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# week 13 short assignments 1220

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This 12 page Bundle was uploaded by Dragon Note on Saturday April 23, 2016. The Bundle belongs to 1220 at University of Missouri - Columbia taught by Y Zhang in Spring 2016. Since its upload, it has received 22 views. For similar materials see College Physics II in Physics 2 at University of Missouri - Columbia.

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Date Created: 04/23/16

Short Assignment by 4/18/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Short Assignment by 4/18/2016 Due: 11:00am on Monday, April 18, 2016 To understand how points are awarded, read theng Policy for this assignment. Problem 30.26 Part A How many photons are emitted per second by a laser that emits 2.0 of power at a wavelength ? Express your answer using two significant figures. ANSWER: = 6.4×10 15 photons/s Answer Requested Part B What is the frequency of the electromagnetic waves emitted by a laser? Express your answer using three significant figures. ANSWER: = 4.74×10 14 Answer Requested The Photoelectric Effect Experiment Learning Goal: To understand the experiment that led to the discovery of the photoelectric effect. In 1887, Heinrich Hertz investigated the phenomenon of light striking a metal surface, causing the ejection of electrons from the metal. The classical theory of electromagnetism predicted that the energy of the electrons ejected should have been proportional to the intensity of the light. However, Hertz observed that the energy of the electrons was independent of the intensity of the light. Furthermore, for low enough frequencies, no electrons were ejected, no matter how great the intensity of the light became. The following problem outlines the methods used to investigate this new finding in physics: the photoelectric effect. Suppose there is a potential difference between the metal that ejects the electrons and the detection device, such that the detector is at a lower potential than the metal. The electrons slow down as they go from higher to lower electric potential; since they must overcome this potential difference to reach the detector, this potential is known as the stopping potential. To reach the detector, the initial kinetic energy of an ejected electron must be greater than or equal to the amount of energy it will lose by moving through the potential difference. Short Assignment by 4/18/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Part A If there is a potential differencbetween the metal and the detector, what is the minimum energy that an electron must have so that it will reach the detector? Express your answer in terms of and the magnitude of the charge on the electron, . Hint 1. Relating potential difference to energy Recall that potential difference is defined as the difference in energy for a particle that is moved between two points, divided by the charge of the particle: , where is the potential difference, is the energy difference, and is the charge of the particle. ANSWER: = Correct For the incident light to cause the ejection of an electron, the light must impart a certain amount of energy to the electron to overcome the forces that constrain it within the metal. The minimum amount of energy required to overcome these forces is called the work function . Different metals will have different values f. For an electron to reach the detector, the light must impart enough energy for the electron to overcome both the work function and the stopping potential. Part B Suppose that the light carries energy . What is the maximum stopping potential that can be applied while still allowing electrons to reach the detector? Express your answer in terms , , and . Hint 1. Find the energy of the ejected electron What will be the energy of the electron immediately after it leaves the metal? Express your answer in terms of and . ANSWER: = ANSWER: = Correct Short Assignment by 4/18/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Part C Classical electromagnetism predicted that should have increased as the intensity of the incident light increased. On the contrary, it was found that increased as the frequency of the light increased. The voltage was found to obey the following linear relationship: , where and are numerical constants (representing the slope and the intercept, respectively). By comparing this equation to your answer from Part B, find an expression for the intercept . (Notice that in this equation changes with different light butis a constant of the metal.) Express your answer in terms of and . ANSWER: = Correct Part D In a 1905 paper that later won him a Nobel Prize, Albert Einstein postulated that the energy of light was proportional to its frequency. The constant of proportionality turned out to be Planck's constant : . Using your previous results, and the equation given in Part C, find an expression for in terms of experimentally determinable quantities. Express your answer in terms of the slope and . ANSWER: = Correct Part E Suppose that two sets of values were recorded in this experiment: Stopping potential Frequency ( ) ( ) Using these data, extrapolate a numerical value for Planck's constant . Express your answer in joule-seconds to three significant figures. Hint 1. Finding the value of from the data In Part C, you were told that the voltage is proportional to the frequency of the light that strikes the metal: . A numerical value for the slope can be found from the two data points, using the fact that Short Assignment by 4/18/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... . By entering this value for into the relationship you obtained in Part D, you can obtain a numerical value for Planck's constant . ANSWER: = 6.630×10 −34 Correct Part F Using the data given, find a numerical value for the work functionof the metal. Express your answer in joules to two significant figures. Hint 1. How to determine the constant in a linear equation In Part C, you were told that the voltage is proportional to the frequency of the light that strikes the metal: . In Part E, you should have determined the numerical value of the slope . By substituting this value of into the equation here, along with one of the sets of the data points (for and ) given in Part E, you can determine the numerical value of . Finally, using the relationship between and determined in Part C, you can obtain the numerical value of the work function. ANSWER: −19 = 3.10×10 Correct Score Summary: Your score on this assignment is 66.7%. You received 2 out of a possible total of 3 points. Short Assignment By 4/22/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Short Assignment By 4/22/2016 Due: 11:00am on Friday, April 22, 2016 To understand how points are awarded, read theing Policy for this assignment. Problem 30.54 An X-ray photon with a wavelength of 0.260 scatters from a free electron at rest. The scattered photon moves at an angle of 105 relative to its incident direction. Part A Find the initial momentum of the photon. ANSWER: −24 = 2.55×10 Answer Requested Part B Find the final momentum of the photon. ANSWER: = 2.52×10 −24 Answer Requested ± The de Broglie Relation Learning Goal: To understand de Broglie waves and the calculation of wave properties. In 1924, Louis de Broglie postulated that particles such as electrons and protons might exhibit wavelike properties. His thinking was guided by the notion that light has both wave and particle characteristics, so he postulated that particles such as electrons and protons would obey the same wavelength-momentum relation as that obeyed by light: , where is the wavelength, the momentum, and Planck's constant. Part A Find the de Broglie wavelength for an electron moving at a speed of . (Note that this speed is low enough that the classical momentum formula is still valid.) Recall that the mass of an electron is , and Planck's constant is . Express your answer in meters to three significant figures. ANSWER: Short Assignment By 4/22/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... = 7.270×10 −10 Answer Requested Part B Find the de Broglie wavelength of a baseball pitched at a speed of 41.1 . Assume that the mass of the baseball is . Express your answer in meters to three significant figures ANSWER: −34 = 1.13×10 Answer Requested As a comparison, an atomic nucleus has a diameter of around . Clearly, the wavelength of a moving baseball is too small for you to hope to see diffraction or interference effects during a baseball game. Part C Consider a beam of electrons in a vacuum, passing through a very narrow slit of width . The electrons then head toward an array of detectors a distance 0.9410 away. These detectors indicate a diffraction pattern, with a broad maximum of electron intensity (i.e., the number of electrons received in a certain area over a certain period of time) with minima of electron intensity on either side, spaced 0.496 from the center of the pattern. What is the wavelengthof one of the electrons in this beam? Recall that the location of the first intensity minima in a single slit diffraction pattern for light is , where is the distance to the screen (detector) anis the width of the slit. The derivation of this formula was based entirely upon the wave nature of light, so by de Broglie's hypothesis it will also apply to the case of electron waves. Express your answer in meters to three significant figures. ANSWER: = 1.05×10 −8 Answer Requested Part D What is the momentum of one of these electrons? Express your answer in kilogram-meters per second to three significant figures. ANSWER: = 6.29×10 −26 Short Assignment By 4/22/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Answer Requested This is much smaller than the usual momentum of electrons used for standard diffraction experiments or electron microscopy. Correspondingly, the wavelength that you found in Part C is much larger than that of these electrons. In order to observe the wave nature of the electron, you need to work at scales similar to or smaller than the diameter of an atom. The momentum that you found in Part C could be given to an electron by accelerating it through a potential difference of around . Electron microscopes frequently use accelerating voltages on the order of tens of kilovolts, yielding wavelengths roughly one thousand times smaller. Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 2 points. Short Assignment by 4/20/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Short Assignment by 4/20/2016 Due: 11:00am on Wednesday, April 20, 2016 To understand how points are awarded, read the Grading Policy for this assignment. Photoelectric Effect The following table lists the work functions of a few common metals, measured in electron volts. Metal Cesium 1.9 Potassium 2.2 Sodium 2.3 Lithium 2.5 Calcium 3.2 Copper 4.5 Silver 4.7 Platinum 5.6 Using these data, answer the following questions about the photoelectric effect. Part A Light with a wavelength of 190 is incident on a metal surface. The most energetic electrons emitted from the surface are measured to have 4.0 of kinetic energy. Which of the metals in the table is the surface most likely to be made of? Hint 1. Find the energy of the incident photon How much energy does a 190- photon have? Enter your answer numerically in electron volts to two significant figures. Hint 1. Energy of a photon The energy of a photon of frequency is . Frequency and wavelength are related as . ANSWER: = 6.5 Hint 2. Photoelectric effect The work function is the energy required to remove an electron from the metal. Thus, by conservation of energy, the work function plus the kinetic energy of the emitted electron will be equal to the energy of the incident photon. ANSWER: cesium potassium sodium lithium calcium copper silver platinum Correct Short Assignment by 4/20/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Part B Of the eight metals listed in the table, how many will eject electrons when a green laser ( ) is shined on them? Hint 1. Find the energy of the incident photon How much energy does a 510- photon have? Enter your answer numerically in electron volts to two significant figures. Hint 1. Energy of a photon The energy of a photon of frequency is . Frequency and wavelength are related as . ANSWER: = 2.4 Hint 2. Photoelectric effect The work function is the energy required to remove an electron from the metal. When a photon is absorbed by a metal, the metal will only emit an electron if the energy of the incident photon is greater than the work function of the metal. ANSWER: 0 1 2 3 4 5 6 7 8 Correct Part C Light with some unknown wavelength is incident on a piece of copper. The most energetic electrons emitted from the copper havof kinetic energy. If the copper is replaced with a piece of sodium, what will be the maximum possible kineticof the electrons emitted from this new surface? Enter your answer numerically in electron volts to two significant figures. Hint 1. How to approach the problem Recall that the work function represents the energy required to remove an electron from a metal. If the work function is smaller, less energy is required to remove an electron. ANSWER: = 4.9 Correct Short Assignment by 4/20/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Cutoff Frequency Ranking Task The six metals have the work functions, . Part A Rank these metals on the basis of their cutoff frequency. Rank from largest to smallest. To rank items as equivalent, overlap them. Hint 1. Definition of the work function The minimum amount of energy needed to eject an electron from a metal surface is called the work function) of the metal. Hint 2. Interpreting the cutoff frequency Since the energy of a single photon is proportional to its frequency, frequencies below a cutoff frequency do not have enough energy to free electrons from metal surfaces. The larger the work function of a metal, the larger the energy of the photon needed to free an electron, so the larger the cutoff frequency. ANSWER: Correct Part B Rank these metals on the basis of the maximum wavelength of light needed to free electrons from their surface. Rank from largest to smallest. To rank items as equivalent, overlap them. Hint 1. Relationship between frequency and wavelength Photons obey the same relationship between frequency and wavelength as classical waves, . Therefore, just as photons above a cutoff frequency are needed to free electrons from a metal surface, photons below a corresponding cutoff wavelength are required to free electrons. ANSWER: Short Assignment by 4/20/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Correct Part C Each metal is illuminated with 400 (3.10 ) light. Rank the metals on the basis of the maximum kinetic energy of the emitted electrons. (If no electrons are emitted from a metal, the maximum kinetic energy is zero, so rank that metal as smallest.) Rank from largest to smallest. To rank items as equivalent, overlap them. Hint 1. Energy conservation Applying energy conservation to the photoelectric effect results in a relationship for the kinetic energy of the ejected electrons. The incoming energy is in the form of photon energy. Some of this energy goes toward freeing the electrons from the metal surface; the remainder (if any) appears as kinetic energy of the ejected electrons. Therefore, , or . Of course, if the energy of the photon is less than the work function,, no electrons are emitted. ANSWER: Short Assignment by 4/20/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... All attempts used; correct answer displayed Score Summary: Your score on this assignment is 92.2%. You received 1.84 out of a possible total of 2 points.

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