19 & 28)


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5. How many complete fringes appear between the first minima of the diffraction envelope to either side of thecentral maximum for a double slit pattern if ë = 550 nm, d = 0.15 mm and a = 0.030 mm? (HRW10e 36.43a; seealso 39a&b and 42)

6. Light of wavelength 480-nm falls normally on four slits. Each slit is 2 ì m wide and is separated from the next by 6 ì m. (a) Find the angle from the center to the first point of zero intensity of the single-slit diffraction pattern ona distant screen. (b) Find the angles of any bright interference maxima that lie inside the central diffractionmaximum. (c) Find the angular spread between the central interference maximum and the first interference

minimum on either side of it. (T33.55)

7. Sodium light of wavelength 589 nm falls normally on a square diffraction grating that is 2.0 cm on a side and isruled with 4000 lines per centimeter. The Fraunhofer diffraction pattern is projected onto a screen at 1.5 m by alens of focal length 1.5 m placed immediately in front of the grating. Find (a) the positions of the first two intensitymaxima on one side of the central maximum, (b) the width of the central maximum, and (c) the resolution in thefirst order. (T 33.49)

8. Design a grating that will spread the first-order spectrum through an angular range of 20 o if the spectrum rangesfrom ë 1 = 430 nm to ë 2 = 680 nm. (HRW10e 36.63; see also HRW10e 36.49 & 52)

9. A square diffraction grating with an area of 25 cm2

has a resolution of 22,000 in the fourth order. At what angleshould you look to see a wavelength of 510-nm in the fourth order? (T33.59; see also HRW10e 36.56 & 76)


1. (a) Slit width is smaller in B than A from .(b) Slit separation is larger in B than A from .(c) Ratio d/a greater for B than for A.

2. (a) Width of lines decreases.(b) Separation of lines remains the same.(c) Remain in place.

3. No - it’s because the other waves have much larger wavelengths. Diffraction effects are not observed for a wave unless theobstacle the wave encounters has dimensions comparable to the wavelength of the wave.

4. Answer (c) only because where m = 1 and .

5. Slit width less than or equal to the wavelength of the light.


12/15

SR Assignments: Special Relativity

Questions:

1. You are standing on a train platform watching a high-speed train pass by. A light inside one of the train carsis turned on and then a little later it is turned off. (a) Who can measure the proper time interval for the durationof the light: you or a passenger on the train? (b) Who can measure the proper length of the train car, you or a

passenger on the train? (c) Who can measure the proper length of a sign attached to a post on the train platform, you or a passenger on the train? (YF12e Q37.1; see also HRW10e 37.6Q)

2. A rocket is moving to the right at the speed of light relative to the earth. A light bulb in the center of aroom inside the rocket suddenly turns on. Call the light hitting the front end of the room event A and the lighthitting the back of the room event B . Which event occurs first, A or B or are they simultaneous, as viewed by(a) an astronaut riding in the rocket and (b) a person at rest on the earth? (YF12e Q37.3)

3. Describe qualitatively (non-mathematically) how the length contraction effect is a consequence of the

disagreement between observers in two frames of reference about the synchronization of clocks in the twoframes. Reason from the two fundamental postulates of Special Relativity. (D. Brown)

4. When a monochromatic light source moves toward an observer, its wavelength appears to be shorter than thevalue measured when the source is at rest. Does this contradict the hypothesis that the speed of light is the samefor all observers? Explain. (YF12e Q37.12)

Problems:

1. The proper mean lifetime of a muon is 2 ì s. Muons in a beam are traveling at 0.999c. (a) What is their mean life-time as measured in the lab? (b) How far do they travel, on the average, before they decay? (T34.5;see also HRW10e 37.4 & 7)

2. The length of a spaceship is measured to be exactly half its rest length. (a) What is the speed of thespaceship relative to the observer’s frame? (b) By what factor do the spaceship’s clocks run slow, compared toclocks in the observer’s frame? (HRW10e 37.12 modified; see also 13 & 15 & 70)

3. In frame S, event B occurs 2 ì s after event A and 1.5 km away from event A. How fast must an observer bemoving along the x-axis so that events A and B occur simultaneously? Is it possible for event B to precedeevent A for some observer? (T 34.53; see also HRW10e 37.25 & 26)

4. A spaceship is moving east at speed 0.90c relative to the earth. A second spaceship is moving west at speed0.90c relative to the earth. What is the speed of one spaceship relative to the other? (T34.31)

5. Two spaceships, each 100 m long when measured at rest, travel toward each other with speeds of 0.85crelative to the earth. (a) How long is each ship as measured by someone on earth? (b) How fast is each shiptraveling as measured by an observer on the other? (c) How long is one ship when measured by an observer onthe other? (d) At time t = 0 on earth, the fronts of the ships are together as they just begin to pass each other.At what time on earth are their ends together? (T34.57)


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6. An armada of spaceships that is 1.00 ly long (in its rest system) moves with speed 0.800c relative to groundstation S. A messenger travels from the rear of the armada to the front with a speed of 0.950c relative to S.How long does the trip take as measured (a) in the messenger’s rest system, (b) in the armada’s rest system,and (c) by an observer in system S? (HRW10e 37.33; see also 31 & 68)

7. A distant galaxy is moving away from the earth with a speed that results in each wavelength received onearth being shifted such that ë = 2 ë o . Find the speed of the galaxy relative to the earth. (T 34.25; see alsoHRW10e 37.36 & 37)

8. Quasars are thought to be the nuclei of active galaxies in the early stages of their formation. A typical quasar radiates energy at the rate of 10 41 W. At what rate is the mass of this quasar being reduced to supply thisenergy? (HRW10e 37.57P; see also 45, 47, & 51)

9. The total energy of a particle is twice its rest energy. (a) Find v/c for the particle. (b) Show that itsmomentum is given by p = %3 mc. (T 34.40)

10. A spaceship of mass 10 6 kg is coasting through space when it suddenly becomes necessary to accelerate.The ship ejects 10 3 kg of fuel in a very short time at a speed of c/2 relative to the ship. (a) Neglecting anychange in the rest mass of the system, calculate the speed of the ship in the frame in which it was initially at rest.(b) Calculate the speed of the ship using classical, Newtonian mechanics. (c) Use your results from part (a) toestimate the change in the rest mass of the system. (T 34.68)

11. A particle of rest mass (1 Mev)/c 2 and kinetic energy 2 Mev collides with a stationary particle of rest mass(2 Mev)/c 2. After the collision, the particles stick together. For the first particle, find (a) its speed before thecollision and (b) its total energy before the collision. For the system, find (c) its initial total momentum, (d) itstotal kinetic energy after the collision, and (e) its rest mass after the collision. (T 34.72)


1. (a) passenger; (b) passenger; (c) you (see also Question HRW10e 37.6: (a) Sam; (b) neither)2. (a) simultaneous; (b) B precedes A

3. Consult lecture notes.

4. No - because the frequency increases in the equation to compensate.


14/15

MP Assignments: Modern Physics

Questions:

1. As a body is heated to a very high temperature and becomes self-luminous, the apparent color of the emittedradiation shifts from red to yellow to white and finally to blue as the temperature increases. Why does the color shift? What other changes in the character of the radiation occur? (YF12e Q38.18)

2. Photon A is from an ultraviolet tanning lamp, and photon B is from a television transmitter. Which has thegreater (a) wavelength, (b) energy, (c) frequency, and (d) momentum? (HRW7e Q38.9)

3. In a photoelectric effect experiment, which of the following will increase the maximum kinetic energy of the photoelectrons; (a) Use light of greater intensity; (b) use light of higher frequency; (c) use light of longer wavelength; (d) use a metal surface with a larger work function. (YF12e Q38.12)

4. If a proton and an electron have the same speed, which has the longer de Broglie wavelength? (YF12eQ39.2)

5. Why can an electron microscope have a greater magnification than an ordinary microscope? (YF12e Q39.15)

6. A hydrogen atom is in the third excited state. To what state (give the quantum number n ) should it jump to(a) emit light with the longest possible wavelength, (b) emit light with the shortest possible wavelength, and (c)absorb light with the longest possible wavelength? (HRW7e Q39.17)

Problems:

1. Suppose that a 100-W source radiates light of wavelength 600 nm uniformly in all directions and that the eye

can detect this light if at least 20 photons per second enter a dark-adapted eye having a 7-mm diameter pupil.How far from the source can the light be detected under these rather extreme conditions? (T35.41; see alsoHRW10e 38.3, 7, & 9)

2. You wish to pick a substance for a photocell operable with visible light. Which of the following will do(work function in parenthesis): tantalum (4.2 eV), tungsten (4.5 eV), aluminum (4.2 eV), barium (2.5 eV),lithium (2.3 eV)? (HRW10e 38.18)

3. Light of wavelength 200 nm falls on an aluminum surface. In aluminum 4.2 eV are required to remove anelectron. What is the kinetic energy of (a) the fastest and (b) the slowest emitted photoelectrons? (c) What isthe stopping potential? (d) What is the cutoff wavelength for aluminum? (HRW10e 38.23; see also 25 & 26)

4. A neutron has a kinetic energy of 10 Mev. What size object is necessary to observe neutron diffractioneffects? Is there anything in Nature of this size that could serve as a target to demonstrate the wave nature of 10-Mev neutrons? (T 36.14; see also HRW10e 38.48 )

5. If the de Broglie wavelength of a proton is 100 fm, (a) what is the speed of the proton and (b) through whatelectric potential would the proton have to be accelerated to acquire this speed? (HRW10e 38.59 )


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6. A microscope using photons is employed to locate an electron in an atom to within a distance of 10 pm.What is the minimum uncertainty in a measurement of the momentum of the electron located in this way?(HRW4e 44.41; see also HRW10e 38.68 )

7. The Sun has a total radiation rate of approximately 3.9 × 10 26 W. The Earth orbits the Sun at a meandistance of 1.5 10 11 m. Assume that the Earth absorbs all the solar radiation that falls on it. Assume that thisheats the surface of the Earth to a uniform temperature T. Assume that the Earth radiates like a black body.And assume that in every second the Earth radiates exactly as much energy as it receives from the Sun in onesecond; i.e. assume that the Earth is in thermal equilibrium. The calculate (a) the surface temperature of theEarth and (b) the region of the electromagnetic spectrum in which the Earth has peak emissivity. (Based on HR 49.6; see also HRW10e 38.42 )

8. A hydrogen atom undergoes a transition from state n = 3 to n = 1. Find the:

a. energy of the emitted photon, b. momentum of the emitted photon, &c. wavelength of the emitted photon.d. What is the recoil speed of the atom?

(HRW7e 39.27; see also HRW10e 39.42 & 52)

9. The binding energy of an electron is the minimum energy required to remove the electron from its groundstate to a large distance from the nucleus. What is the binding energy for the hydrogen atom? (T35.49; seealso HRW10e 39.44)


1. Color shifts because the peak of the emitted energy curve shifts to shorter wavelengths as the temperature increases. Intensity(brightness) also increases with temperature. (See the Mon. May 24 lecture notes & slides.)

2. (a) B; (b) A; (c) A; (d) A.3. (b) only4. electron5. Electrons have a shorter (de Broglie) wavelength than for visible light, and so the electron microscope has higher resolution - byRayleigh’s criterion.

6. (a) n = 3; (b) n = 1; (c) n = 5

all assignments (2016)

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