MP_Assignment#8_soln

MP_Assignment#8_soln - Assignments 4/23/11 2:36 PM Student...

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Unformatted text preview: Assignments 4/23/11 2:36 PM Student View Summary View Print View withEdit Assignment Answers Diagnostics View Settings per Student MP_Assignment#8 [ Print ] Due: 10:03am on Monday, April 18, 2011 Note: You will receive no credit for late submissions. To learn more, read your instructor's Grading Policy ± The Wavelength of an Electron Description: ± Includes Math Remediation. Find the momentum and the kinetic energy of an electron, given its de Broglie wavelength. An electron has de Broglie wavelength 2.85×10 −10 . Part A Determine the magnitude of the electron's momentum Hint A.1 . The de Broglie wavelength For a particle with momentum , its de Broglie wavelength is defined as , where is Planck's constant. Express your answer in kilogram meters per second to three significant figures. ANSWER: = Part B Determine the kinetic energy Hint B.1 of the electron. Find the kinetic energy as a function of momentum Given the momentum of a particle of mass , what is the kinetic energy of the particle? Hint B.1.1 The kinetic energy and momentum of a particle A particle of mass moving with speed has kinetic energy and momentum . ANSWER: http://session.masteringphysics.com/myct/assignments?courseID=1035557 Page 1 of 11 Assignments 4/23/11 2:36 PM ANSWER: Express your answer in joules to three significant figures. ANSWER: = Part C Determine the electron's kinetic energy in electron volts. Hint C.1 The relation between electron volts and joules The conversion from electron volts to joules is . Express your answer in electron volts to three significant figures. ANSWER: = Single - Slit Diffraction Conceptual Question Description: Conceptual question on the effect of changing variables, such as the width of the slit and the distance between the slit and the screen, on the angles at which the diffraction minima appear. An experiment is conducted in which red light is diffracted through a single slit. Then, each of the following alterations to the original experiment is made, one at a time, and the experiment is repeated. After each alteration, the experiment is returned to its original configuration. http://session.masteringphysics.com/myct/assignments?courseID=1035557 Page 2 of 11 Assignments 4/23/11 2:36 PM A The slit width is halved. The distance between the slits and the screen is B halved. C The slit width is doubled. D A green, rather than red, light source is used. E The experiment is conducted in a water- filled tank. The distance between the slits and the screen is F doubled. Part A Which of these alterations decreases the angles at which the diffraction minima appear ? Hint A.1 Minima of single - slit diffraction The angles of the interference minima in a single- slit experiment obey the relationship , where Hint A.2 is the order of the minima, is the wavelength of the light, and is the slit width. Effect of moving the screen The linear positions of the diffraction minima will change when the location of the viewing screen is changed; however, the angles of the minima are constant. Hint A.3 Wavelength of light in water The wavelength of light is altered by the index of refraction of the material the light passes through. When passing through a material with index , the wavelength of light in the material ( ) compared to the wavelength of light in vacuum ( ) is reduced by a factor of : . Enter the letters of the correct statements in alphabetical order. For example, if statements A and B http://session.masteringphysics.com/myct/assignments?courseID=1035557 Page 3 of 11 Assignments 4/23/11 2:36 PM are corrent, enter AB. ANSWER: CDE Exposure of a Photographic Film Description: Find the maximum wavelength to which a silver bromide (AgBr) emulsion is sensitive. Also, given the energy of a photon, determine its color. Photographic films are simply polyester or acetate sheets coated with a light- sensitive emulsion. The emulsion is composed of several layers of small crystal grains of silver salts suspended in a gelatin base. The silver - salt crystals act as photon detectors; when they are exposed to light, a photochemical reaction takes place. The light energy is absorbed by the crystal, initiating a process of dissociation of the silver - salt molecule. This chemical reaction eventually leads to formation of stable metallic silver atoms. Throughout this problem use = 6.63×10 −34 for Planck's constant, = 3.00×10 8 for the speed of = 6.02×10 23 for Avogadro's number. light, and Part A The typical silver salt used in ordinary photographic films is silver bromide, energy needed to initiate the chemical process of dissociation of a What is the wavelength . The minimum amount of molecule is about 4.00×10 −19 . that a photon may have to be able to initiate the dissociation of a molecule ? Hint A.1 How to approach the problem When a photon strikes a molecule, its energy is absorbed by the molecule. If the incident photon has an energy equal to or greater than 4.00×10 −19 , the reaction. Consider, then, a photon of energy 4.00×10 −19 molecule undergoes a chemical and find its wavelength. Hint A.2 Find the frequency of the photon What is the frequency of a photon of energy 4.00×10 −19 ? Hint A.2.1 Energy of a photon The energy of a photon of frequency is given by , where 6.63×10 −34 is Planck's constant. Express your answer in hertz. ANSWER: = http://session.masteringphysics.com/myct/assignments?courseID=1035557 Page 4 of 11 Assignments 4/23/11 2:36 PM Hint A.3 Find the wavelength of a photon What is the wavelength of a photon of frequency ? ANSWER: Express your answer in nanometers to three significant figures. ANSWER: = Silver bromide- based emulsions are naturally sensitive only to short wavelengths in the violet - blue spectrum. To widen the range of light sensitivity, photographic emulsions are normally treated with special sensitizing dyes. Part B The addition of small amounts of dyes to the emulsion lowers the minimum energy needed to initiate the process of dissociation of the silver - salt molecule. Thus treated emulsions become more sensitive to photons with what sorts of wavelengths and energy? Hint B.1 Energy of a photon Recall that the energy of a photon is inversely proportional to its wavelength. ANSWER: shorter wavelengths and higher energy longer wavelengths and higher energy shorter wavelengths and lower energy longer wavelengths and lower energy Part C In color films, there are separate layers of photosensitive emulsion for each of the three primary colors of emitted light (red, blue, and green). The process of film exposure is again based on absorption of light energy, but now each layer is treated to react to only one- third of the spectrum. For example, the redsensitive emulsion is specially treated to react to light only in the portion of the visible spectrum that http://session.masteringphysics.com/myct/assignments?courseID=1035557 Page 5 of 11 Assignments 4/23/11 2:36 PM includes longer wavelengths. When a single photon of energy 2.89×10 −19 strikes a color film, in what layer of emulsion will it be absorbed ? Hint C.1 How to approach the problem From the energy of the photon, you can determine its wavelength. Recall that the visible wavelength range is 400 to 700 nanometers. Typical wavelengths are 680 nanometers for red light, 550 nanometers for green light, and 450 nanometers for blue light. Hint C.2 Find the wavelength of the photon What is the wavelength of a photon of energy 2.89×10 −19 ? Hint C.2.1 Equation for wavelength Recall that the wavelength of a photon with energy is given by , where 6.63×10 −34 is Planck's constant, 3.00×10 8 is the speed of light in vacuum, and is the wavelength. Express your answer in nanometers to three significant figures. ANSWER: = ANSWER: in the red - sensitive layer in the green - sensitive layer in the blue- sensitive layer Problem 25.16 Description: (a) What is the length (in mm) of the smallest box in which you can confine an electron if you want to know for certain that the electron’s speed is no faster than 10 m/s? Part A What is the length (in ) of the smallest box in which you can confine an electron if you want to know for certain that the electron’s speed is no faster than 10 ? Express your answer using two significant figures. http://session.masteringphysics.com/myct/assignments?courseID=1035557 Page 6 of 11 Assignments ANSWER: 4/23/11 2:36 PM = Problem 25.22 Description: A 1000 kHz AM radio station broadcasts with a power of 20 kW. (a) How many photons does the transmitting antenna emit each second? A 1000 kHz AM radio station broadcasts with a power of 20 kW. Part A How many photons does the transmitting antenna emit each second? ANSWER: Problem 25.24 Description: A typical incandescent light bulb emits approx 3 * 10^18 visible - light photons per second. Your eye, when it is fully dark adapted, can barely see the light from an incandescent light bulb 10 km away. (a) How many photons per second are incident at... A typical incandescent light bulb emits visible - light photons per second. Your eye, when it is fully dark adapted, can barely see the light from an incandescent light bulb 10 away. Part A How many photons per second are incident at the image point on your retina ? The diameter of a dark adapted pupil is . Express your answer using two significant figures. ANSWER: = Problem 25.38 Description: It can be shown that the allowed energies of a particle of mass m in a two - dimensional square box of side L are E_nm =((h^2)/(8mL^2)) ( n^2+m^2 ) . The energy depends on two quantum numbers, n and m, both of which must have an integer value 1, 2,... http://session.masteringphysics.com/myct/assignments?courseID=1035557 Page 7 of 11 Assignments 4/23/11 2:36 PM It can be shown that the allowed energies of a particle of mass are in a two - dimensional square box of side The energy depends on two quantum numbers, and , both of which must have an integer value 1, 2, 3, ... Part A What is the minimum energy for a particle in a two - dimensional square box of side ? ANSWER: = Part B What are the five lowest allowed energies? Give your values as multiples of . Express your answer using two significant figures. Enter your answers in ascending order separated by commas. ANSWER: , , , , = ± Accelerating Electrons Description: ± Includes Math Remediation. Find the potential difference needed to accelerate electrons so that they have a certain wavelength or a certain energy. Part A Through what potential difference must electrons be accelerated (from rest) so that they will have the same wavelength as an x - ray of wavelength 0.180 Hint A.1 ? How to approach the problem When an electron is accelerated through a potential difference, the change in kinetic energy of the http://session.masteringphysics.com/myct/assignments?courseID=1035557 Page 8 of 11 Assignments 4/23/11 2:36 PM electron equals the work done on the electron by the electric force. Thus, you can write an expression that links the accelerating potential to the kinetic energy of the electron. Then, you need to express the kinetic energy of the electrons in terms of their wavelength. Hint A.2 Find the work done on an electron by the electric force An electron, initially at point a , is accelerated to point b through a potential difference . What is the work done on the electron by the electric force? Hint A.2.1 Potential difference From the definition of electric potential as electric potential energy per unit charge, it follows that the potential difference , the difference between the potential at point A and the potential at point B, equals the work done by the electric force when a unit charge moves from A to B. Let be the magnitude of the charge of an electron. ANSWER: Hint A.3 Find the kinetic energy of the electrons What is the kinetic energy 0.180 of an electron that has the same wavelength as an x - ray of wavelength ? Hint A.3.1 Kinetic energy as a function of momentum The kinetic energy of a particle with mass the momentum and velocity is defined as . However, given of the particle, the kinetic energy of the particle can also be expressed as . Hint A.3.2 Find the momentum of the electrons What is the momentum 0.180 ? of an electron that has the same wavelength as an x - ray of wavelength Hint A.3.2.1 The de Broglie wavelength The de Broglie wavelength of a particle with momentum http://session.masteringphysics.com/myct/assignments?courseID=1035557 is defined as Page 9 of 11 Assignments 4/23/11 2:36 PM , = 6.63×10 −34 where Use 6.63×10 −34 is Planck's constant. for Planck's constant. ANSWER: = Use 6.63×10 −34 for Planck's constant and 9.11×10 −31 for the mass of an electron. ANSWER: = Now set the work done on the electron equal to the kinetic energy of the electron and solve for the potential difference. Use 6.63×10 −34 1.60×10 −19 for Planck's constant, 9.11×10 −31 for the mass of an electron, and for the charge on an electron. ANSWER: = Part B Through what potential difference must electrons be accelerated so they will have the same energy as the x - ray in Part A? Hint B.1 How to approach the problem As in the previous part, it is useful to write an expression that links the accelerating potential to the kinetic energy of the electrons. However, this time you need to express the energy of the electrons in terms of the energy of x - rays of given wavelength. Hint B.2 Find the energy of the x - ray What is the energy of an x - ray of wavelength 0.180 http://session.masteringphysics.com/myct/assignments?courseID=1035557 ? Recall that x - rays are electromagnetic Page 10 of 11 Assignments 4/23/11 2:36 PM waves and are subject to the same quantum relations as those of photons of light. Hint B.2.1 The energy of a photon Given the wavelength of a photon, its energy is , where = 3.00×10 8 Use 6.63×10 −34 is the speed of light and = 6.63×10 −34 for Planck's constant and 3.00×10 8 is Planck's constant. for the speed of light in a vacuum. ANSWER: = Now set the work done on the electron by the electric force equal to the energy of the x - ray and solve for the potential difference. Use 6.63×10 −34 1.60×10 −19 for Planck's constant, 3.00×10 8 for the speed of light in a vacuum, and for the charge on an electron. ANSWER: = Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 8 points. http://session.masteringphysics.com/myct/assignments?courseID=1035557 Page 11 of 11 ...
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