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# weekly assignment 13 1220

Mizzou

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This 15 page Class Notes was uploaded by Dragon Note on Saturday April 23, 2016. The Class Notes belongs to 1220 at University of Missouri - Columbia taught by Y Zhang in Spring 2016. Since its upload, it has received 32 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

Weekly Assignment 13 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Weekly Assignment 13 Due: 9:00pm on Tuesday, April 26, 2016 To understand how points are awarded, read the Policy for this assignment. Problem 30.41 Part A What is the frequency of a photon that has the same momentum as a neutron moving with a speed of 170? Express your answer using two significant figures. ANSWER: 18 = 1.3×10 Correct Problem 30.55 An X-ray photon scatters from a free electron at rest at an anglerelative to the incident direction. Part A If the scattered photon has a wavelength of 0.33, what is the wavelength of the incident photon? ANSWER: = 0.325 All attempts used; correct answer displayed Part B Determine the energy of the incident photon. ANSWER: = 3.82 Correct Part C Determine the energy of the scattered photon. Weekly Assignment 13 https://session.masteringphysics.com/myct/assignmentPrintView?displ... ANSWER: = 3.77 Correct Part D Find the kinetic energy of the recoil electron. Express your answer using one significant figure. ANSWER: = 60 Correct The de Broglie Wavelength Part A How does the de Broglie wavelength of an electron change if its momentum increases? Hint 1. The de Broglie wavelength The de Broglie wavelength of an electron of momentum is defined as , where is Planck's constant. That is, the de Broglie wavelength of an electron is inversely proportional to its momentum. ANSWER: The de Broglie wavelength of the electron increases. The de Broglie wavelength of the electron decreases. The de Broglie wavelength of the electron is unchanged. Correct The larger the electron's momentum, the shorter its de Broglie wavelength will be. Part B How does the de Broglie wavelength of an electron change if its kinetic energy decreases? Weekly Assignment 13 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Hint 1. How to approach the question Recall that magnitude of an object's momentum is the product of its mass and speed, . The de Broglie wavelength of an electron, then, can be expressed as , where and are the mass and speed of the electron. Note that the de Broglie wavelength of an electron is inversely proportional to its speed. Use this information along with the relation between kinetic energy and speed of an object to determine how the de Broglie wavelength of an electron changes with its kinetic energy. ANSWER: The de Broglie wavelength of the electron increases. The de Broglie wavelength of the electron decreases. The de Broglie wavelength of the electron is unchanged. Correct The lower the electron's energy, the larger its de Broglie wavelength will be. This agrees with the result from Part A. ± The Wavelength of an Electron An electron has de Broglie wavelength 2.76×10 −10 . Part A Determine the magnitude of the electron's momentum . Express your answer in kilogram meters per second to three significant figures. Hint 1. The de Broglie wavelength For a particle with momentum , its de Broglie wavelength is defined as , where is Planck's constant. ANSWER: −24 = 2.40×10 Correct Weekly Assignment 13 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Part B Determine the kinetic energy of the electron. Express your answer in joules to three significant figures. Hint 1. 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 1. The kinetic energy and momentum of a particle A particle of mass moving with speed has kinetic energy and momentum . ANSWER: ANSWER: = 3.17×10 −18 Correct Part C Determine the electron's kinetic energy in electron volts. Express your answer in electron volts to three significant figures. Hint 1. The relation between electron volts and joules The conversion from electron volts to joules is . ANSWER: = 19.8 Weekly Assignment 13 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Correct Problem 30.68 Diffraction effects become significant when the width of an aperture is comparable to the wavelength of the waves being diffracted. Part A At what speed will the de Broglie wavelength of a 65 student be equal to the 0.77 width of a doorway? Express your answer using two significant figures. ANSWER: = 1.3×10 −35 Correct Part B At this speed, how long will it take the student to travel a distance of 1? (For comparison, the age of the universe is approximately .) Express your answer using two significant figures. ANSWER: = 7.5×10 31 Correct ± Uncertainty in the Atomic Nucleus Rutherford's scattering experiments gave the first indications that an atom consists of a small, dense, positively charged nucleus surrounded by negatively charged electrons. His experiments also allowed for a rough determination of the size of the nucleus. In this problem, you will use the uncertainty principle to get a rough idea of the kinetic energy of a particle inside the nucleus. Consider a nucleus with a diameter of roughly meters. Part A Consider a particle inside the nucleus. The uncertainty in its position is equal to the diameter of the nucleus. What is the uncertainty of its momentum? To find this, use . Express your answer in kilogram-meters per second to two significant figures. Weekly Assignment 13 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Hint 1. The uncertainty relation Recall that Heisenberg's uncertainty principle is written , where is the uncertainty in position, is the uncertainty in momentum, and is Planck's constant divided by . Thus . ANSWER: = 2.10×10 −20 Correct Part B The uncertainty sets a lower bound on the average momentum of a particle in the nucleus. If a particle's average momentum were to fall below that point, then the uncertainty principle would be violated. Since the uncertainty principle is a fundamental law of physics, this cannot happen. Using kilogram-meters per second as the minimum momentum of a particle in the nucleus, find the minimum kinetic energy of the particle. Use kilograms as the mass of the particle. Note that since our calculations are so rough, this serves as the mass of a neutron or a proton. Express your answer in millions of electron volts to two significant figures. Hint 1. Choosing the kinetic energy formula Because this is a rough calculation and the kinetic energy is a small fraction of the rest energy, the classical equation for kinetic energy will suffice. However, if the momentum were a factor of two larger, or if you were calculating to three or more significant figures, the classical equation would no longer be accurate enough, and so the relativistic equation would be necessary. Recall that the classical equation has the form . ANSWER: = 0.81 Correct Compare this to the normal energy scale for electrons in an atom, which is on the order of single electron volts. The characteristic energy scale for the nucleus seems to be roughly one million times that for electrons in an atom. This difference can be seen in calculations of the energy output per unit mass from coal-burning power plants, which utilize chemical energy (energy associated with the electrons of an atom) compared to the energy output from nuclear reactors (power plants that harness the much higher energies of nuclei). ± Simultaneous Measurements of Position and Velocity Part A Weekly Assignment 13 https://session.masteringphysics.com/myct/assignmentPrintView?displ... The x coordinate of an electron is measured with an uncertainty of 0.200 . What is , the x component of the electron's velocity, if the minimum percentage uncertainty in a simultaneous measurement of is 1.00 ? Use the following expression for the uncertainty principle: , where is the uncertainty in the x coordinate of a particle, is the particle's uncertainty in the x component of momentum, and , where is Planck's constant. Express your answer in meters per second to three significant figures. Hint 1. How to approach the problem Since the electron's uncertainty in position is known, one can easily calculate the electron's minimum uncertainty in velocity from the uncertainty principle and the definition of momentum. You can relate the minimum uncertainty in velocity to ; . Hint 2. Find the electron's minimum uncertainty in velocity Find the electron's minimum uncertainty in the x component of the velocity. Express your answer in meters per second to three significant figures Hint 1. Find the electron's minimum uncertainty in momentum Given the uncertainty in the electron's x coordinate, what is the minimum uncertainty in the x component of its momentum? Express your answer in kilogram meters per second to three significant figures. ANSWER: = 5.27×10 −31 ANSWER: = 0.579 ANSWER: = 57.9 Correct Part B Repeat Part A for a proton. Express your answer in meters per second to three significant figures. Weekly Assignment 13 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Hint 1. How to approach the problem The calculations that you did to solve Part A are not limited to the case of an electron. Repeat them for a proton and simply take into account that protons and electrons have different masses. ANSWER: −2 = 3.16×10 Correct Problem 30.75 An excited state of a particular atom has a mean lifetime of 6.0×10 , which we may take as the uncertainty . Part A What is the minimum uncertainty in any measurement of the energy of this state? Express your answer using two significant figures. ANSWER: −25 = 1.8×10 Correct Electron Transitions and Spectral Lines Conceptual Question The spectrum of a hypothetical atom is shown in the figure. Three distinct spectral series are shown, with the center series corresponding to transitions to a final state of . The indicated spectral line corresponds to the transition from an initial state of to the final state . Weekly Assignment 13 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Part A Which of the lettered spectral lines corresponds to the transition froto ? Hint 1. Spectral series In many atoms, the spectral lines corresponding to transitions to the same final state are naturally grouped together into spectral series. (In hydrogen, these series are given the names Lyman, Balmer, Paschen, etc.) In the hypothetical atom under investigation, the same phenomenon occurs, where the middle series corresponds to all of the transitions involving the final sta.e Hint 2. Finding lines within a series Within any series, the lines furthest to the right correspond to the longest wavelength, and hence lowest energy, transitions. As you move to the left within a series, the energy involved in the transition increases. ANSWER: A B C D E F G H Correct Part B Which of the lettered spectral lines corresponds to the transition froto ? Hint 1. Identifying different series Series are arranged such that transitions involving larger amounts of energy are to the left of series involving smaller amounts of energy. Since the energy difference between successive energy levels gets smaller as increases, this allows you to differentiate between different series. Hint 2. Identify the series The series involves transitions with a final energy state . Since the energy difference between successive energy levels gets smaller asincreases, is the series to the right or left of the series? ANSWER: Weekly Assignment 13 https://session.masteringphysics.com/myct/assignmentPrintView?displ... right left ANSWER: A B C D E F G H Correct Part C Which of the lettered spectral lines corresponds to the transitoon fro? ANSWER: A B C D E F G H Correct ± Absorption and Emission in the Hydrogen Atom A monochromatic laser is exciting hydrogen atoms fromstate to the state. Part A What is the wavelengtof the laser? Weekly Assignment 13 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Express your answer to three significant digits in nanometers. Hint 1. Energy levels and conservation of energy Find the energy difference that corresponds to a transition between the state to the state. The amount of energy that the hydrogen atom gains is the energy of the photon that excited it. ANSWER: = 435 Correct Part B Eventually, all of the excited hydrogen atoms will emit photons until they fall back to the ground state. How many different wavelengths can be observed in this process? Hint 1. Hydrogen ground state The ground state of the hydrogen atom corresponds to . Hint 2. Energy level diagram Draw the energy level diagram. This will aid you in figuring out what transitions are possible as the hydrogen atom drops down to the ground state. Hint 3. More on energy levels The hydrogen atom is not required to drop directly from the state to the ground state. It can drop to an intermediate state before it drops down to the ground state. Thus, there are many different wavelengths, each corresponding to a different energy difference, that can be observed. ANSWER: 10 Correct Part C What is the longest wavelength that is observed? Express your answer to three significant digits in nanometers. Hint 1. Long wavelengths The longest wavelength corresponds to the lowest energy photon. Weekly Assignment 13 https://session.masteringphysics.com/myct/assignmentPrintView?displ... ANSWER: = 4059 Correct Part D What is the shortest wavelength observed? Express your answer to three significant digits in nanometers. Hint 1. Short wavelengths The shortest wavelength corresponds to the highest-energy photon. ANSWER: = 95.1 Correct Problem 31.17 Part A How much energy is required to ionize hydrogen when it is = 4 state? ANSWER: = 0.850 Correct Problem 31.39 Part A What are the allowed values when the principal quantum number is ? Check all that apply. ANSWER: Weekly Assignment 13 https://session.masteringphysics.com/myct/assignmentPrintView?displ... -5 -4 -3 -2 -1 0 1 2 3 4 5 Correct Problem 31.41 Part A Give the value of the quantum number , if one exists, for a hydrogen atom whose orbital angular momentum has a magnitude of . ANSWER: =2 =3 =6 no solution exist Correct Part B Give the value of the quantum number , if one exists, for a hydrogen atom whose orbital angular momentum has a magnitude of . ANSWER: Weekly Assignment 13 https://session.masteringphysics.com/myct/assignmentPrintView?displ... =3 =5 =15 no solution exist Correct Part C Give the value of the quantum number , if one exists, for a hydrogen atom whose orbital angular momentum has a magnitude of . ANSWER: =5 =6 =30 no solution exist Correct Part D Give the value of the quantum number , if one exists, for a hydrogen atom whose orbital angular momentum has a magnitude of . ANSWER: =2 =6 =36 no solution exist Correct Problem 31.40 Part A How many different values of are possible when the principal quantum number is= 3? Weekly Assignment 13 https://session.masteringphysics.com/myct/assignmentPrintView?displ... ANSWER: 5 All attempts used; correct answer displayed Score Summary: Your score on this assignment is 92.2%. You received 14.75 out of a possible total of 16 points.

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