Worksheet 1: Velocity of EMR 1) Why did Galileo's attempt to measure speed of light fail? 2) How did Huygens measure distance and time when he used Roemer's data to compute the speed of light? 3) If in Roemer's observations the end of an eclipse of Io took 7:20 on the Spring Solstice and at 7:43 on the Fall Solstice what would be the velocity of light (assuming 3.00 x 10 11 m as the diameter of the earth's? (2.17 x 10 8 m/s) 4) State and explain three of Newton s objections to the wave theory of light? 5) The apparatus is being used in an experiment similar to one conducted by Michelson for calculating the speed of light. The 8-sided mirror is rotating at a rate of 6.0 x 10 4 rpm: 10) Who will hear the voice of a singer first - a person in the balcony 50.00 m away from the stage or a person 3000. km away at home whose ear is next to the radio? Assume that the microphone is 3.000 cm away from the singer and the speed of sound in the auditorium is 343.0 m/s. How much sooner does the one person hear it than the other? (home by 0.1356 s) 11) The distance to a planet is measured using EMR. If the time between the transmission of the signal and the reception of the reflected signal is 8.70 s, how far away is the planet? (1.31 x 10 9 m) Worksheet 2: Interference 1) If a wave λ = 12.0 cm and a = 2.0 cm meets a wave of λ = 5.00 cm and a = 3.0 cm, traveling in the same direction: a) When will the interference pattern start to repeat? b) What is the maximal possible height of the interference pattern? 2) A radio station uses two antennas that are equidistant from the main transmitter. The main transmitter broadcasts a steady tone at a frequency of 6.00 x 10 3 Hz. - June 93 a) If the incident light and the reflected light touch the same section of the mirror, determine the time interval required for the light to return to the rotating mirror. b) Calculate the apparent speed of light for this experiment. c) Calculate the percentage error in your calculated value for the speed of light. (2.5 x 10-4 s, 2.4 x 10 8 m/s, 20 %) 5) What would be the approximate speed in rev/min of Michelson's rotating eight-sided mirror if the fixed mirror was 35.2 km away? (3.20 x 10 4 rev/min) 7) A radio station broadcasts a radio wave whose wavelength is 274 m. a) What is the frequency of the wave? (1.09 x 10 6 Hz) b) Is this radio wave AM or FM? (AM) a) Calculate the wavelength of the emitted signals. b) A home is 19.2 km from one antenna and 23.7 km from the other. If a receiver in the home is tuned to the radio station, is the carrier signal likely to be constructive or destructive. c) What property of electromagnetic radiation is used in answering part b of this question? (5.00 x 10 2 m, partially in phase good) 3) Explain how the reflection of laser light from a compact disc can be used to read the information stored on the disc. 4) A student set up standing waves using a microwave generator. If the frequency of the microwaves is 4.60 x 10 9 Hz, how far apart are the nodes of the standing wave produced? (3.26 x 10-2 m) 5) Why does a soap bubble display a variety of colors if it is a transparent surface? 8) Magnetic resonance imaging or MRI and positron emission tomography or PET scanning are two medical diagnostic techniques. Both employ electromagnetic waves. For these waves, find the ratio of the MRI wavelength (frequency = 6.38 x 10 7 Hz) to the PET scanning wavelength (frequency = 1.23 x 10 20 Hz). (1.93 x 10 12 :1) 9) A radar signal transmitted from the earth and reflected back from the moon was found to take 2.52 s for the round trip. How far, in km, is the moon from the earth? Explain how the presence of the earth's atmosphere will affect the result of your calculations. (3.78 x 10 8 m) 6) Account for the bright and dark pattern of Newton's rings and explain why the central spot is dark? 7) A thin film of oil (n = 1.20) sits on top of water (n = 1.33). Explain the type of reflections that occur on the upper and lower surfaces of the oil. 9) Why does the color pattern in soap bubbles and oil films change over time? S. Molesky @ Notre Dame Page 1
10) Some coated lenses appear greenish-yellow when seen by reflected light. What wavelengths do you suppose they are designed to eliminate completely? Worksheet 3: Polarization: 1) A person sitting at the beach is wearing a pair of Polaroid sunglasses and notices little discomfort due to the glare from the water on a bright sunny day. When she lies on her side, however, she notices that the glare increases. Why? 2) Describe three sources and three uses of polarized light. 3) a) Is there a difference between a polarizer and an analyzer? In other words, can a polarizer be used as an analyzer? b) In order to cut out light, should the axes of two polarizing filters be parallel or perpendicular to each other? 4) What is the difference between non-polarized and planepolarized light? ordinary light polarized light On the diagram, draw arrows to show the orientation of the electromagnetic vibrations of the non-polarized light before striking the surface, and draw arrows to show the vibration plane of the reflected polarized light. 8) When red light in a vacuum is incident at the Brewster angle on a certain type of glass, the angle of refraction is 29.9. What are: (a) the Brewster angle (60.1 o ) (b) the index of refraction of the glass? (1.74) Worksheet 4: Refraction Material Index vacuum 1.00 lucite or plexiglass 1.51 air 1.0003 polyethylene 1.52 water 1.33 sodium chloride 1.53 ethanol 1.36 diamond 2.42 glass fused quartz 1.46 crown glass 1.52 light flint 1.58 polarizing filter On the diagram, draw arrows to show the orientation of electromagnetic vibrations of the non-polarized light before entering the filter and draw arrows to show the vibration plane of the polarized light beyond the filter. 5) A shopper looking into a store window sees reflections from the street, that prevent her from seeing clearly into the store. Being a serious physics student, she thinks about reflection and polarization and remembers that she has polarized sunglasses in her purse. How could she: a) Determine the direction of polarization from the surface? b) In what direction should the light reflected from the vertical window be polarized? 1) What is the name given to the bending of light when it passes from one medium into another? What causes the bending? 2) A ray of light traveling from air into glass makes an angle, to the normal, of 20 o on one side of the surface and of 13 o on the other. How could you use these angles to determine the index of refraction? Do not compute. 3) A ray of light coming from water at an angle of 27 to the normal passes into a diamond surface. Find the angle of refraction to the nearest degree. (14 ) 4) A ray of light enters a clear plastic block as shown in the diagram. 6) The diagram shows an ordinary light ray about to enter a polarizing filter such as in certain sunglasses. 7) Ordinary light strikes a reflecting surface such as pavement on a road. Calculate the time it takes the light to travel along the path AB. (2.29 x 10-9 s) 5) A ray of light passes from air into water at an angle of 30. Find the angle of refraction to the nearest degree. (22 o ) S. Molesky @ Notre Dame Page 2
6) Light is incident upon a piece of diamond at an angle of 45. a) What is the angle of refraction? b) Does glass or diamond bend light more? (17 o, diamond) 7) A ray of light is incident upon a piece of quartz at an angle of 45. What is the angle of refraction to the nearest degree? (29 ) 8) Electromagnetic radiation with a wavelength of 7.05 x 10-7 m in air passes into water. The index of refraction of water is 1.33. a) What is the wavelength of the electromagnetic radiation in water? b) What is the period of the electromagnetic radiation in air? c) What is the period of the electromagnetic radiation in water? (5.30 x 10-7 m, 2.35 x 10-15 s, no change) 18). Explain each of the following. Support your explanation with a diagram. a) stars appear to be higher in the night-time sky than they really are. b) the mountains appear to be closer to Calgary than they really are c) on a hot summer's day there appears to be water on the road 19) Light strikes an equilateral glass prism at an angle of incidence of 35 o. If the index of refraction is 1.51, what angle with respect to the normal does the ray make at the point of emergence? What is the total angular deviation? (42 o ) 9) A ray of light travels from air into a liquid. The ray is incident upon the liquid at an angle of 30.0. The angle of refraction is 22.0. a) What is the index of refraction of the liquid b) Could the substance be any of those on the table above? (1.33, water) 10) On order to determine the index of refraction of a certain material, a student measures the angles in air and in the material for a refracted ray. If the angle in air is 50.0 o and that in the material is 30.0 o, find the index of refraction and the speed of light in the material. (1.54, 1.95 x 10 8 m/s) 11) A light pipe in air will totally internally reflect light if its angle of incidence is at least 40.0. If the light pipe is placed in water, what is the smallest angle of incidence for total internal reflection? (58.7 o ) 12) The critical angle for a certain liquid-air surface is 67. What is the index of refraction of the liquid? (1.09) 13) A pool of water is 2.00 m deep. Find its apparent depth when viewed vertically through the air. (1.50 m) 14) What is the critical angle for a diamond-ethanol interface? (For diamond n = 2.42 and for ethanol n = 1.36 (34.2 o ) 16) Calculate the critical angle for diamond in air. Diamond has a refractive index of 2.42. (24.4 o ) 17) Light is incident on an equilateral crown glass prism at 45 o angle to one face. Calculate the angle at which light emerges from the opposite face. Assume that n = 1.56 (58 o ) 20) Show by means of a diagram and explanation why: a) a star in the night sky appears to be higher than it actually is. b) the sunset is always red and never blue. 21) Light strikes the isosceles prism (n = 1.52) shown below with an incident angle of 28 o. What angle with respect to the normal does the ray make at the point of emergence? What is the total angular deviation? (11 o ) Worksheet 5: Dispersion and the Doppler Effect 1) Explain with the aid of a diagram what happens when a rainbow is formed. 2) Why do the colors of the rainbow separate when they pass through a medium other than a vacuum? 3) Why is the sky blue and sunrises and sunsets always red and not green or yellow? 4) Why do molecules in the air scatter light? 6) What can be inferred from the inversion of colors whenever there is a double rainbow? 7) A Physics 30 student was recently charged with running a red light and presented this case to the judge. He reasoned that although the light had changed to red (λ = 700 nm), it S. Molesky @ Notre Dame Page 3
appeared green to him due to the Doppler effect. Since he was approaching the light, the wavelength changes according to the formula: v + vd f' = f v - vs If the wavelength of green light is 500 nm would the judge, an honours physics graduate accept his plea? Show by calculation which way the decision went. (1.20 x 10 5 km/s) 8) Light from distant galaxies is said to be red-shifted. Explain what this means. If a yellow star (λ = 5.75 x 10-7 m ) is moving away from the earth at 0.0025 c, what will be its apparent wavelength? (5.8 x 10-7 m) 9) Spectral lines 1, 2, 3, 4, and 5 represent a bright line from the helium spectrum. Line 1 was observed with a standard stationary source in a laboratory. Lines 2, 3 4 and 5 represent the same line observed from moving sources. 4) If a concave mirror produces a real image, is the image necessarily inverted? 5) Fill in the following summary chart for the images formed by convex and concave mirrors. Classify the image as real or virtual, erect or inverted, smaller, larger or same sized and tell where the image is formed Object distance Concave Convex Between F and V At F Betwee n F and C At C Beyond C At infinity 6) What are the differences between real and virtual images formed by mirrors? 7) Draw a ray diagram to locate the image of a candle 20.0 cm long in a concave mirror of 50 cm focal length. The candle is 30 cm from the mirror. a) What is the distance to the image? b) What is the size of the image? (a. d i = - 75 cm, b. 50 cm) 8) What is the radius of curvature of a mirror which produces a smaller, erect image 20.0 cm in the mirror when an object is placed 120 cm in front of the mirror? (r = -48.0 cm) a) Find the frequency of the helium line in the diagram b) Two sources traveling with constant but different velocities approach a stationary observer. The observer examining the spectral line of the source with the greater velocity would see which of the lines shown in the diagram? c) The spectra lines 4 and 5 could have been emitted by what type of source? d) The apparent shift of the radiation is a phenomenon whose explanation is credited to which scientist? Worksheet 6: Reflection and Mirrors 1) The radius of curvature of a spherical mirror is 50 cm. What Is the focal length? (25 cm) 2) With the aid of a diagram show why an object's image appears to be as far behind the mirror as the object is in front of the mirror surface. 9) An object is placed 30. cm in front of a curved mirror. A real image is formed at a distance of 10. cm from the mirror. What is the radius of curvature of the mirror? (r = 15 cm) 10) A diverging mirror with a focal length of -5.00 cm produces an image of an object 15.0 cm from the mirror. a) What is the distance of the image from the mirror? (-3.75 cm) b) What is the magnification? (0.25 x) 11) A convex mirror has a radius of curvature of 60. cm. Describe the image in each of the following cases: (a) object at 10. cm (0.75 x mag) (b) object at 20. cm (0.60 x mag) 3) What is spherical aberration? State two methods of reducing spherical aberration. S. Molesky @ Notre Dame Page 4
Worksheet 7: Refraction and Lenses 1) Match the following diagrams of lenses to the terms which describe their shapes: 7) The focal length of a lens is determined, using red light from a helium-neon laser. How will the focal length compare with that measured using the green light from an argon laser? What term explains this effect? 8) A small insect is placed 4.00 cm from a simple magnifying glass whose focal length is 5.00 cm. a) Calculate the distance from the image from the lens. (-20.0 cm) b) Is the image real or virtual? Explain. c) How many times is the object magnified? (5.00 x) 1) plano concave 2) convex meniscus 3) double convex 4) concave meniscus 5) double concave 6) plano concave 2) Fill in the following table summarizing the images formed by the two types of lenses. In each case, tell if the image is real or virtual, erect or inverted, smaller, larger or the same size, and where the image is located. 9) A sharp image is located 60.0 mm behind a 50.0 mm focal length converging lens. Calculate the object distance. What is the magnification of the lens? (d o = 300. mm, -0.200 x) 10) A pin is placed 6.0 cm from a diverging lens having a focal length of 4.00 cm. a) Calculate the distance between the image and the lens. (d i = 2.4 cm) b) What is the size of the image? (0.40 x) Worksheet 8: Diffraction Object distance Between F and V At F Betwee n F and 2F At 2F Beyond 2F At infinity 1) Sketch two graphs representing the intensity distributions for the interference patterns produced by single and double slit diffractions. State two differences between the graphs. Converging Diverging 3) A certain lens focuses an object 22.5 cm away as an image 33.0 cm on the other side of the lens. a) What type of lens is this and what is its focal length? (ƒ = 13.4 cm) b) Is the image real or virtual? c) If the image had been located instead 33.0 cm on the same side of the lens as the object, describe the image characteristics (ƒ = 70.7 cm) 4) A leaf is placed 77.0 cm in front of a -98.0 mm focal length lens. Where is the image? Is it real or virtual? (d i = -8.69 cm) 5) A converging lens of diamond and a lens of crown glass have the same shape. Which lens will have the larger focal length? Explain your answer. 2) Monochromatic sodium light (589 nm) passes through a single slit 1.10 x 10-3 cm wide. If a screen is placed 2.00 m from the slit, calculate the positions of the first and second minimums, measured from the centre of the pattern. (10.7 cm and 21.4 cm) 3) Blue light of wavelength 3.5 x 10-7 m falls upon a single slit 0.0195 cm wide. A screen 120.0 cm away reveals a third-order dark band located at what distance from the bright central band? (6.5 x 10-3 m) 4) Blue - green light of wavelength 3.86 x 10-7 m falls upon a single slit 0.0295 cm wide. A screen 120.0 cm away reveals a second-order dark band located at what distance from the bright central band? (3.14 x 10-3 m) 5) If 600 nm light falls on a single slit 1.5 x 10-2 mm wide, what is the angular width of the central maximum? (4.6 ) 6) An interference pattern is formed on a screen when heliumneon laser light (λ = 6.328 x 10-7 m) is directed towards it through two slits. If the slits are 43 µm apart and the screen is 2.5 m away, what will be the separation of adjacent nodal lines? (3.7 cm) S. Molesky @ Notre Dame Page 5
7) When yellow sodium light with wavelength 5.89 x 10-7 m falls on a diffraction grating, its first-order peak on a screen 20.0 cm away falls 2.12 cm from the central peak. When another source is used, it produces a line 3.61 cm from its central peak. What is the wavelength of the second source? What type of light is this? 5) What is the wavelength of a photon that has energy of 1.50 ev? (8.29 x 10-7 m) 6) How many photons are emitted from a 1.50 x 10-3 W laser each second if the frequency of the laser light is 4.75 x 10 14 Hz? (4.76 x 10 15 ) 7) 5.0% of the electric energy supplied to a tungsten filament (incandescent) light bulb is converted into light energy. How many photons are emitted each second by a 40.0 W light bulb? (Assume the wavelength of the photons to be 5.5 x 10-7 m) (5.5 x 10 18 ) 8) A 2.0 W laser (f = 5.8 x 10 14 Hz) is used by doctors in an eye operation. How many photons are emitted by this laser if it operates for 0.12 s? (6.2 x 10 17 ) 8) A student produced an interference pattern using microwaves by placing a double slit grating in front of a microwave generator. If the slits are 5.00 cm apart and the maxima of the pattern are 14.5 cm apart at a distance of 1.50 m from the viewing screen to the slits, at what frequency are the microwaves generated? (6.24 x 10 10 Hz) 9) What is the difference in the interference patterns formed by two slits 1 x 10-4 cm apart and by a diffraction grating containing 1 x 10 4 lines/cm? 10) The first order line of 550 nm light falling on a diffraction grating is observed at a 12 o angle to the central antinodal. How far apart are the slits? ( 2.6 x 10-6 m) Worksheet 9: Black Body Radiation Planck 1) A pendulum swings back and forth with a frequency of 0.100 Hz. What is the difference between the allowed energy values? (That is, what is the energy of the quantum?) (6.63 x 10-35 J) 2) If the pendulum in the first problem has a mass of 25 g, what is the minimum allowed change in height of the pendulum? (note: We are suggesting that if the pendulum can only have certain energy levels, it can only have certain allowed heights - sounds strange! Now you understand why Planck's quantum hypothesis seemed too radical.) (2.7 x 10-34 m) 3) A helium-neon laser produced light with a frequency of 4.74 x 10 14 Hz. What is the energy of the photons produced by this laser? (3.14 x 10-19 J) 4) What is the energy of a light quantum (now known as a photon) that has a wavelength of 6.00 x 10-7 m? (3.32 x 10-19 J) 9) If a laser (λ = 625 nm) emits 2.0 x 10 19 photons each second, what is its power? (6.36 W) 10) What is the wavelength of a photon that has 2.1 ev of energy? (5.9 x 10-7 m) 11) What is the energy of a photon that has a frequency of 4.50 x 10 14 Hz? (2.98 x 10-19 J) Worksheet 10: Photoelectric Effect 1) Light with a wavelength of 5.30 x 10-7 m falls on a photoelectric surface that has a work function of 1.70 ev. What is the maximum energy of the ejected electrons? (1.03 x 10-19 J) 2) A photoelectric surface has a work function of 3.30 x 10-19 J. What is the threshold frequency of the incident light? (4.98 x 10 14 Hz) 3) What is the energy of a photon that has a wavelength of 4.66 x 10-7 m? (4.27 x 10-19 J) 4) A photoelectric surface has a work function of 3.10 ev. What is the maximum wavelength of light that will cause photoelectron emission from this surface? (4.01 x 10-7 m) 5) A photoelectric surface has a work function of 2.75 ev. What is the minimum frequency light needed to cause electrons to be ejected from this surface? (6.64 x 10 14 Hz) 6) Light with a wavelength of 425 nm falls on a photoelectric surface that has a work function of 2.0 ev. What is the maximum speed of the ejected electron? (5.7 x 10 5 m/s) 7) Electrons are ejected from a photoelectric surface with maximum energy of 1.20 ev. If the incident light has a wavelength of 4.10 x 10 2 nm, what is the work function of the surface? (2.93 x 10-19 J) S. Molesky @ Notre Dame Page 6
8) A photoelectric surface requires a light of maximum wavelength of 675 nm to cause electron emission. What is the work function of this surface? (2.95 x 10-19 J) 9) Electrons are ejected from a photoelectric surface with a maximum speed of 4.20 x 10 5 m/s. If the work function of this surface is 2.55 ev, what is the wavelength of the incident light? (4.07 x 10-7 m) 10) Measurements of the kinetic energy of electrons emitted from potassium metal were made at a number of frequencies. The results are shown What is the minimum energy of a light photon that can eject an electron from potassium metal? The work function for silver metal is higher than the work function for potassium metal. Draw in a line of best fit for silver on the grid above. 11) What is the "stopping" voltage of an electron that has 5.40 x 10-19 J of kinetic energy? (3.38 V) 12) A photoelectric surface is illuminated with white light (λ = 4.0 x 10 2 nm to 7.0 x 10 2 nm). What is the maximum kinetic energy of the electrons ejected from the photoelectric surface whose work function is 2.30 ev? (1.3 x 10-19 J) 13) The table below contains some predictions for the behaviour of light incident on a shiny metal sheet. Complete the table by placing a.y. (Yes) or.n. (No) in the appropriate boxes if the prediction is supported by the wave and/or particle model of light. Frequency of Maximum Kinetic Radiation Energy (x 10 14 Hz) (x 10-19 J) 6.21 2.56 5.35 2.00 4.27 1.31 3.49 0.90 2.89 0.45 a) Draw a calculator graph showing the maximum kinetic energy of the electrons ejected from the photoelectric surface and the frequency of the incident light b) Using only your graph, what is: i) the value of Planck s constant (6.25 x 10-34 Js) ii) the work function (1.33 x 10-19 J) iii) the cut off frequency (2.13 x 10 14 Hz) 16) In a photoelectric experiment similar to Millikan's, a student obtained the following data: Frequency of Stopping Voltage Radiation (V s) (x 10 14 Hz) 6.79 0.122 8.81 0.952 10.79 1.781 11.83 2.195 12.65 2.507 13.74 3.027 a) Draw a calculator graph showing the stopping voltage as a function of the frequency of the incident radiation b) Using only your graph, what is: i) the value of Planck s constant (6.63 x 10-34 Js) ii) the work function (4.31 x 10-19 J) iii) the minimal frequency ((6.51 x 10 14 ) 17) In a photoelectric experiment, a student found that when a certain photoelectric surface was illuminated with monochromatic light (f = 6.00 x 10 14 Hz) the stopping voltage was 1.40 V, and when she illuminated the same surface with monochromatic light (f = 5.20 x 10 14 Hz), the stopping voltage was 1.10 V. From this data find a) Planck's constant (6.00 x 10-34 J s) b) the work function of the surface (1.36 x 10-19 J) c) the threshold frequency (2.27 x 10 14 Hz) 18) Radiation with a frequency of 6.67 x 10 14 Hz is used to illuminate a photoelectric surface (W = 2.50 ev). The ejected electrons are now deflected by a perpendicular magnetic field (β = 3.11 x 10-5 T). What is the maximum radius of these deflected electrons? (5.57 x 10-2 m) 14) For a photoelectric cell a stopping voltage of 2.00 V reduced the current through the cell to zero. What is the maximum speed of the electrons ejected from the photoelectric surface when there is no stopping voltage? (8.38 x 10 5 m/s) 15) In a photoelectric experiment similar to Millikan's, a student obtained the following data: Worksheet 11: X-rays and The Compton Effect 1) Electrons are accelerated from rest in a cathode ray tube through a potential difference of 7.5 x 10 3 V. What is the maximum frequency of the x-rays produced? (1.8 x 10 18 Hz) 2) What is the speed of a photon produced by an x-ray tube whose operating potential is 2.70 x 10 4 V? (3.00 x 10 8 m/s) S. Molesky @ Notre Dame Page 7
3) The potential difference in a TV picture tube is 2.0 x 10 4 V. What is the maximum energy of the photons emitted when electrons hit the phosphorescent screen (3.2 x 10-15 J) 4) X-rays can be diffracted using a crystal. If this crystal has spacing of 1.8 x 10-10 m, calculate the smallest angle of deviation of the x-rays that are produced by an x-ray tube using an accelerating voltage of 16 kv. (26 ) 5) The crystal used to diffract x-rays has a spacing of 2.8 x 10-10 m between atoms. If the minimum angle of deviation of the x-rays is 3.5, what is the accelerating voltage used to produce these x-rays? (7.3 x 10 4 V) 6) The minimum wavelength of an x-ray produced in a cathode ray tube can be measured for different accelerating voltages: λ (x10-10 m) V (x10 3 V) 2.8 4.4 3.7 3.3 4.4 2.8 4.9 2.5 5.5 2.2 8.0 1.6 a) Sketch a graph of the wavelength as a function of the accelerating voltage b) Manipulate the data so you can produce a straight line graph on your calculator. Draw a calculator graph of this information. (a = 1.3 x 10-6 Vm, b = -2.5 x 10-11 m, r 2 = 0.99673 ) c) Using your graph, determine Planck's constant and determine the experimental error in the value) ( 6.9 x 10-34 J s, 4.6%) 7) Calculate the momentum of a photon whose wavelength is 1.25 x 10-10 m. (5.30 x 10-24 kg m/s) 8) What is the momentum of an electron travelling at 0.110 c? (3.01 x 10-23 kg m/s) 9) Is the photoelectric equation (E kmax = hf - W) an example of the law of conservation of momentum? Use the following information and calculations to answer this question. When monochromatic light (λ = 415 nm) is incident on a surface (W = 3.50 x 10-19 J), electrons are ejected. a) Calculate the momentum of the incident photon. (1.60 x 10-27 kg m/s) b) Calculate the maximum momentum of the ejected electron. (4.85 x 10-25 kg m/s) 10) A photon collides with a free electron. What is the maximum change in wavelength for this photon? (4.85 x 10-12 m) 11) X rays with a wavelength of 4.50 x 10-12 m are used in a Compton effect experiment and are scattered at an angle of 53.0 o. What is the wavelength of the scattered radiation? (5.47 x 10-12 m) 12) X rays bombard electrons in a metal foil and the x-rays experience a change in wavelength of 3.33 x 10-13 m. What is the scattering angle of the x-rays? (30.4 o ) 13) A photon with a frequency of 4.45 x 10 22 Hz is scattered at an angle of 18.0 o after colliding with an electron. What is the change in the electron's momentum after the collision? (-9.31 x 10-20 kg m/s) 14) An electron is accelerated in an x-ray tube through a potential difference of 3000 V. a) If the x-ray produced is scattered at an angle of 35.5 o, what is the velocity of the scattered Compton electron? (1.07 x 10 6 m/s) b) Using the conservation of momentum in the y-direction find the scattering angle of the electron (73.1 o ) Worksheet 12: De Broglie Matter Waves 1) Calculate the wavelength of an electron that has a speed of 2.25 x 10 7 m/s. (3.23 x 10-11 m) 2) Calculate the wavelength of an electron that has kinetic energy of 7.50 x 10-3 MeV. (1.42 x 10-11 m) 3) What is the frequency of an electron that has a speed of 9.20 x 10 5 m/s? (1.16 x 10 15 Hz) 4) What is the speed of an electron that would have a wavelength of 7.00 x 10 2 nm? (1.04 x 10 3 m/s) 5) Calculate the wavelength of an electron that is accelerated from rest through a potential difference of 1.00 x 10 3 V. (3.88 x 10-11 m) 6) Calculate the wavelength of a ball that has a mass of 1.30 kg and a speed of 3.2 x 10 1 m/s. (1.6 x 10-35 m) 7) What is the kinetic energy of an alpha particle that has a wavelength of 1.46 x 10-15 m? (1.55 x 10-11 J) 8) Calculate the speed of a proton that has a wavelength of 5.88 x 10-12 m. (6.75 x 10 4 m/s) 9) Through what potential difference must an electron be accelerated so that its wavelength is 2.75 x 10-11 m? (1.99 x 10 3 V) 10) What is the kinetic energy of an alpha particle whose wavelength is the same as that of a 1.00 MeV photon? (2.14 x 10-17 J) 11) If an electron is moving in a circular path (R = 0.75 m) through a perpendicular magnetic field (β = 2.3 x 10-4 T), what is the wavelength of the electron? (2.4 x 10-11 m) S. Molesky @ Notre Dame Page 8