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GRE Physics Test Practice Book

GRE Physics Test Practice Book

GRE ® Practice Book

This practice book contains n one actual, full-length GRE® Physics Test n test-taking strategies

Become familiar with n test structure and content n test instructions and answering procedures

Compare your practice test results with the performance of those who took the test at a GRE administration.

www.ets.org/gre Table of Contents Overview...... 3 Test Content...... 3 Preparing for the Test...... 4 Test-Taking Strategies...... 4 What Your Scores Mean...... 5 Taking the Practice Test...... 5 Scoring the Practice Test...... 5 Evaluating Your Performance...... 5 Practice Test...... 7 Worksheet for Scoring the Practice Test...... 87 Score Conversion Table...... 88 Answer Sheet...... 89

Test takers with disabilities or health-related needs who need test preparation materials in an alternate format should contact the ETS Office of Disability Services at [email protected]. For additional , visit www.ets.org/gre/disabilities

Copyright © 2017 by Educational Testing Service. All rights reserved. ETS, the ETS logo, MEASURING THE POWER OF LEARNING, GRADUATE RECORD EXAMINATIONS, and GRE are registered trademarks of Educational Testing Service (ETS) in the United States and other countries. Overview from a nationwide survey of undergraduate physics curricula. The percentages reflect the The GRE® Physics Test consists of about committee’s determination of the relative 100 multiple-choice questions. Testing is emphasis placed on each topic in a typical 2 hours and 50 minutes; there are no separately- undergraduate program. These percentages are timed sections. given below along with the major subtopics This publication provides a comprehensive included in each content category. overview of the GRE Physics Test to help you get Nearly all the questions in the test relate ready for test day. It is designed to help you: to material in this listing; however, there may • Understand what is being tested be occasional questions on other topics not explicitly listed here. • Gain familiarity with the question types I. Classical (20%) • Review test-taking strategies (such as , Newton’s laws, • Understand scoring and , oscillatory , rotational • Practice taking the test motion about a fixed axis, dynamics of of , central and To learn more about the GRE Subject Tests, , three-dimensional visit www.ets.org/gre. dynamics, Lagrangian and Hamiltonian formalism, non-inertial Test Content reference frames, elementary topics in The test consists of approximately 100 five- dynamics) choice questions, some of which are based on II. (18%) such materials as diagrams, graphs, experimental (such as , currents and DC data and descriptions of physical situations. The circuits, magnetic fields in free , aim of the test is to determine the extent of Lorentz , induction, Maxwell’s the test takers’ grasp of fundamental principles and their applications, and their ability to apply these principles in electromagnetic , AC circuits, the solution of problems. Most test questions magnetic and electric fields in ) can be answered on the of a mastery of III. and Phenomena (9%) the first three years of undergraduate physics. (such as wave properties, superposition, The test questions are constructed to simplify interference, , geometrical mathematical manipulations. As a result, neither optics, , Doppler effect) calculators nor tables of are needed. If the solution to a problem requires the use of IV. and Statistical logarithms, the necessary values are included Mechanics (10%) with the question. (such as the , The International (SI) of units is used thermodynamic processes, equations predominantly in the test. A table of information of state, ideal , kinetic , representing various physical constants and a few ensembles, statistical concepts and conversion factors among SI units is presented calculation of thermodynamic quantities, in the test book. Whenever necessary, additional thermal expansion and transfer) values of physical constants are printed with the V. Mechanics (12%) text of the question. (such as fundamental concepts, solutions The approximate percentages of the test of the Schrödinger [including on the major content topics have been square wells, harmonic oscillators by the committee of examiners, with input and hydrogenic ], , angular

GRE ® Physics Test Practice Book 3 | Page momentum, wave function , test. However, the test covers a broad elementary ) range of subject matter, and no one is VI. (10%) expected to be familiar with the content (such as properties of , Bohr of every question. model, energy , atomic • Become familiar with the types of structure, atomic spectra, selection rules, questions in the GRE Physics Test, paying black-body , x-rays, atoms in special attention to the directions. If you electric and magnetic fields) thoroughly understand the directions VII. (6%) before you take the test, you will have (such as introductory concepts, time more time during the test to focus on the dilation, length contraction, simultaneity, questions themselves. energy and momentum, four-vectors and , velocity addition) Test-Taking Strategies VIII. Methods (6%) The questions in the practice test illustrate the (such as data and error analysis, types of multiple-choice questions in the test. electronics, instrumentation, radiation When you take the actual test, you will mark detection, counting statistics, your answers on a separate machine-scorable of charged particles with matter, answer sheet. and optical interferometers, dimensional The following are some general test-taking analysis, fundamental applications of strategies you may want to consider. and statistics) • Read the test directions carefully, and IX. Specialized Topics (9%) work as rapidly as you can without being Nuclear and (such as careless. For each question, choose the nuclear properties, radioactive decay, best answer from the available options. fission and fusion, reactions, fundamental • All questions are of equal value; do not properties of elementary particles), waste time pondering individual questions Condensed Matter (such as you find extremely difficult or unfamiliar. structure, x-ray diffraction, thermal properties, theory of metals, • You may want to work through the test , superconductors), quickly, first answering only the questions Miscellaneous (such as , about which you feel confident, then going mathematical methods, back and answering questions that require applications) more thought, and concluding with the most difficult questions if there is time. Preparing for the Test • If you decide to change an answer, make sure you completely erase it and fill in the GRE Subject Test questions are designed to oval corresponding to your desired answer. measure skills and knowledge gained over a long period of time. Although you might increase • Your score will be determined by the your scores to some extent through preparation number of questions you answer correctly. a few weeks or months before you take the test, Questions you answer incorrectly or for last minute cramming is unlikely to be of further which you mark no answer or more than help. The following information may be helpful. one answer are counted as incorrect. Nothing is subtracted from a score if you • A general review of your college courses answer a question incorrectly. Therefore, is probably the best preparation for the to maximize your score it is better for you

4 | Page GRE ® Physics Test Practice Book to guess at an answer than not to respond answers on the answer sheet. Stop working on the at all. test when 2 hours and 50 minutes have elapsed. • Record all answers on your answer sheet. Answers recorded in your test book will Scoring the Practice Test not be counted. The worksheet on page 87 lists the correct • Do not wait until the last few minutes of answers to the questions. The “Correct Response” a testing session to record answers on your columns are provided for you to mark those answer sheet. questions for which you chose the correct answer. Mark each question that you answer correctly. What Your Scores Mean Then, add up your correct answers and enter your total number of correct answers in the space The number of questions you answered correctly labeled “Total Correct” at the bottom of the page. on the whole test (total correct score) is Next, use the “Total Score” conversion tables on converted to the total reported scaled score. page 88 to find the corresponding scaled score. This conversion ensures that a scaled score For example, suppose you chose the correct reported for any edition of a GRE Physics Test is answers to 67 of the questions on the test. The comparable to the same scaled score earned on “Total Correct” entry in the conversion table of any other edition of the test. Thus, equal scaled 67 shows that your total scaled score is 820. scores on a particular test indicate essentially equal levels of performance regardless of the test Evaluating Your Performance edition taken. GRE Physics Test total scores are reported on Now that you have scored your test, you may a 200 to 990 score scale in ten-point increments. wish to compare your performance with the Test scores should be compared only with performance of others who took this test. other scores on the Physics Test. For example, The data in the worksheet on page 87 are a 780 on the Physics Test is not equivalent to a based on the performance of a sample of the test 780 on the Test. takers who took the GRE Physics Test in the United States. Taking the Practice Test The numbers in the column labeled “P+” on the worksheet indicate the percentages of The practice test begins on page 7. The total examinees in this sample who answered each time that you should allow for this practice test question correctly. You may use these numbers as is 2 hours and 50 minutes. An answer sheet is a guide for evaluating your performance on each provided for you to mark your answers to the test question. test questions. Interpretive data based on the scores earned It is best to take this practice test under timed by a recent cohort of test takers are available on conditions. Find a quiet place to take the test the GRE website at www.ets.org/gre/subject/ and make sure you have a minimum of 2 hours scores/understand. The interpretive data show, and 50 minutes available. for selected scaled score, the percentage of test To simulate how the administration will be takers who received lower scores. To compare conducted at the test center, print the answer yourself with this population, look at the sheet (pages 89 and 90). Then go to the back percentage next to the scaled score you earned cover of the test book (page 86) and follow the on the practice test. Note that these interpretive instructions for completing the identification areas data are updated annually and reported on GRE of the answer sheet. When you are ready to begin score reports. the test, note the time and begin marking your

GRE ® Physics Test Practice Book 5 | Page It is important to realize that the conditions By comparing your performance on this practice under which you tested yourself were not test with the performance of other individuals exactly the same as those you will encounter who took GRE Physics Test, however, you will be at a test center. It is impossible to predict how able to determine your strengths and weaknesses different test-taking conditions will affect test and can then plan a program of study to prepare performance, and this is only one factor that yourself for taking the GRE Physics Test under may account for differences between your standard conditions. practice test scores and your actual test scores.

6 | Page GRE ® Physics Test Practice Book FORM GR1777 77

GRADUATE RECORD EXAMINATIONS®

PHYSICS TEST

Copyright © 2013 by Educational Testing Service. All rights reserved. GRE, GRADUATE RECORD EXAMINATIONS, ETS, EDUCATIONAL TESTING SERVICE and the ETS logos are registered trademarks of Educational Testing Service.

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TABLE OF INFORMATION

−31 Rest of the electron me = 9.11 × 10 kg

Magnitude of the electron e = 1.60 × 10−19 C Avogadro’s number = 6.02 × 1023 NA

Universal constant R = 8.31 J/(mol ∑ K) Boltzmann’s constant k = 1.38 × 10−23 J/K Speed of c = 3.00 × 108 m/s

−34 −15 Planck’s constant h = 6.63 × 10 J ∑ s = 4.14 × 10 eV ∑ s j = h/2 p

hc = 1240 eV ∑ nm

−12 2 2 Vacuum permittivity ⑀0 = 8.85 × 10 C /(N ∑ m )

−7 Vacuum permeability m 0 = 4 p × 10 T ∑ m/A

−11 3 2 Universal gravitational constant G = 6.67 × 10 m /(kg ∑ s ) Acceleration due to g = 9.80 m/s2 1 atmosphere pressure 1 atm = 1.0 × 105 N/m 2 = 1.0 × 105 Pa

1 angstrom 1Å = 1 × 10−10 m = 0.1 nm

Prefixes for Powers of 10 Rotational about center of mass

−15 1 10 femto f Rod 2 12 MA 10−12 pico p 1 Disc 2 10−9 nano n 2 MR −6 2 10 micro m Sphere 2 5 MR 10−3 milli m

10−2 centi c 103 kilo k 106 mega M 109 giga G 1012 tera T 1015 peta P

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PHYSICS TEST

Time—170PHYSICS minutesTEST Time—170100 Questions minutes 100 Questions Directions: Each of the questions or incomplete statements below is followed by five suggested answers or completions. Select the one that is best in each case and then fill in the corresponding space on the answer sheet. Directions: Each of the questions or incomplete statements below is followed by five suggested answers or

completions. Select the one that is best in each case and then fill in the corresponding space on the answer sheet.

1. A net force FA acts on object A, and a net force

1. AFB net acts force on object FA acts B .on The object mass A,of objectand a netB forceis twice the mass of object A, and the acceleration FB acts on object B. The mass of object B is of object B is twice that of object A. Which of twice the mass of object A, and the acceleration the following is true of forces F and F ? of object B is twice that of objectA A. WhichB of the following is true of forces F and F ? 1 A B 2. Two objects sliding on a frictionless , (A) FFB = A 4 as represented above, collide and stick together. 1 2. Two objects sliding on a frictionless surface, (A) FB = 1 F A How much is converted to heat (B) FF= 4 as represented above, collide and stick together. B 2 A during the ? 1 How much kinetic energy is converted to heat (B) F = F B 2 A during1 the collision? (C) FFB = A (A) J 9 (C) F F 1 B = A (A) 1 J (D) FFB = 2 A (B) 9 J 6 1 (D) FB = 2 FA (B) 1 J (E) FF= 4 (C) 6 J B A 2 1 (E) FB = 4 FA (C) 3 J (D) 2 J 4 3 (D) 5 J (E) 4 J 6 5 (E) J 6

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3. Two simple pendulums A and B consist 6. The electric of a plane electromagnetic wave

3. Twoof identical simple massespendulums suspended A and from B consis stringst 6. ofThe wave electric number field kof anda plane angular electromagnetic frequency w wave is of identicallength L Amasse and sL suspendedB , respectively. from strings The two ofgiven wave by number E = E0 (ke x and+ ey angular) sin(kz -frequency wt). Which w ofis pendulums oscillate in equal gravitational fields. the following gives the direction of the associated of length LA and LB , respectively. The two given by E = E0(ex + ey) sin(kz - wt). Which of If the period of pendulum B is twice the period pendulums oscillate in equal gravitational fields. magneticthe following field gives B ? the direction of the associated Ifof thependulum period ofA ,pendulum which of theB is following twice the is period true magnetic(A) ez field B ? of the lengths of the two pendulums? of pendulum A, which of the following is true (B) -e + e (A) ez x y of the lengths1 of the two pendulums? (A) L = L (B)(C) -ex +- ey B 4 A x y 1 (D) e - e (A) L = L (C) -xex - zey B 14 A (B) L = L (D)(E) ey - ez B 2 A x z 1 (E) e - e (B) LB = LA y z 2 (C) LB = LA 7. Which of the following is true about any system

that undergoes a reversible thermodynamic (C) LB = LA 7. Which of the following is true about any system process? (D) LB = 2LA that undergoes a reversible thermodynamic (D) L = 2L (A)process? There are no changes in the internal energy B A of the system. (E) L = 4L (A) There are no changes in the internal energy B A (B) The of the system remains of the system. (E) L = 4L constant during the process. B A (B) The temperature of the system remains (C) The of the system and its constant during the process. remains unchanged. (C) The entropy of the system and its (D) The entropy of the system and its environment remains unchanged. environment must increase. (D) The entropy of the system and its (E) The net work done by the system is zero. environment must increase.

(E) The net work done by the system is zero. 8. For which of the following thermodynamic

processes is the increase in the internal energy 8. For which of the following thermodynamic 4. For the circuit shown in the figure above, what is of an ideal gas equal to the heat added to the gas? the current i through the 2 W resistor? processes is the increase in the internal energy 4. For the circuit shown in the figure above, what is (A)of an Constant ideal gas temperature equal to the heat added to the gas? (A)the current 2 A i through the 2 W resistor? (B) Constant volume (B) 4 A (A) Constant temperature (A) 2 A (C) Constant pressure (C) 5 A (B) Constant volume (B) 4 A (D) Adiabatic (D) 10 A (C) Constant pressure (C) 5 A (E) Cyclic (E) 20 A (D) Adiabatic (D) 10 A (E) Cyclic (E) 20 A 5. By definition, the electric displacement current

through a surface S is proportional to the 5. By definition, the electric displacement current through(A) magnetic a surface Sthrough is proportional S to the (B) rate of change of the through S (A) magnetic flux through S (C) time of the magnetic flux through S (B) rate of change of the magnetic flux through S (D) electric flux through S (C) time integral of the magnetic flux through S (E) rate of change of the electric flux through S (D) electric flux through S

S (E) rate of change of the electric flux through

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9. The root-mean-square speed of in an 12. A single-electron has the electron in the

ideal gas of molar mass M at temperature T is 2 state. The number of allowed values of 9. The root-mean-square speed of molecules in an 12. AA =single-electron atom has the electron in the the quantum number m is (A)ideal gas0 of molar mass M at temperature T is A = 2 state. The numberA of allowed values of

(A) 0 the(A) quantum1 number mA is RT (B) (B) 2 M (A) 1 RT (C) 3 (B) (D)(B) 42 M RT (E)(C) 53 (C) M (D) 4 RT (E) 5 (C) 13. A particle of mass m is confined inside a M 3RT one-dimensional box (infinite square well) of (D) 13. A particle of mass m is confined inside a M length a. The particle’s ground state energy is 3RT one-dimensional box (infinite square well) of (D) which of the following? M length a. The particle’s ground state energy is 3RT (E) which(A) of= the following? M 8ma 3RT (E) (A) =2 M (B) 8ma= 10. Light of frequency n shines on the metal 2 8ma2 surface of a photoelectric tube. Einstein’s theory = 10. Light of variable frequency n shines on the metal (B) 2 of the predicts that the 2 (C) 8=ma surface of a photoelectric tube. Einstein’s theory 2 ma2 of(A) the work photoelectric function of eff theect metal predicts is proportional that the = (C) 22 to the frequency p2 (A) work function of the metal is proportional (D) ma= (B) work function of the metal is proportional 2 2ma22 to the wavelengthfrequency = p (D) 22 (B) work function of the metal is proportional a 2 (C) current in the tube is a linear function of (E) 2=ma to the 2 the wavelength 2mc 22a (C) current in the tube is a linear function of (E) = (D) potential difference necessary to stop the 2 theemitted wavelength electrons is a linear function of 14. The Planck2mc length is the only combination of (D) potentialthe frequency difference above necessary the threshold to stop frequency the the factors G (Newton’s gravitational constant), emitted electrons is a linear function of 14. The is the only combination of (E) potential difference necessary to stop the (Planck’s constant / 2π ), and c (the speed of the frequency above the threshold frequency = emitted electrons is equal to the work thelight) factors that has G units(Newton’s of length. gravitational Which of constant), the (E) potential difference necessary to stop the (Planck’s constant / π ), and c (the speed of function following= gives the Planck2 length? emitted electrons is equal to the work light) that has units of length. Which of the function 1/2 11. Characteristic X rays, appearing as sharp lines followingG gives the Planck length? (A) Ê= ˆ on a continuous background, are produced ËÁ3 ¯˜ 11. Characteristic X rays, appearing as sharp lines c 1/ 2 when high-energy electrons bombard a metal (A) Ê =G ˆ on a continuous background, are produced Á3 ˜ target. Which of the following processes results (B) Ë= Gc ¯ whenin the high-energycharacteristic electrons X rays? bombard a metal c3 target. Which of the following processes results (B) =G 32 in(A) the Electrons characteristic producing X rays? Čerenkov radiation (C) Gc =c (B) Electrons colliding with in the metal (A)(C) Electrons fillingproducing inner Č erenkovshell vacancies radiation that are (C) =c (B) Electronscreated in colliding the metal with atoms phonons in the metal (D) =cG (C)(D) Electrons fillingcombining inner with shell protons vacancies to form that are created in the metal atoms (D) =cG neutrons (E) =G (D)(E) Electrons combiningundergoing with Coulomb protons scattering to form c neutrons (E) =G with nuclei c (E) Electrons undergoing Coulomb scattering with nuclei

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15. The inside of a nonmagnetic 18. Two identical satellites, A and B, are in circular material with a dielectric constant around . The orbital radius of A is 15. The speed of light inside of a nonmagnetic 18. Two identical satellites, A and B, are in circular of 4.0 is twice that of B. Which of the following gives dielectric material with a dielectric constant orbits around Earth. The orbital radius of A is the ratio of the of A to the of 4.0 is 9 twice that of B. Which of the following gives (A) 1.2 ¥ 10 m/s angular momentum of B ? 8 the ratio of the angular momentum of A to the (B)(A) 3.01.2 ¥ 109 m/s 8 angular momentum of B ? (B)(C) 3.01.5 ¥ 108 m/s (A) 4 8 (C)(D) 1.01.5 ¥ 108 m/s (A) 4 7 (B) 2 (D)(E) 7.51.0 ¥ 108 m/s

(E) 7.5 ¥ 107 m/s (B) 2 16. Fermat’s principle of ray optics states, “A ray of (C) 2

light follows the path between two points which 16. Fermat’s principle of ray optics states, “A ray of (C) 2 requires the least time.” This principle can be 1 light follows the path between two points which (D) used to derive which of the following? 12 requires the least time.” This principle can be (D) 1 usedI. toSnell’s derive law which of of the following? (E) 2 2 II. The law of reflection 1 I. Snell’s law of refraction (E) III. Rayleigh’s criterion for resolution 2 II. The law of reflection 19. A 10 kg box slides horizontally without friction

(A)III. IRayleigh’s only criterion for resolution at a speed of 1 m/s. At one point, a constant 19. A 10 kg box slides horizontally without friction (B) II only force is applied to the box in the direction of its (A) I only at a speed of 1 m/s. At one point, a constant (C) III only motion. The box travels 5 m with the constant (B) II only force is applied to the box in the direction of its (D) I and II force applied. The force is then removed, leaving (C) III only motion. The box travels 5 m with the constant (E) II and III the box with a speed of 2 m/s. Which of the (D) I and II force applied. The force is then removed, leaving following gives the magnitude of the applied (E) II and III the box with a speed of 2 m/s. Which of the 17. Consider two identical systems, 1 and 2, each force? following gives the magnitude of the applied consisting of a in circular about a (A) 1 N 17. Consider two identical systems, 1 and 2, each force? much heavier . For system 1 the radius of (B) 2 N consisting of a planet in circular orbit about a (A) 1 N the orbit is a, and for system 2 the radius of (C) 3 N much heavier star. For system 1 the radius of (B) 2 N the orbit is 4a. Which of the following gives (D) 4 N the orbit is a, and for system 2 the radius of (C) 3 N T (E) 5 N the orbit is 1 4a. Which of the following gives (D) 4 N the ratio, , of the period of system 1 to the T2 (E) 5 N 1 20. What is the magnitude of the at the periodthe ratio, of system, of 2the ? period of system 1 to the T2 center of a circular conducting loop of radius a 20. What is the magnitude of the magnetic field at the periodT of system 2 ? that is carrying current I ? (A) 1 = 1 center of a circular conducting loop of radius a T2 that is carrying2 current I ? (A) 1 = 1 (A) 4pm0Ia T1 1 (B) 2 = 2 (A) 4pm0Ia T2 2 T1 1 (B) m0Ia (B) T = T21 21 (C) = (B) m0Ia T2 4 (C) 0 T1 1 (C) T = T21 14 (C) 0m I (D) = (D) o T2 8 T1 1 2a (D) = mo I T1 81 (D) m I (E) 2 = (E) 2a o T2 16 2 T1 1 4mp aI (E) = (E) o T2 16 2 4pa

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21. Let wp , wd , and wa be the cyclotron 24. Which of the following gives the total spin quantum number of the electrons in the ground frequencies of protons, deuterons, and 24. Which of the following gives the total spin 21. Let w p , wd , and wa be the cyclotron state of neutral nitrogen (Z = 7) ? quantum number of the electrons in the ground particles,frequencies respectively, of protons, indeuterons, the same andmagnetic alpha state 1of neutral nitrogen (Z = 7) ? (A) field.particles, The respectively, frequencies arein therelated same by magnetic which 2 1 of the following? (Assume that the particle (A) field. The frequencies are related by which (B) 21 are in the ratio 1 : 2 : 4.) of the following? (Assume that the particle 3 (C)(B) 1 (A)masses w are= win the = wratio 1 : 2 : 4.) 2 p d a 3 (C) (B)(A) w =w >= w 25 p d a (D) 2 (B)(C) w p= w d > < w a 5 p d a (D) 27 (C)(D) w p<= w dd =< w a (E) 2 (E) w w w 7 (D) w p<>w d d = wa (E) 2 ˆ (E) w p> w d = wa 25. Consider a Hermitian operator A with the 22. The of the doubly ionized property Aˆ 4 1 . Which of the ˆfollowing lithium atom Li++ (Z = 3, A = 7) is identical 25. Consider a Hermitian= operator A with the 22. The emission spectrum of the doubly ionized ˆ to that of a hydrogen atom in which all the isproperty an allowed Aˆ 4 pair1 . of Which eigenvalues of the following of A ? lithium atom Li++ (Z = 3, A = 7) is identical = are to that of a hydrogen atom in which all the is(A) an 0,allowed 1 pair of eigenvalues of Aˆ ? (A)wavelengths decreased are by a factor of 9 (B)(A) 1,0, -1 1 (B) decreased by a factor of 49 (C) 1, i (A) decreased by a factor of 9 (B) 1, 1 (C) decreased by a factor of 81 - (B) decreased by a factor of 49 (D) 1, -i (D) increased by a factor of 9 (C) 1, i (C) decreased by a factor of 81 (E) 1 + i, 1 - i (E) increased by a factor of 81 (D) 1, -i (D) increased by a factor of 9 (E) 1 + i, 1 - i (E) increased by a factor of 81 23. In an atom of hydrogen, the electron is bound to 2 a proton. In an atom of positronium, the electron ˆ pˆ 23. In an atom of hydrogen, the electron is bound to T ∫ is bound to a positron instead of a proton. Which 2m2 a proton. In an atom of positronium, the electron ˆ pˆ of the following gives the approximate Rydberg T ˆ∫2 is bound to a positron instead of a proton. Which ˆ p 2m constant for positronium? (For a nucleus of H∫ + Vx()ˆ of the following gives the approximate Rydberg 2pˆm2 me4 Hˆ ∫ + Vx()ˆ infiniteconstant mass, for positronium? R = e (For.) a nucleus of 2m • 24 3 26. Consider the kinetic energy operator Tˆ and the 8eme0 ch infinite mass, R = e .) ˆ • 2 3 26. ConsiderHamiltonian the operatorkinetic energy H above. operator Which Tˆ and the (A) 0.0005R 8e0 ch • ofHamiltonian the following operator pairs ofHˆ above. Which can be (B)(A) 0.00050.5R R • • measuredof the followi simultaneouslyng pairs of observables with no restriction can be (C) 0.999R (B) 0.5R• • onmeasured their precision? simultaneously with no restriction (D) 2R (C) 0.999• R• (A)on their xˆand precision?p ˆ (E)(D) 18802R R• • (B)(A) xˆ and Tpˆ ˆ (E) 1880R • (C) Hˆˆ and ˆ pˆ (B) x and T

(D)(C) HHTˆˆ and pˆ

(D)(E) THˆˆ andand pTˆˆ (E) Tˆ and pˆ

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27. Electromagnetic radiation emitted from a nucleus is most likely to be in the form of 27. Electromagnetic radiation emitted from a nucleus is(A) most gamma likely rays to be in the form of (B) microwaves (A) gamma rays (C) radiation (B) microwaves (D) visible light (C) ultraviolet radiation (E) radiation (D) visible light (E) infrared radiation

28. A sample of nitrogen gas undergoes the cyclic thermodynamic process shown above. Which of the 28. A sample of nitrogen gas undergoes the cyclic following gives the net heat transferred to the system thermodynamic process shown above. Which of the followingin one complete gives thecycle net 1 heat Æ 2 transferred Æ 3 Æ 1 ?to the system (A)in one -80 complete J cycle 1 Æ 2 Æ 3 Æ 1 ? (A)(B) -8040 J (C) 40 J (B) -40 J (D) 80 J (C) 40 J (E) 180 J (D) 80 J (E) 180 J

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29. For an ideal gas, consider the three thermodynamic processes—labeled 1, 2, and 3 —shown in the PV diagram 29. For an ideal gas, consider the three thermodynamic above. Each process has the same initial state and the same processes—labeled 1, 2, and 3 —shown in the PV diagram final volume. One process is adiabatic, one is isobaric, and above. Each process has the same initial state and the same one is isothermal. Which of the following correctly identifies final volume. One process is adiabatic, one is isobaric, and the three processes? one is isothermal. Which of the following correctly identifies the threeAdiabatic processes? Isobaric Isothermal (A) 1 2 3 Adiabatic Isobaric Isothermal (B) 2 1 3 (A) 1 2 3 (C) 2 3 1 (B) 2 1 3 (D) 3 1 2 (C) 2 3 1 (E) 3 2 1 (D) 3 1 2

(E) 3 2 1

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30. The driver of a police car hears an echo of the 34. A rod measures 1.00 m in its rest system. How car’s siren from a wall toward which the car is fast must an observer move parallel to the rod 30. The driver of a police car hears an echo of the 34. A rod measures 1.00 m in its rest system. How moving with a speed of 3.5 m/s. If the speed of to measure its length to be 0.80 m? car’s siren from a wall toward which the car is fast must an observer move parallel to the rod is 350 m/s and the frequency of the siren is moving with a speed of 3.5 m/s. If the speed of to(A) measure 0.50c its length to be 0.80 m? 600 Hz, the driver hears the echo at a frequency sound is 350 m/s and the frequency of the siren is (B) 0.60c nearest to which of the following? (A) 0.50c 600 Hz, the driver hears the echo at a frequency (C) 0.70c (B) 0.60c nearest(A) 588 to Hz which of the following? (D) 0.80c (C) 0.70c (B) 594 Hz (E) 0.90c (A) 588 Hz (D) 0.80c (C) 600 Hz (B) 594 Hz (E) 0.90c (D) 606 Hz 35. A particle decays in 2.0 ms in its rest frame. If (C) 600 Hz (E) 612 Hz the same particle moves at u = 0.60c in the lab (D) 606 Hz 35. A particle decays in 2.0 ms in its rest frame. If frame, how far will it travel in the lab before (E) 612 Hz the same particle moves at u = 0.60c in the lab 31. The first five harmonics produced by an organ decaying? frame, how far will it travel in the lab before pipe open at both ends are 50 Hz, 100 Hz, 150 Hz, 31. The first five harmonics produced by an organ decaying?(A) 150 m 200 Hz, and 250 Hz. Which of the harmonics, pipe open at both ends are 50 Hz, 100 Hz, 150 Hz, (B) 288 m if any, will survive once the pipe is closed at (A) 150 m 200 Hz, and 250 Hz. Which of the harmonics, (C) 360 m one end? (B) 288 m if any, will survive once the pipe is closed at (D) 450 m (C) 360 m one(A) end? 50 Hz, 150 Hz, and 250 Hz only (E) 750 m (D) 450 m (B) 100 Hz and 200 Hz only (A) 50 Hz, 150 Hz, and 250 Hz only (E) 750 m (C) 150 Hz and 250 Hz only 36. The rest mass of a particle with total energy (B) 100 Hz and 200 Hz only (D) 200 Hz only 5.0 GeV and momentum 4.9 GeV/c is (C) 150 Hz and 250 Hz only 36. The rest mass of a particle with total energy (E) None approximately (D) 200 Hz only 5.0 GeV and momentum 4.9 GeV/c is

(E) None approximately 2 32. A refracting consists of two converging (A) 0.1 GeV/c 2 lenses separated by 100 cm. The eye-piece lens (B)(A) 0.20.1 GeV/c2 32. A refracting telescope consists of two converging 2 has a focal length of 20 cm. The angular (C) 0.5 GeV/c2 lenses separated by 100 cm. The eye-piece lens (B) 0.2 GeV/c2 magnification of the telescope is (D) 1.0 GeV/c2 has a focal length of 20 cm. The angular (C) 0.5 GeV/c (E) 1.5 GeV/c2 magnification(A) 4 of the telescope is (D) 1.0 GeV/c2

(B) 5 (E) 1.5 GeV/c2 (A) 4 37. If charge +Q is located in space at the point (C) 6 (B) 5 (x = 1 m, y = 10 m, z = 5 m), what is the total (D) 20 37. If charge +Q is located in space at the point (C) 6 electric flux that passes through the yz-plane? (E) 100 (x = 1 m, y = 10 m, z = 5 m), what is the total (D) 20 electric(A) • flux that passes through the yz-plane? (E) 100 33. The best type of with which to

do over a range of visible (B)(A) 1• 33. The best type of laser with which to wavelengths is Q do spectroscopy over a range of visible (C)(B) 1 wavelengths(A) a dye laser is eQ0 (B) a helium-neon laser (C) (A) a dye laser Q (C) an excimer laser (D) e0 (B) a helium-neon laser 2e (D) a ruby laser Q0 (C) an excimer laser (D) (E) a neodymium-YAG laser 2e (D) a ruby laser (E) 0 0

(E) a neodymium-YAG laser (E) 0

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38. A point charge Q is placed at the center of a hollow, conducting spherical shell of inner radius 38. A point charge Q is placed at the center of a a and outer radius b, as shown above. A net hollow, conducting spherical shell of inner radius charge q is placed on the conducting shell. If the a and outer radius b, as shown above. A net electric potential is assumed to be 0 at , the charge q is placed on the conducting shell. If the magnitude of the electric potential at r, where electric potential is assumed to be 0 at infinity, the a < r < b, is magnitude of the electric potential at r, where (A) 0 a < r < b, is

(A) 0 Q (B) 4pe0r Q (B) 4pe0r Qq+ (C) 4pe r 0 Qq+ (C) 4pe0 r Q (D) 4pe0a Q (D) 4pe0 a Qq+ (E) 4pe b 0 Qq+ (E) 4pe b 0

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39. The figure above shows three arrangements of

one electron (e) and two protons (p). Which of the 39. The figure above shows three arrangements of following is true about the magnitude F of the net one electron (e ) and two protons (p). Which of the electrostatic force acting on the electron due to the following is true about the magnitude F of the net protons? electrostatic force acting on the electron due to the (A)protons? FFF1> 2 > 3 (B) FFF (A) F1 >= F 2 > F 3 (C) FFF (B) F1 >= F 32 > F 23 (D) FFF (C) F12 >> F 31 > F 23 (E) FFF (D) F2 > F 13 > F 31 (E) F > F > F 2 3 1

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40. A AC circuit with impedance Z consists

of resistor R, inductor L, 40. and Acapacitor series AC C ,circuit with impedance Z consists

as shown above. The ideal emf sourceof resistor has R, inductor L, and capacitor C,

as shown above. The ideal emf source has a sinusoidal output given by e = emax sin wt , and the current is given by I Isin(w t f ). =a sinusoidalmax -output given by e = emax sin wt ,

What is the average power dissipatedand the in current the is given by I = I max sin( wt - f).

circuit? ( Irms is the root-mean-squareWhat iscurrent.) the average power dissipated in the

2 circuit? ( Irms is the root-mean-square current.) (A) IRrms

(A) I 2 R 1 rms (B) IR2 2 rms 1 (B) IR2 1 rms (C) IZ2 2 2 rms 1 (C) IZ2 1 rms (D) IR2 cosf 2 2 rms 1 (D) IR2 cos f 1 rms (E) IZ2 cosf 2 2 rms 1 (E) IZ2 cos f 2 rms

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41. The quantum efficiency of a detector is 0.1. If 100 are sent into the detector, one after the 41. The quantum efficiency of a photon detector is 0.1. other, the detector will detect photons If 100 photons are sent into the detector, one after the (A)other, exactly the detector 10 will detect photons (B) an average of 10 times, with an rms deviation of (A) exactly 10 times about 0.1 (B) an average of 10 times, with an rms deviation of (C) an average of 10 times, with an rms deviation of about 1 about 0.1 (D) an average of 10 times, with an rms deviation of about 2 (C) an average of 10 times, with an rms deviation of about 1 (E) an average of 10 times, with an rms deviation of about 3 (D) an average of 10 times, with an rms deviation of about 2 (E) an average of 10 times, with an rms deviation of about 3

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42. Two students perform an in which 44. A particle in an infinite square well has as they drop a ball from rest from a known height 42. Two students perform an experiment in which 44. Aits particleinitial wave in an function infinite squarean equal well mixture has as of above the ground and measure the speed of they drop a ball from rest from a known height the ball just before it strikes the ground. From itsthe initial first three wave orthonormal function an stationaryequal mixture states: of above the ground and measure the speed of repeated measurement, the students estimate Y x,0 = Ay x + y x + y x . the ball just before it strikes the ground. From the( first ) three[ orthonormal1 () 2 () stationary 3 () states:] the in the measured speed of the repeated measurement, the students estimate TheY x value,0 ofA they normalizationx y x yconstant x . A is ball to be 10 percent. Which of the following ()= [ 1 ()+ 2 ()+ 3 ()] the uncertainty in the measured speed of the gives the uncertainty in the kinetic energy of equalThe value to which of the of normalization the following? constant A is ball to be 10 percent. Which of the following the ball? (Assume the uncertainty in the ball’s gives the uncertainty in the kinetic energy of equal 1to which of the following? mass is negligibly small.) (A) the ball? (Assume the uncertainty in the ball’s 13 (A) 5% (A) 1 mass is negligibly small.) (B) 3 (B) 10% (A) 5% 1 2 (C) 15% (B) (B) 10% (D) 20% (C) 1 2 (C) 15% (E) 40% (D) 20% (C) 1 (D) 2 (E) 40% 43. Which of the following wave functions represents

a solution to the Schrödinger equation for an (D) 2 43. Which of the following wave functions represents (E) 3 electron in the 2s state of a hydrogen atom? a solution to the Schrödinger equation for an (E) 3 ( c is a constant and a0 is the Bohr radius.) electron in the 2s state of a hydrogen atom? (A)( c isc acos constantq and a0 is the Bohr radius.)

(A) ccosq Êr ˆ (B) cexp - ËÁa ¯˜ Ê r0 ˆ (B) cexp Á - ˜ ÊË ra ˆ¯ Ê r ˆ (C) c 1--0 exp ËÁ2a ¯˜ ËÁ 2 a ¯˜ Ê r 0 ˆ Ê r 0 ˆ (C) cÁ1 - ˜ exp Á - ˜ ÊË 2ra ˆ¯ ÊË 2 ra ˆ¯ (D) c 1--0 exp0 cos q 45. A matter wave of energy E > 0 and wave ËÁ2a ¯˜ ËÁ 2 a ¯˜ Ê r 0 ˆ Ê r 0 ˆ number k is incident from the left on a potential (D) cÁ1 - ˜ exp Á - ˜ cos q 45. A matter wave of energy E > 0 and wave ÊË 2ra ˆ¯ ÊË 2 ra ˆ¯ well of width L and depth V0. The top of the (E) c 1--0 exp0 sinq exp ()±i f number k is incident from the left on a potential ËÁ2a ¯˜ ËÁ 2 a ¯˜ well is at zero energy and the bottom of the well Ê r 0 ˆ Ê r 0 ˆ well of width L and depth V0. The top of the (E) c 1 - exp - sin q exp (±i f) is at -V , as shown in the figure above. The ËÁ 2a ¯˜ ËÁ 2a ¯˜ well is at0 zero energy and the bottom of the well 0 0 spatial part of the wave function in region 3 has is at -V0, as shown in the figure above. The

spatialwhich ofpart the of following the wave forms?function (A in is region a constant.) 3 has

(A)which Aofe ikxthe following forms? (A is a constant.) (B)(A) Aesinikxkx (B)(C) Asincos kxkx (D)(C) AeAcosik¢ x kx() k <¢ k (D)(E) Aeik-k ¢xx ( (kk real<¢ k ) and positive) (E) Ae -k x (k real and positive)

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46. Spring 1 has force constant k1 and spring 2 has 48. A uniform disk starts from rest and rolls down an inclined plane without slipping. After force constant k , where k> k . If the same 48. A uniform solid disk starts from rest and rolls 46. Spring 1 has force2 constant 1k1 and 2 spring 2 has some time, what fraction of the disk’s total kinetic down an inclined plane without slipping. After externalforce constant force isk applied, where to bothk > springs,k . If the which same energy is rotational kinetic energy? of the following is2 true about1 the extensions 2 some time, what fraction of the disk’s total kinetic external force is applied to both springs, which energy1 is rotational kinetic energy? (ofD thex1 andfollowing Dx2 ) andis true the about stored the potential extensions (A) 4 ( UD1x and and U D2x) of) andthe twothe storedsprings? potential energies 1 1 2 (A) 1 (U and U ) of the two springs? (B) 4 1 Extension2 Stored Potential Energy 3 1 Extension Stored Potential Energy (B) 1 (A) Dx1 U 1 1 2 1 2 (C) 2 (D) 2 (B)(C) DD=Dx1 < U 2 3 1 2 1 2 2 (C)(D) D=Dx x UUU = U (D) 3 D=D1 2 1< 2 (E) 3 4 (D)(E) D=DDx >D x UUU = U 3 1 2 1 2 (E) 4 (E) Dx1 >Dx2 U1 = U 2 49. Two projectiles are launched from ground level

49. Twowith theprojectiles same initial are l aspeed.unched The from maximum ground levelheight reached by projectile 1 is twice the maximum withh1 the same initial speed. The maximum height

heighth1 reached h2 reached by projectile by projectile 1 is twice 2. Ifthe θ 1maximum and θ2 denote the respective launch angles, as measured height h2 reached by projectile 2. If θ1 and θ2 denotefrom the the horizontal, respective these launch angles angles, satisfy as measured which of fromthe following the horizontal, relationships? these angles satisfy which of 47. A stone is glued to the top of a light wooden the following relationships? block that floats in a pool of water, as shown in (A) cosθ1 = 2 cosθ2 47. A stone is glued to the top of a light wooden Figure 1 above. Assume that exactly 50 percent (B) θ = θ block that floats in a pool of water, as shown in (A) sincos θ11 = 22 sincos θ22 of the block is under water, and that the stone Figure 1 above. Assume that exactly 50 percent (C) tanθ = 2 tanθ has half the weight of the block. If the block and (B) sin θ1 1 = 2 sin θ22 of the block is under water, and that the stone stone are flipped over, as shown in Figure 2, and (D)(C) sinθ θ = 2sin θ θ has half the weight of the block. If the block and tan 11 = 2 tan2 2 replaced in the pool, the amount of the block stone are flipped over, as shown in Figure 2, and (D)(E) sincos θθ1 == 2sin 2cos θθ2 under water will be 1 2 replaced in the pool, the amount of the block (E) cosθ1 = 2cos θ2 under(A) less water than will 50% be (B) still 50% (A) less than 50% (C) between 50% and 75% (B) still 50% (D) between 75% and 100% (C) between 50% and 75% (E) 100%, since the stone and block sink (D) between 75% and 100%

(E) 100%, since the stone and block sink

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50. When an object is located 25 cm from lens 1, an inverted image is produced 100 cm from the lens, as shown in Figure 1 50. When an object is located 25 cm from lens 1, an inverted above. A second lens with a focal length of +20 cm is placed image is produced 100 cm from the lens, as shown in Figure 1 110 cm from the first lens, as shown in Figure 2 above. above. A second lens with a focal length of +20 cm is placed Which of the following is true of the image produced by 110 cm from the first lens, as shown in Figure 2 above. lens 2 ? Which of the following is true of the image produced by lens(A) It2 ?is real and inverted relative to the object. (B) It is real and upright relative to the object. (A) It is real and inverted relative to the object. (C) It is virtual and inverted relative to the object. (B) It is real and upright relative to the object. (D) It is virtual and upright relative to the object. (C) It is virtual and inverted relative to the object. (E) An image cannot be produced in this situation. (D) It is virtual and upright relative to the object.

(E) An image cannot be produced in this situation.

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51. A grating can just barely resolve 53. A microwave line has a laboratory wavelength of two wavelengths of 500 nm and 502 nm, 51. A grating spectrometer can just barely resolve 53. Al m microwavem. If the Hubble line has constant a laboratory H ª 75 wavelength (km/s)/Mpc, of respectively. Which of the following gives the observed wavelength for the line from a two wavelengths of 500 nm and 502 nm, l mm. If the Hubble constant H ª 75 (km/s)/Mpc, the resolving power of the spectrometer? 100 Mpc distant is about respectively. Which of the following gives the observed wavelength for the line from a the(A) resolving 2 power of the spectrometer? galaxy(A) 250 100 nm M shorterpc distant is about (B) 250 (A) 2 (B) 25 nm shorter (C) 5,000 (A) 250 nm shorter (B) 250 (C) the same (D) 10,000 (B) 25 nm shorter (C) 5,000 (D) 25 nm longer (E) 250,000 (C) the same (D) 10,000 (E) 250 nm longer (D) 25 nm longer (E) 250,000 52. A gas cell with an optical path length of 10 cm is (E) 250 nm longer

placed in one arm of a Michelson interferometer. 52. A gas cell with an optical path length of 10 cm is If the light source for the interferometer is a laser placed in one arm of a Michelson interferometer. with wavelength l = 632.2 nm, then 100 fringes If the light source for the interferometer is a laser are counted as the gas cell is evacuated. What is with wavelength l = 632.2 nm, then 100 fringes the index of refraction of the original gas? are counted as the gas cell is evacuated. What is (A)the index 1.00063 of refraction of the original gas? (B) 1.00032 (A) 1.00063 (C) 1.00016 (B) 1.00032 (D) 0.99968 (C) 1.00016 (D)(E) -1.000160.99968

(E) -1.00016

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54. The AC circuit shown above contains an ideal rectifying diode. If the function supplies 54. Thee()t AC= Vcircuit0 sin w shown t , which above of the contains following an ideal describes rectifying the voltage diode. acrossIf the functionthe resistor? generator supplies t V sin wt , which of the following describes the voltage across the resistor? (A)e() = 0 (A)

(B) (B)

(C) (C)

(D) (D)

(E) (E)

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55. The Fourier series expansion of a function fx() that is 55. Theperiodic Fourier with series period expansion 2p is of a function fx() that is • • periodic awith0 period 2p is f() x = + an cos( nx )+ bn sin( nx ). 2 • • a n=1 n=1 f() x = 0 + a cos( nx ) + b sin( nx). If fx is2 given byn the graph above, n which of the following () n=1 n=1 statementsIf fx() is givenabout bythe the coefficients graph above, is true? which of the following (A)statements an = 0 aboutfor all then coefficients is true? (B) bn = 0 for all n (A) an = 0 for all n (C) an = 0 for even n only (B) bn = 0 for all n (D) bn = 0 for even n only (C) an = 0 for even n only (E) an = bn for all n (D) bn = 0 for even n only (E) a = b for all n n n

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57. Which of the following statements is (are) true for a Maxwell-Boltzmann description of an ideal gas 57. Which of the following statements is (are) true for of atoms in equilibrium at temperature T ? a Maxwell-Boltzmann description of an ideal gas of atomsI. The inaverage equilibrium velocity at temperatureof the atoms Tis ?zero. II. The distribution of the speeds of the atoms I. The average velocity of the atoms is zero. has a maximum at u = 0. II. The distribution of the speeds of the atoms III. The probability of finding an atom with zero has a maximum at u = 0. kinetic energy is zero. III. The probability of finding an atom with zero (A) Ikinetic only energy is zero. 56. A sample of N molecules has the distribution of (B) II only (A) I only 56. Aspeeds sample shown of N in moleculesthe figure hasabove. the distributionP()uu d is an of (C) I and II (B) II only estimate of the number of molecules with speeds (D) I and III speeds shown in the figure above. P ()udu is an (C) I and II (E) II and III estimatebetween ofu theand number u + du of, and molecules this number with isspeeds (D) I and III

nonzero only up to 3u , where u is constant. (E) II and III between u and u + du0 , and this number0 is 58. A monatomic ideal gas changes from an initial

Whichnonzero of only the followingup to 3u ,gives where the uvalue is constant. of a ? 0 0 58. Astate monatomic ( , Vi , idealTi, ngasi) tochanges a final fromstate an (P finitial , Vf , Which of theN following gives the value of a ? Tf , nf ), where Pi < Pf , Vi = Vf , Ti < Tf and (A) a = state (Pi , Vi , Ti, ni) to a final state (Pf , Vf , 3u0 N nTi ,= nf ),. Whichwhere ofP the < Pfollowing, V = V gives, T < the T change and (A) a = N f f i f i f i f (B) a = 3u 0 nin =entropy n . Which of the of gas? the following gives the change 2u i f N0 in entropy3 ofÊ theTf ˆgas? (B) a = N (A) nR ln (C) a = 2 u0 2 ÁT ˜ u 3 ÊËTif ˆ ¯ N0 (A) nR ln (C) a = 2 Á T ˜ u3 N 3 ÊË Ti ˆ¯ (D) a = 0 (B) nR lnÁ ˜ 2u 2 ËTf ¯ 3 N0 3 Ê Ti ˆ (D) a = (B) nR ln 2 u 2 ÁÊTf ˜ ˆ (E) a= N 0 5 Ë f ¯ (C) nR lnÁ ˜ 2 ÊËTTi ˆ ¯ (E) a = N 5 f (C) nR lnÁ ˜ 25 ÊË Ti ˆ¯ (D) nR lnÁ ˜ 2 ËTf ¯ 5 Ê Ti ˆ (D) nR ln 2 Á T ˜ (E) 0 Ë f ¯

(E) 0

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59. Low-energy electrons are accelerated between electrodes in a tube filled with a gas in the Franck-Hertz apparatus represented above. A plot of current collected versus accelerating voltage is also shown. The 59. Low-energy electrons are accelerated between electrodes in a tube filled with a gas in the Franck-Hertz data provide evidence for which of the following? apparatus represented above. A plot of current collected versus accelerating voltage is also shown. The (A)data Electronicprovide evidence energy forlosses which due of only the tofollowing? elastic (B) Excitation energies of the gas atoms of 4.9, 9.8, and 14.7 eV (A) Electronic energy losses due only to elastic collisions (C) Excitation energy of the gas atoms of 4.9 eV only (B) Excitation energies of the gas atoms of 4.9, 9.8, and 14.7 eV (D)(C) AtomicExcitation energy energy levels of the of -gas4.9, atoms -9.8, of and 4.9 - eV14.7 only eV (E)(D) Atomic energy levels of -4.94.9, and -9.8, -9.8 and eV -14.7 only eV

(E) Atomic energy levels of -4.9 and -9.8 eV only

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60. A photon of wavelength l is scattered 63. The operators for the total angular momentum

from an electron through an angle q . ˆ ˆ ˆ ˆ 60. A photon of wavelength l is scattered 63. Theand itsoperators three projections for the total are angular J and momentumJx , Jy , Jz , Which of the following correctly gives the from an electron through an angle q . respectively. The commutatorˆ betweenˆ twoˆ ˆ wavelength l of the scattered photon? and its three projections are J and Jx , Jy , Jz , Which of the following¢ correctly gives the ˆ ˆ ˆˆ ˆ ˆ ˆ ˆ respectively.operators A andThe Bcommutator is ÎÈA, B ˚˘ between∫ AB - BAtwo. wavelength l¢ h of the scattered photon? (A) l¢ = l +1 - cosq Whichoperators of theAˆ and following Bˆ is È isAˆ ,true? Bˆ ˘ ABˆ ˆ BA ˆ ˆ. mc () Î ˚ ∫ - h (A) l¢ = l + h (1 - cos q) (A)Which ÈJˆ of2 , Jthe ˆ ˘ following 0 is true? (B) l¢ = l +mc 1 + cosq Îz ˚ = mc () h ˆ 2 ˆ (A) È Jˆ 2 , J ˆ z ˘ = 0 ˆ (B) l¢ = l + h (1 + cos q) (B) ÈÎJ , Jz ˘˚ = iJ= y (C) l¢ = l -mc ()1 - cosq Î ˚ mc ˆ 2 ˆ ˆ h (B) È Jˆˆ , J z ˘ = iJ= y (C) l¢ = l - h (1 - cos q) (C) ÎÈJJx, y ˚ ˘ = 0 (D) l¢ = l -mc ()1 + cosq mc (C) ÈJJˆˆ, ˘ 0 h (D) ÈÎ Jˆˆx, J y ˘˚ = iJ ˆ (D) l¢ = lh - (1 + cos q) Î x z˚ = = z (E) l¢ =1mc - cosq mc () (D) ÈJˆˆ, J ˘ iJ ˆ h (E) ÈÎJˆx +z iJ ˚ ˆˆ =, J= ˘ z = 0 (E) l¢ = (1 - cos q) Î x y z ˚ mc ˆ ˆˆ 61. Excited states of the helium atom can be (E) ÈJx + iJy , Jz ˘ = 0 64. The suspensionÎ cable˚ of a 1,000 kg elevator characterized as para- (antiparallel electron 61. Excited states of the helium atom can be snaps, sending the elevator moving downward spins) and ortho- (parallel electron spins). 64. The suspension cable of a 1,000 kg elevator characterized as para- (antiparallel electron through its shaft. The emergency brakes of The observation that an ortho- state has lower snaps, sending the elevator moving downward spins) and ortho- (parallel electron spins). the elevator stop the elevator shortly before it energy than the corresponding para- state can be through its shaft. The emergency brakes of The observation that an ortho- state has lower reaches the bottom of the shaft. If the elevator understood in terms of which of the following? the elevator stop the elevator shortly before it energy than the corresponding para- state can be fell a of 100 m starting from rest, the reaches the bottom of the shaft. If the elevator understood(A) The Heisenberg in terms ofuncertainty which of theprinciple following? heat that the brakes must dissipate to bring the (B) The Pauli exclusion principle fell a distance of 100 m starting from rest, the (A) The Heisenberg elevator safely to rest is (C) The Bohr model of the atom heat that the brakes must dissipate to bring the (B) The Pauli exclusion principle (D) Nuclear hyperfine elevator(A) safely 100 toJ rest is (C) The Bohr model of the atom (B) 1,000 J (E) Maxwell-Boltzmann statistics (A) 100 J (D) Nuclear hyperfine coupling (C) 10,000 J (B) 1,000 J (E) Maxwell-Boltzmann statistics (D) 100,000 J 62. A particle of mass m and spin zero is in a (C) 10,000 J (E) 1,000,000 J 62. Athree-dimensional particle of mass isotropicm and spin well zero described is in a (D) 100,000 J (E) 1,000,000 J

three-dimensional1 22 isotropic well described by Vr= mw r, where r2 = x2 + y2 + z2. () 2 1 22 2 2 2 2 by Vr()= mw r , where r 7= x + y + z . How many states2 have energy =w ? 2 7 How many states have energy =w ? (A) 1 2 (B) 2 (A) 1 (C) 4 (B) 2 (D) 6 (C) 4 (E) 8 (D) 6

(E) 8

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65. A uniform rod of length L and mass M is released from rest at q = 0 and rotates about a 65. A uniform rod of length L and mass M is horizontal axis through its base, as shown in the released from rest at q 0 and rotates about a figure above. What is the= of 66. Two identical, ideal springs, each with force horizontal axis through its base, as shown in the the rod as a function of q ? (Ignore the effects of constant k, are attached in series and hung figure above. What is the angular acceleration of 66. Two identical, ideal springs, each with force friction and air resistance.) vertically. When a block of mass m is attached constant k, are attached in series and hung the rod as a function of q ? (Ignore the effects of to the two-spring system, the block moves down vertically. When a block of mass m is attached frictiong and air resistance.) a distance x from the relaxed state, as shown in (A) to the two-spring system, the block moves down 2L the figure above. Which of the following gives the g a distance x from the relaxed state, as shown in (A) g of the block when it oscillates (B) 2L q the figure above. Which of the following gives the L vertically? g angular frequency of the block when it oscillates (B) 6gq L vertically?2k (C) cosq (A) 6Lg m 2k (C) 3g cos q (A) (D) L sinq km 2L (B) 3g m (D) 12gsin q k (E) 2L sinq (B) L mk 12g (C) (E) sinq 2m L k (C) 2mk (D) 2p x k (D) 2p 2x k (E) 2p x 2k (E) 2p x

67. A block attached to a spring is moving along the

x-axis on a frictionless horizontal surface. What is 67. A block attached to a spring is moving along the the Hamiltonian for the block? x-axis on a frictionless horizontal surface. What is the(A) HamiltonianH = 0 for the block? (A) H = 0 (B) H = -kx (B) H kx = -k (C) H= x2 2 k 2 (C) H = p2x k (D) H=2 - x2 2m2 2 p k 2 (D) H = p2 - k x (E) H=2 m + 2 x2 2m2 2 p k (E) H = + x 2 2 m 2

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68. A conducting sphere is solid except for three spherical cavities inside. Cavity A contains a point charge of +2q, 68. A conducting sphere is solid except for three spherical cavitiescavity B inside. contains Cavity a point A containscharge of a point-4q, charge and cavity of +2 Cq ,is empty, as shown above. What charges are induced on the cavity B contains a point charge of -4q, and cavity C is inner of the spherical cavities? empty, as shown above. What charges are induced on the inner Cavity surfaces A of the Cavityspherical B cavities?Cavity C

(A) Cavity-2q A Cavity+4q B Cavity0 C

(A)(B) -2q +4q 0- 2q (B)(C) -2q +4q -26q (C)(D) - +22q +4-4q -06 q (E) +2q +2q +2q (D) +2q -4q 0

(E) +2q +2q +2q

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69. A magnetic field is directed perpendicular to the 71. Consider the Pauli spin matrices sx , sy , and 2 plane of a circular coil of area 0.2 m and 250 sz. The product sx sy is equal to which of the 69. A magnetic field is directed perpendicular to the 71. Consider the Pauli spin matrices sx , sy , and turns. If the magnetic field is increased2 from following? plane of a circular coil of area 0.2 m and 250 sz. The product sx sy is equal to which of the turns.0.01 T If to the 0.06 magnetic T during field a time is increased interval offrom 0.25 s, following?(A) 0 the average induced EMF in the coil is 0.01 T to 0.06 T during a time interval of 0.25 s, (A)(B) s0 z the(A) average 0.04 V induced EMF in the coil is (B)(C) s-s z (B) 0.1 V z (A) 0.04 V (D) s s (C) 2.5 V (C) -sy z x (B) 0.1 V (D) 10 V (E) -s s (C) 2.5 V (D) sy ys x x (E) 50 V (D) 10 V (E) -s s 72. The bindingy x energy per is greatest for (E) 50 V which of the following nuclei? 72. The binding energy per nucleon is greatest for which3 of the following nuclei? (A) 2 He (A) 43He (B) 2 He (B) 564 He (C) 262 Fe (C) 23556 Fe (D) 2692 U

(D) 238235 U (E) 92 U

70. The figure above depicts a step potential with 238 (E) 92 U Ux()= 0, forx £ 0 (region 1), - 70. The figure above depicts a step potential with 73. The negative muon, m , has properties Ux()= � U, for x> 0 (region 2). most similar to which of the following? Ux ()= 0,0 for x £ 0 (region 1), 73. The negative muon, m -, has properties A beam of particles with E > 0 is incident from Ux() = �U0 , for x > 0 (region 2). (A)most simila r to which of the following? the left. The momentum of the particle in each (B) Boson A beam of particles with E > 0 is incident from (A) Quark region has the form =k . The reflection coefficient (C) Photon the left. The momentum of the particle in each (B) Boson R for the interface at x = 0 is (D) Meson region has the form =k . The reflection coefficient (C) Photon (E) Electron R(A) for R the= 0interface at x = 0 is (D) Meson

(A) R = 0 (E) Electron 4kk (B) R 12 = 2 ()k14kk+ k 2 (B) R = 12 2 (k1 + k 2 ) ()k+ k 2 (C) R = 1 2 2 (()k k1 +- k 2 ) (C) R = 1 2 2 (k1 - k2 ) ()k- k 2 (D) R = 1 2 2 (()k k1 -+ k 2 ) (D) R = 1 2 2 (k1 + k 2 ) -4kk (E) R 12 = 2 ()k-14+kk k 2 (E) R = 12 (k + k )2 1 2

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74. Which of the following correctly gives the quark and antiquark content of a and a baryon? 74. Which of the following correctly gives the quark and antiquark Lepton content of a lepton andBaryon a baryon? Antiquarks Quarks Antiquarks Lepton Baryon (A) 0 0 3 0 Quarks Antiquarks Quarks Antiquarks (B) 0 0 1 1 (A) 0 0 3 0 (C) 1 0 1 1 (B) 0 0 1 1 (D) 1 1 2 0 (C) 1 0 1 1 (E) 1 1 3 0 (D) 1 1 2 0

(E) 1 1 3 0

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75. Under certain conditions, a beam of electrons impinging on a crystal surface will diffract and 75. Under certain conditions, a beam of electrons a scattering of the beam can be obtained. impinging on a crystal surface will diffract and What is the approximate kinetic energy of the a scattering pattern of the beam can be obtained. electrons needed in order to see the pattern? What is the approximate kinetic energy of the (Assume the spacing of the crystal to electrons needed in order to see the pattern? be 0.4 nm.) (Assume the lattice spacing of the crystal to (A) 0.1 eV be 0.4 nm.) (B) 1 eV (A) 0.1 eV (C) 10 eV (B) 1 eV (D) 100 eV (C) 10 eV (E) 1000 eV (D) 100 eV (E) 1000 eV

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76. A beam of positive ions is initially moving in the + x-direction with nonrelativistic velocity. The beam enters a velocity 76. A beam of positive ions is initially moving in the +x-direction selector in which the E is oriented along the with nonrelativistic velocity. The beam enters a velocity +y-direction and the magnetic field B is oriented along the selector in which the electric field E is oriented along the +z-direction, as shown above. Which of the following gives +y-direction and the magnetic field B is oriented along the the critical speed u at which the ion beam is not deflected +z-direction, as shownc above. Which of the following gives as it moves through the velocity selector? the critical speed uc at which the ion beam is not deflected as(A) it movesu E throughB the velocity selector? c = (A) u = E1B (B) uc = c EB 1 (B) uc = B2 (C) u = EB c E B2 (C) u = B (D) uc = E c E B (D) uc = E (E) u = E c B E (E) u = c B

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77. Under ideal conditions, the electric and magnetic fields inside a superconductor 77. Under ideal conditions, the electric and are zero. Maxwell’s equations imply that magnetic fields inside a superconductor which of the following must be true just are zero. Maxwell’s equations imply that outside the surface of the superconductor? which of the following must be true just outside(A) B = the 0 surface of the superconductor? (B) B is perpendicular to the surface. (A) B = 0 (C) B is tangential to the surface. (B) B is perpendicular to the surface. (D) B is time independent. (C) B is tangential to the surface. 79. A block with mass m that slides on a frictionless (E) The magnetic flux is quantized. 1 (D) B is time independent. 79. Atable block is attached with mass by am massless that slides on overa frictionless a (E) The magnetic flux is quantized. massless, frictionless 1pulley to a hanging ball table is attached by a massless string over a with mass m , as shown in the figure above. massless, frictionless2 pulley to a hanging ball The in the string must be with mass m2 , as shown in the figure above. The(A) tension equal to in m the2 g string must be (B) greater than m2 g (A) equal to m2 g (C)(B) lessgreater than than m2 gm g 2 (D) equal to m1g (C) less than m2 g (E) greater than m1g 78. A positive charge, +q, oscillates up and down, (D) equal to m1g as represented in the figure above. What is the 78. A positive charge, +q, oscillates up and down, (E) greater than m1g direction of the S at point P ? as represented in the figure above. What is the (Assume P is located far to the right of +q.) direction of the Poynting vector S at point P ? (A)(Assume Toward P isthe located left far to the right of +q.) (B) Toward the right (A) Toward the left (C) Toward the top of the page (B) Toward the right (D) Toward the bottom of the page (C) Toward the top of the page (E) Into the page (D) Toward the bottom of the page (E) Into the page

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80. Two of mass m revolve around a star of

80. Twomass planetsM in a of circle mass of m radius revolve r , asaround shown a starin the of 82. As represented in the figure above, a light ray mass M in a circle of radius r , as shown in the refracts from air into a rectangular block of plastic figure above. The two planets are always on 82. As represented in the figure above, a light ray with an index of refraction n > 1. At a point on refracts from air into a rectangular block of plastic oppositefigure above. sides The of the two star. planets The areorbital always period on T of the side of the block, the ray partly reflects (at an with an index of refraction n > 1. At a point on r3 angle of 60 ) and partly refracts. The value of the theopposite planets sides is of of the the form star. TThe= orbital2p period. T of the side of the∞ block, the ray partly reflects (at an GM3 ¢ angle a is r angle of 60∞) and partly refracts. The value of the Whatthe planets is the isvalue of the of form M ?T = 2p . ¢ GM ¢ angle(A) 30 a∞ is What is them value of M ¢ ? (A) M - (A) 30∞ 2 m (B) 60∞ (A) M - m (B) M - 2 (B) 60∞ n 4 (C) cos-1 m 2 (C)(B) M - n 4 (C) cos -1 m 1 n (C)(D) M + (D) sin- 2 4 2 m -1 n (D) M + m (D) sin (E) M + 4 (E) tan-1 n2 2 m (E) M + (E) tan-1 n 2 83. Assume that the solar flux at Earth’s surface 81. White light is normally incident on a puddle of is 1,000 W/m2 and that the sunlight is normal water (index of refraction 1.33). A thin (500 nm) 83. Assume that the solar flux at Earth’s surface 81. White light is normally incident on a puddle of to a completely reflecting surface with an area layer of oil (index of refraction 1.5) floats on the is 1,000 W/m2 and that the sunlight is normal water (index of refraction 1.33). A thin (500 nm) 2 surface of the puddle. Of the following, the most toof a3 completelym . What is reflecting the total radiationsurface with force an exerted area layer of oil (index of refraction 1.5) floats on the strongly reflected wavelength is on the 2surface? surface of the puddle. Of the following, the most of 3 m . What is the total radiation force exerted -6 (A)strongly 500 reflectednm wavelength is (A)on the 2 ¥surface? 10 N 5 (B) 550 nm (B) 1 ¥ 10-6 N (A) 500 nm (A) 2 ¥ 10 N (C) 600 nm -5 (B) 550 nm (C) 2 ¥ 10-5 N (D) 650 nm (B) 1 ¥ 10 N (C) 600 nm (D) 3 N -5 (E) 700 nm (C) 2 ¥ 10 N (D) 650 nm (D)(E) 63 N (E) 700 nm (E) 6 N

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84. The hydrogen lines observed in the spectrum of 85. Protons used in cancer therapy are typically the quasar 3C9 are shifted so far into the red that accelerated to about 0.6c . How much work must 84. The hydrogen lines observed in the spectrum of 85. Protons used in cancer therapy are typically their wavelengths are three times as long as those be done on a particle of mass m in order for it to the quasar 3C9 are shifted so far into the red that accelerated to about 0.6c . How much work must observed in the light from hydrogen atoms at rest reach this speed, assuming it starts at rest? their wavelengths are three times as long as those in a laboratory on Earth. If it is assumed that the be done on a particle of mass m in order for it to observed in the light from hydrogen atoms at rest 2 shift is entirely due to the relative motion of (A)reach 0.25 thismc speed, assuming it starts at rest? in a laboratory on Earth. If it is assumed that the 3C9 and Earth, the relative speed of the quasar is 2 shift is entirely due to the relative motion of (B)(A) 0.250.60mc 2 3C9(A) 2andc Earth, the relative speed of the quasar is (C)(B) 0.600.67mc2 (B) c (A) 2c (D) 1.25mc22 (C) 0.8c (C) 0.67mc (B) c 2 (D) 0.5c (E)(D) 1.251.60mc2 (C) 0.8c (E) 0.3c (D) 0.5c (E) 1.60mc2 86. The sign of the charge carriers in a doped (E) 0.3c can be deduced by measuring 86. The sign of the charge carriers in a doped which of the following properties? semiconductor can be deduced by measuring which(A) Specific of the followingheat properties? (B) Thermal conductivity (A) Specific heat (C) Electrical resistivity (B) Thermal conductivity (D) Magnetic susceptibility (C) Electrical resistivity (E) Hall coefficient (D) Magnetic susceptibility

(E) Hall coefficient

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87. In the experimental setup above, two masses, m1 and m2 , are connected by a massless string over a massless pulley. 87. In the experimental setup above, two masses, m1 and m2 , Mass m slides on a frictionless surface. The values of the are connected1 by a massless string over a massless pulley. two masses can be measured, as well as the distance d and Mass m1 slides on a frictionless surface. The values of the twothe speed masses of canmass be mmeasured,1 as it passes as well x1 asand the again distance at x 2d. Theand experiment can be used to do which of the following? the speed of mass m1 as it passes x1 and again at x2. The experimentI. Demonstrate can be momentumused to do which conservation of the following? II. Demonstrate I. Demonstrate momentum conservation III. Measure the value of the acceleration due to gravity II. Demonstrate energy conservation (A)III. IMeasure only the value of the acceleration due to gravity (B) II only (A) I only (C) III only (B) II only (D) I and II (C) III only (E) II and III (D) I and II

(E) II and III

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88. An airplane drops a payload while traveling due 89. Two balls, identical in every way except that one north, parallel to the ground, at a constant speed has twice the mass of the other, are dropped from 88. An airplane drops a payload while traveling due 89. Two balls, identical in every way except that one of 100 m/s. If air resistance is neglected, what is rest from the same height so that they both reach north, parallel to the ground, at a constant speed has twice the mass of the other, are dropped from the velocity of the payload relative to the plane terminal speed before hitting the ground. If it is of 100 m/s. If air resistance is neglected, what is rest from the same height so that they both reach 4.0 s after it is released? assumed that the drag force varies like the speed the velocity of the payload relative to the plane terminal speed before hitting the ground. If it is squared, what is the ratio of the terminal speeds 4.0(A) s0 after it is released? assumed that the drag force varies like the speed of the balls? (Note: The subscripts h and l (B) 40 m/s down squared, what is the ratio of the terminal speeds (A) 0 denote the heavy and light masses, respectively.) (C) 80 m/s down of the balls? (Note: The subscripts h and l (B) 40 m/s down (D) 100 m/s north and 40 m/s down denote the heavy and light masses, respectively.) (C) 80 m/s down uh (E) 100 m/s south and 40 m/s down (A) = 1 (D) 100 m/s north and 40 m/s down ul uh (E) 100 m/s south and 40 m/s down (A) = 1 uh (B) l = 2 u l (B) h = 2 uh (C) l = 2 u l (C) h = 2 u (D) hl = 22 u l (D) h = 22 u (E) hl = 4 u l (E) h = 4 u l

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90. One end of a horizontal, massless spring is attached to a wall.

A mass of 0.30 kg is attached to the other end of the spring 90. One end of a horizontal, massless spring is attached to a wall. and rests on a table. The mass is displaced 0.030 m from its A mass of 0.30 kg is attached to the other end of the spring equilibrium position and released. It has a speed of 0.040 m/s and rests on a table. The mass is displaced 0.030 m from its as it passes through its equilibrium position. In the absence of equilibrium position and released. It has a speed of 0.040 m/s friction, what is the total mechanical energy of the system? as it passes through its equilibrium position. In the absence of (A)friction, 0.24 what mJ is the total mechanical energy of the system? (B) 0.38 mJ (A) 0.24 mJ (C) 0.48 mJ (B) 0.38 mJ (D) 0.75 mJ (C) 0.48 mJ (E) 0.96 mJ (D) 0.75 mJ

(E) 0.96 mJ

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93. An inertial reference frame S moves at constant ¢ 93. Anspeed inertial with respectreference to framea second S¢ inertialmoves atreference constant speedframe withS. An respect observer to a in second S measures inertial thereference energy frameE, momentum S. An observer p, and in position S measures x of athe moving energy Eparticle, momentum at time pt , for and a positionparticular x . of a moving An particleobserver at in time S¢ measurest for a particular energy Eevent.¢ , momentum An p , and position x at time t for the same observer¢ in S¢ measures¢ energy¢ E¢ , momentum movingp¢ , and particleposition at x the¢ at same time event.t¢ for Which the same of the movingfollowing particle is an expression at the same of event. a relativistic Which of the 91. The diagram above shows a Carnot cycle for an followinginvariant for is anthis expression event? of a relativistic 91. Theideal diagram air conditioner, above shows which a isCarnot to cool cycle a house for an on a invariant(A) x= for x¢ this event? hotideal summer air conditioner, day. The whichair conditioner is to cool absorbs a house heat on a (B)(A) xp = xp¢ ¢ athot the summer lower temperatureday. The air insideconditioner and pumps absorbs it toheat (B)(C) tp == tp¢ ¢ theat the environment lower temperature at the higher inside temperature and pumps outside.it to (C)(D) tE ==t¢E ¢ 2 2 2 2 Whichthe environment of the following at the higher gives thetemperature ratio of the outside. heat (E)(D) E =-E() ¢pc = E¢ - ( p ¢ c ) Q absorbed in the house (i.e., between points b 2 2 2 2 Whichbc of the following gives the ratio of the heat (E) E - ()pc = E¢ -(p ¢ c ) 94. Consider three identical, ideal capacitors. The first Qandbc absorbedc on the cycle)in the houseto the work(i.e., betweendone during points the b cycle? capacitor is charged to a voltage V and then and c on the cycle) to the work done during the 94. Consider three identical, ideal capac0 itors. The first disconnected from the battery. The other two cycle?(A) 0 capacitor is charged to a voltage V0 and then (B) 0.033 capacitors, initially uncharged and connected in (A) 0 disconnected from the battery. The other two (C) 0.97 (B) 0.033 capacitors,series, are then initially connected uncharged across and the connected first in (D) 1.0 (C) 0.97 capacitor. What is the final voltage on the first (E) 30. series, are then connected across the first (D) 1.0 capacitor.capacitor? What is the final voltage on the first (E) 30. 92. A particle in an infinite square well with walls at capacitor?V (A) 0 9 22p 92. xA = particle 0 and inx =an L infinite has energy square E well= =with walls. The at V5 2 (A) 0 92mL22p V x = 0 and x = L has energy E = . The 50 probability that the particle is between= 2x = 0 and (B) 2mL V3 probabilityx = L/6 is that the particle is between x = 0 and (B) 0 V3 (C) 0 x(A) = L1/36/6 is V2 (B) 1/6 (C) 0 (A) 1/36 22 V (C) 1/3 (D) 0 (B) 1/6 (D) 1/2 2V 3 (C) 1/3 0 (E) 1 (D) (E) V03 (D) 1/2 (E) 1 (E) V 0

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95. A charge of 5.0 µC is distributed uniformly 96. The magnetic field inside a long coil of wire - around a ring 1.0 m in radius. A point charge of (solenoid) has a certain magnitude and direction 95. A charge of -5.0 µC is distributed uniformly 96. The magnetic field inside a long coil of wire +3.0 µC is at the center of the ring. The work when the coil is air filled. If a diamagnetic around a ring 1.0 m in radius. A point charge of (solenoid) has a certain magnitude and direction required to move the point charge 1.0 m in a material is inserted in the coil, how do the +3.0 µC is at the center of the ring. The work when the coil is air filled. If a diamagnetic direction normal to the plane of the ring is most magnitude and direction of the magnetic field required to move the point charge 1.0 m in a material is inserted in the coil, how do the nearly change? direction normal to the plane of the ring is most magnitude and direction of the magnetic field Magnitude Direction nearly(A) 40 mJ change? (B) 80 mJ (A) MagnitudeIncreases SameDirection (A) 40 mJ (C) 100 mJ (B) Increases Opposite (B) 80 mJ (A) Increases Same (D) 140 mJ (C) Decreases Same (C) 100 mJ (B) Increases Opposite (E) 270 mJ (D) Decreases Opposite (D) 140 mJ (C) Decreases Same (E) 270 mJ (E) No change Opposite (D) Decreases Opposite

(E) No change Opposite

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97. The figure above shows two identical simple pendulums, each with mass m and suspended by a massless rod of length a. The pendulums are coupled by a massless spring of force constant k. The coordinates q measure 97. The figure above shows two identical simple pendulums, each with mass m and suspended by a masslessi rod the angular displacements from vertical, as shown. Which of the following gives the Lagrangian for the system? of length a. The pendulums are coupled by a massless spring of force constant k. The coordinates qi measure (Assume small angular displacements q .) the angular displacements from vertical,i as shown. Which of the following gives the Lagrangian for the system? (Assume small1 angular displacements1 qi .) 1 (A) L= ma2q 2 + q  2 -mga q2 + q 2 -ka 2 () q - q 2 2 ()()1 2 2 1 2 2 2 1 1 2 2 2 1 2 2 1 2 2 (A) L = 1 ma q + q - 1 mga q + q - 1 ka (q - q ) (B) L=2 ma2(q 21 + q  2 ) +2 mga(q21 + q 2 ) -2 ka 2 () q2 - q 1 2 2 ()()1 2 2 1 2 2 2 1 1 2 2 2 1 2 2 1 2 2 (B) L = 1 ma q + q + 1 mga q + q - 1 ka (q - q ) (C) L=2 ma2(q 21 + q  2 ) -2 mga(q21 + q2 ) +2 ka 2 () q2 - q1 2 2 ()()1 2 2 1 2 2 2 1 1 2 2 2 1 2 2 1 2 2 (C) L = 1 ma q + q - 1 mga q + q + ka (q - q ) (D) L=2 ma2( q 21 + q  2 )( +2 mga q 21 + q 2 ) 2 2 1 2 ()()1 2 2 1 2 1 2 2 2 1 2 2 (D) L = 1 ma q + q + 1 mga q + q (E) L=2 ma2(q 21 + q  2 ) +2 ka 2 ()( q1 - q 22) 2 ()1 2 2 2 1 1 1 (E) L = ma 2 q 2 + q 2 + ka 2 (q - q )2 2 ( 1 2 ) 2 2 1

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98. The spacing between the parallel Bragg planes in 99. Consider an electron in the n =4,A = 1 state in a certain crystal is d . Electrons of fixed energy, 98. The spacing between the parallel Bragg planes in 99. hydrogen.Consider an Which electron of thein thefollowing n 4, final 1states state can in corresponding to a given wavelength l , are = A = a certain crystal is d . Electrons of fixed energy, NOT be reached by an allowed transition? incident on the crystal. Which of the following is hydrogen. Which of the following final states can corresponding to a given wavelength l , are the minimal condition for strong reflection for at NOT(A) n be= reached3,A = 2by an allowed transition? incident on the crystal. Which of the following is least two different angles? (B) n 3, 1 the minimal condition for strong reflection for at (A) n = 3, A = 2 (C) n 3, 0 least(A) ltwo> ddifferent angles? (B) n = 3, A = 1 d (D) n =2,A = 0 (B)(A) l > d (C) n = 3, A = 0 2 (E) n 1, 0 d (D) n = 2, AA == 0 (C)(B) l <> 2d 2 (E) n = 1, A = 0

(D)(C) l < 2dd

d (D)(E) l < d 2 d (E) l < 2

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100. A room-temperature Mössbauer absorption spectrum for the 14.4 keV gamma-ray transition of 57Fe is 3 - illustrated in the figure above. From the data, it can be deduced that the lifetime of the excited state is 2 approximately (A) 100 ms (B) 100 ms (C) 100 ns (D) 100 ps (E) 100 fs

If you finish before time is called, you may check your work on this test.

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100. A room-temperature Mössbauer absorption spectrum for the 14.4 keV gamma-ray transition of 57Fe is 3 - illustrated in the figure above. From the data, it can be deduced that the lifetime of the excited state is 2 approximately (A) 100 ms (B) 100 ms (C) 100 ns (D) 100 ps (E) 100 fs

If you finish before time is called, you may check your work on this test.

85 -78- -79- NOTE: To ensure prompt processing of test results, it is important that you fill in the blanks exactly as directed. I SUBJECT TEST

A. Print and sign your full name PRINT: ______(LAST) (FIRST) (MIDDLE) in this box: SIGN: ______

6. TITLE CODE Copy this code in box 6 on Copy the Test Name and Form Code in box 7 on your answer your answer sheet. Then 7 7 9 7 6 sheet. fill in the corresponding 0 0 0 0 0 1 1 1 1 1 TEST NAME ______ovals exactly as shown. 2 2 2 2 2 Physics 3 3 3 3 3 4 4 4 4 4 FORM CODE ______GR1777 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9 9 9

GRADUATE RECORD EXAMINATIONS SUBJECT TEST B. The Subject Tests are intended to measure your achievement in a specialized field of study. Most of the questions are concerned with subject matter that is probably familiar to you, but some of the questions may refer to areas that you have not studied. Your score will be determined by the number of questions you answer correctly. Questions you answer incorrectly or for which you mark no answer or more than one answer are counted as incorrect. Nothing is subtracted from a score if you answer a question incorrectly. Therefore, to maximize your score, it is better for you to guess at an answer than not to respond at all. You are advised to use your time effectively and to work as rapidly as you can without losing accuracy. Do not spend too much time on questions that are too difficult for you. Go on to the other questions and come back to the difficult ones later if you can. YOU MUST INDICATE ALL YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. No credit will be given for anything written in this examination book, but you may write in the book as much as you wish to work out your answers. After you have decided on your response to a question, fill in the corresponding oval on the answer sheet. BE SURE THAT EACH MARK IS DARK AND COMPLETELY FILLS THE OVAL. Mark only one answer to each question. No credit will be given for multiple answers. Erase all stray marks. If you change an answer, be sure that all previous marks are erased completely. Incomplete erasures may be read as intended answers. Do not be concerned that the answer sheet provides for more answers than there are questions in the test.

Example: Sample Answer

What city is the capital of France? A B C D E CORRECT ANSWER (A) Rome PROPERLY MARKED A B C D E (B) Paris A B C D E (C) London IMPROPER MARKS (D) Cairo A B C D E (E) Oslo A B C D E

DO NOT OPEN YOUR TEST BOOK UNTIL YOU ARE TOLD TO DO SO.

® Educational Testing Service 86 Princeton, New Jersey 08541 Worksheet for the GRE Physics Test, Form GR1777 Answer Key and Percentages* of Test Takers Answering Each Question Correctly

QUESTION CORRECT QUESTION CORRECT P+ P+ Number Answer RESPONSE Number Answer RESPONSE 1 E 92 51 B 33 2 E 41 52 B 29 3 E 70 53 D 39 4 B 64 54 B 56 5 E 30 55 B 45 6 B 47 56 B 64 7 C 59 57 D 46 8 B 64 58 A 69 9 D 91 59 C 20 10 D 59 60 A 57 11 C 41 61 B 50 12 E 79 62 D 36 13 D 77 63 A 63 14 A 76 64 E 78 15 C 48 65 D 43 16 D 53 66 C 52 17 D 74 67 E 77 18 C 34 68 A 71 19 C 70 69 D 52 20 D 60 70 D 43 21 E 43 71 E 32 22 A 49 72 C 49 23 B 50 73 E 74 24 C 31 74 A 53 25 B 51 75 C 19 26 E 66 76 E 74 27 A 71 77 C 43 28 C 47 78 B 41 29 D 63 79 C 54 30 E 32 80 D 26 31 E 32 81 C 20 32 A 39 82 D 59 33 A 23 83 C 25 34 B 82 84 C 55 35 D 53 85 A 38 36 D 56 86 E 50 37 D 52 87 E 66 38 E 24 88 B 44 39 C 86 89 B 47 40 A 23 90 A 70 41 E 28 91 E 25 42 D 44 92 B 55 43 C 41 93 E 70 44 A 85 94 D 24 45 A 37 95 A 22 46 A 76 96 C 34 47 A 53 97 A 52 48 B 52 98 D 22 49 B 49 99 B 48 50 C 30 100 C 21

Total Correct: ______

Total Scaled: ______

* The numbers in the P+ column indicate the percentages of test takers in the United States who answer each question correctly.

GRE ® Physics Test Practice Book 87 | Page Score Conversions for the GRE Physics Test, Form GR1777

TOTAL SCORE

Total Correct Scaled Score Total Correct Scaled Score 84-100 990 43 590 83 980 42 580 82 970 41 570 81 960 40 560 80 950 38-39 550

79 940 37 540 78 930 36 530 77 920 35 520 76 910 33-34 510 75 900 32 500

74 890 31 490 73 880 30 480 72 870 28-29 470 71 860 27 460 70 850 26 450

69 840 25 440 68 830 23-24 430 67 820 22 420 66 810 21 410 65 800 20 400

64 790 18-19 390 63 780 17 380 62 770 16 370 61 760 14-15 360 60 750 13 350

59 740 12 340 58 730 11 330 57 720 9-10 320 56 710 8 310 55 700 7 300

54 690 6 290 53 680 5 280 52 670 4 270 51 660 1-3 260 50 650 0 250

49 640 48 630 47 620 46 610 44-45 600

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Q O GRE ® Physics Test Practice Book 89 | Page SIDE 2 CERTIFICATION STATEMENT Please write the following statement below, DO NOT PRINT. “I certify that I am the person whose name appears on this answer sheet. I also SUBJECT TEST agree not to disclose the contents of the test I am taking today to anyone.” Sign and date where indicated.

COMPLETE THE CERTIFICATION STATEMENT, THEN TURN ANSWER SHEET OVER TO SIDE 1.

SIGNATURE: DATE: Month Day Year

BE SURE EACH MARK IS DARK AND COMPLETELY FILLS THE INTENDED SPACE AS ILLUSTRATED HERE: . YOU MAY FIND MORE RESPONSE SPACES THAN YOU NEED. IF SO, PLEASE LEAVE THEM BLANK.

116 A B C D E 148 A B C D E 180 A B C D E 212 A B C D E 117 A B C D E 149 A B C D E 181 A B C D E 213 A B C D E 118 A B C D E 150 A B C D E 182 A B C D E 214 A B C D E 119 A B C D E 151 A B C D E 183 A B C D E 215 A B C D E 120 A B C D E 152 A B C D E 184 A B C D E 216 A B C D E 121 A B C D E 153 A B C D E 185 A B C D E 217 A B C D E 122 A B C D E 154 A B C D E 186 A B C D E 218 A B C D E 123 A B C D E 155 A B C D E 187 A B C D E 219 A B C D E 124 A B C D E 156 A B C D E 188 A B C D E 220 A B C D E 125 A B C D E 157 A B C D E 189 A B C D E 221 A B C D E 126 A B C D E 158 A B C D E 190 A B C D E 222 A B C D E 127 A B C D E 159 A B C D E 191 A B C D E 223 A B C D E 128 A B C D E 160 A B C D E 192 A B C D E 224 A B C D E 129 A B C D E 161 A B C D E 193 A B C D E 225 A B C D E 130 A B C D E 162 A B C D E 194 A B C D E 226 A B C D E 131 A B C D E 163 A B C D E 195 A B C D E 227 A B C D E 132 A B C D E 164 A B C D E 196 A B C D E 228 A B C D E 133 A B C D E 165 A B C D E 197 A B C D E 229 A B C D E 134 A B C D E 166 A B C D E 198 A B C D E 230 A B C D E 135 A B C D E 167 A B C D E 199 A B C D E 231 A B C D E 136 A B C D E 168 A B C D E 200 A B C D E 232 A B C D E 137 A B C D E 169 A B C D E 201 A B C D E 233 A B C D E 138 A B C D E 170 A B C D E 202 A B C D E 234 A B C D E 139 A B C D E 171 A B C D E 203 A B C D E 235 A B C D E WANT THIS ANSWER SHEET TO BE SCORED TO ANSWER SHEET THIS WANT 140 A B C D E 172 A B C D E 204 A B C D E 236 A B C D E

141 A B C D E 173 A B C D E 205 A B C D E 237 A B C D E full name here: Sign your B. NOT 142 A B C D E 174 A B C D E 206 A B C D E 238 A B C D E 143 A B C D E 175 A B C D E 207 A B C D E 239 A B C D E 144 A B C D E 176 A B C D E 208 A B C D E 240 A B C D E 145 A B C D E 177 A B C D E 209 A B C D E 241 A B C D E 146 A B C D E 178 A B C D E 210 A B C D E 242 A B C D E IF YOU IF YOU DO 147 A B C D E 179 A B C D E 211 A B C D E

TR TW TFS TCS 1R 1W 1FS 1CS 2R 2W 2FS 2CS

FOR ETS USE ONLY 3R 3W 3FS 3CS 4R 4W 4FS 4CS A. Fill in both circles here . . . . . here in both circles Fill A. To cancel your scores from this test administration, you must: you administration, this test from scores cancel your To If you want to cancel your scores from this test administration, complete A and B below. You will not receive scores for this test. No this test. for scores will not receive You A and B below. complete administration, this test from scores cancel your to want If you GRE file. on your this test for will be no scores and there indicated, you the recipients or the cancellation will be sent to of this test record

5R 5W 5FS 5CS 6R 6W 6FS 6CS

90 | Page GRE ® Physics Test Practice Book 120774-007627 • UNLWEB617

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