De Broglie Wavelength - Optics and Modern Physics - Past Paper, Exams of Physics

Download De Broglie Wavelength - Optics and Modern Physics - Past Paper and more Exams Physics in PDF only on Docsity! Physics 228 - Exam 2 8 April 2010 Profs. Rabe and Coleman =⇒ Your name sticker with exam code =⇒ SIGNATURE Turn off and put away cell phones now! 1. The exam will last from 9:40pm to 11:00pm. 2. Use a #2 pencil to make entries on the answer sheet. Enter the following ID information now, before the exam starts. 3. In the section labelled NAME (Last, First, M.I.) enter your last name, then fill in the empty circle for a blank, then enter your first name, another blank, and finally your middle initial. 4. Under STUDENT # enter your 9-digit student ID. 5. Enter 228 under COURSE, and your section number (see label above) under SEC. 6. Under CODE enter the exam code given above. 7. During the exam, you may use pencils, a calculator, and one handwritten 8.5 x 11 inch sheet with formulas and notes, with- out attachments. 8. There are 16 multiple-choice questions on the exam. For each question, mark only one answer on the answer sheet. There is no deduction of points for an incorrect answer, so even if you cannot work out the answer to a question, you should make an educated guess. At the ened of the exam, hand in the answer sheet and the cover page. Retain this question paper for future reference and study. 9. When you are asked to open the exam, make sure that your copy contains all 16 questions. Raise your hand if this is not the case, and a proctor will help you. Also raise your hand during the exam if you have a question. 10. Please SIGN the cover sheet under your name sticker and have your student ID ready to show to the proctor during the exam. Useful information c = speed of light = 3.00 × 108 m/s qe = −e = charge on an electron = −1.602 × 10 −19 Coulombs qp = +e = charge on a proton = +1.602 × 10 −19 Coulombs me = electron mass = 9.11 × 10 −31 kg mec 2 = electron rest energy = 0.511 MeV mp = proton mass = 1.67 × 10 −27 kg mpc 2 = proton rest energy = 938.27MeV mnc 2 = neutron rest energy = 939.57MeV kB = Boltzmann’s constant = 1.38 × 10 −23 J/K Wien’s Constant = 2.898 × 10−3m ·K σ = Stefan’s Constant = 5.670 × 10−8W/(m2K4) h̄ = h 2π h = 6.626 × 10−34 J-s h = 4.136 × 10−15 eV-s (in units of electron volts-second) hc = 1240 eV · nm = 1240 MeV · fm 1 nm = 10−9 m 1 Å = 10−10 m = 0.1 nm 1 µm = 10−6m 1 mHz = 10−3 Hz 1 kHz = 10+3 Hz 1 MHz = 10+6 Hz 1 GHz = 10+9 Hz 1 1. A photon, an electron, and a baseball have the same momentum. Which has the largest de Broglie wavelength? a) photon b) all have the same wavelength c) electron d) baseball and electron e) baseball 2. A particle is confined inside a cube of side length L, with one corner at the origin. The potential height of the walls of the cube is infinite. The normalized wave function of the particle, which is in the ground state, is ψ(x, y, z) = ( 2 L )3/2 sin πx sin πy sin πz, 0 < x, y, z < L What is the maximum value of the probability distribution func- tion for an electron in this state? a) ( 1 L )3/2 b) 8 L3 c) ( 2 L )3/2 d) 1 L3 e) 8 L 3. A perfectly black body at a temperature of 100◦C emits light of intensity I that has strongest intensity at wavelength λ. The temperature of the black body is now increased to 200◦C. The hotter black body now emits light most strongly at a wavelength closest to a) 0.5λ b) λ c) 2λ d) 1.3λ e) 0.8λ 4. An elementary particle with rest mass m spontaneously decays into two equal with rest masses m 3 . What are the kinetic energies of these particles? a) mc 2 3 , mc 2 6 b) mc 2 3 , 0 c) mc 2 3 , mc 2 3 d) mc 2 6 , mc 2 6 e) mc 2 6 , 0 5. If light incident on a metallic surface is doubled in intensity, the maximum kinetic energy of electrons produced by the photoelec- tric effect will change from K to: a) 4K b) 2K c) K/4 d) K/2 e) K (no change) 6. As a spaceship heads directly to earth at a velocity of 0.8c, it sends a radio signal to earth. When those radio waves arrive on earth, their velocity relative to earth is: a) √ c2 + υ2E , where υE is the velocity of the earth. b) c. c) √ (.8c)2 + υ2E , where υE is the velocity of the earth. d) 1.8 c. e) 0.8 c. 7. Accelerating voltages in cathode-ray-tube (CRT) TV’s are about 24.0 kV. What is the shortest wavelength of the x-rays that are produced when the accelerated electrons hit the screen. a) 52nm b) 5.6 ×1018Hz c) 0.008nm d) 0.052 nm e) 7.8nm 2 Physics 228 - Exam 2 8 April 2010 Profs. Rabe and Coleman =⇒ Your name sticker with exam code =⇒ SIGNATURE Turn off and put away cell phones now! 1. The exam will last from 9:40pm to 11:00pm. 2. Use a #2 pencil to make entries on the answer sheet. Enter the following ID information now, before the exam starts. 3. In the section labelled NAME (Last, First, M.I.) enter your last name, then fill in the empty circle for a blank, then enter your first name, another blank, and finally your middle initial. 4. Under STUDENT # enter your 9-digit student ID. 5. Enter 228 under COURSE, and your section number (see label above) under SEC. 6. Under CODE enter the exam code given above. 7. During the exam, you may use pencils, a calculator, and one handwritten 8.5 x 11 inch sheet with formulas and notes, with- out attachments. 8. There are 16 multiple-choice questions on the exam. For each question, mark only one answer on the answer sheet. There is no deduction of points for an incorrect answer, so even if you cannot work out the answer to a question, you should make an educated guess. At the ened of the exam, hand in the answer sheet and the cover page. Retain this question paper for future reference and study. 9. When you are asked to open the exam, make sure that your copy contains all 16 questions. Raise your hand if this is not the case, and a proctor will help you. Also raise your hand during the exam if you have a question. 10. Please SIGN the cover sheet under your name sticker and have your student ID ready to show to the proctor during the exam. Useful information c = speed of light = 3.00 × 108 m/s qe = −e = charge on an electron = −1.602 × 10 −19 Coulombs qp = +e = charge on a proton = +1.602 × 10 −19 Coulombs me = electron mass = 9.11 × 10 −31 kg mec 2 = electron rest energy = 0.511 MeV mp = proton mass = 1.67 × 10 −27 kg mpc 2 = proton rest energy = 938.27MeV mnc 2 = neutron rest energy = 939.57MeV kB = Boltzmann’s constant = 1.38 × 10 −23 J/K Wien’s Constant = 2.898 × 10−3m ·K σ = Stefan’s Constant = 5.670 × 10−8W/(m2K4) h̄ = h 2π h = 6.626 × 10−34 J-s h = 4.136 × 10−15 eV-s (in units of electron volts-second) hc = 1240 eV · nm = 1240 MeV · fm 1 nm = 10−9 m 1 Å = 10−10 m = 0.1 nm 1 µm = 10−6m 1 mHz = 10−3 Hz 1 kHz = 10+3 Hz 1 MHz = 10+6 Hz 1 GHz = 10+9 Hz 1 1. Consider an electron with the free-particle wavefunction ψ(x, t) = A exp[i(kx− ωt)]. Which of the following is false? a) the momentum of the electron is h̄k . b) ψ(x, t) is not a stationary state. c) A can be chosen to be a pure imaginary number. d) the energy of the electron is h̄ω. e) the probability distribution function is independent of x. 2. The uncertainty in position of an electron in a certain state is 5× 10−10 m. The uncertainty in its momentum (in kg·m/s) must be: a) greater than 10−23 b) greater than 10−25 c) less than 10−23 d) less than 10−25 e) greater than 10−20 3. A particle is confined inside a cube of side length L, with one corner at the origin. The potential height of the walls of the cube is infinite. The normalized wave function of the particle, which is in the ground state, is ψ(x, y, z) = ( 2 L )3/2 sin πx sin πy sin πz, 0 < x, y, z < L What is the maximum value of the probability distribution func- tion for an electron in this state? a) ( 2 L )3/2 b) ( 1 L )3/2 c) 1 L3 d) 8 L e) 8 L3 4. ψ(x) is the normalized wave function for a particle moving along the x axis. The probability that the particle is in the interval from x = a to x = b is given by: a) ψ(b) − ψ(a) b) |ψ(b)|2 − |ψ(a)|2 c) ∫ b a |ψ(x)| 2dx d) |ψ(b) − ψ(a)|2 e) ∫ b a ψ(x)dx 5. A perfectly black body at a temperature of 100◦C emits light of intensity I that has strongest intensity at wavelength λ. The temperature of the black body is now increased to 200◦C. The hotter black body now emits light most strongly at a wavelength closest to a) 1.3λ b) 0.8λ c) 0.5λ d) λ e) 2λ 6. A distant star is receding from earth at a speed such that the 434-nm emission line of hydrogen is Doppler shifted to 650 nm. At what speed is the star receding? a) 0.5c b) 0.9999c c) 0.667c d) 0.383c e) 0.995c 7. An electron is trapped in a one-dimensional infinite potential well of width 10−10 m. What is the energy of the photon emitted when the electron makes a transition from the first excited state (n = 2) to the ground state (n = 1)? a) 37.4 eV b) 0.062 eV c) 127 eV d) 113 eV e) 150 eV 2 8. A photon, an electron, and a baseball have the same momentum. Which has the largest de Broglie wavelength? a) baseball and electron b) all have the same wavelength c) photon d) electron e) baseball 9. A meter stick moves in the laboratory along the direction of its length with a speed of 1.2 × 108 m/sec. Its length, as seen by an observer at rest in the laboratory, is: a) 0.84 m b) 1.19 m c) 1.09 m d) 1.00 m e) 0.917 m 10. An elementary particle with rest mass m spontaneously decays into two equal with rest masses m 3 . What are the kinetic energies of these particles? a) mc 2 6 , 0 b) mc 2 6 , mc 2 6 c) mc 2 3 , mc 2 6 d) mc 2 3 , mc 2 3 e) mc 2 3 , 0 11. If light incident on a metallic surface is doubled in intensity, the maximum kinetic energy of electrons produced by the photoelec- tric effect will change from K to: a) K/2 b) K/4 c) 2K d) K (no change) e) 4K 12. The wave character of electrons is best illustrated by which of the following? a) The diffraction pattern observed when a beam of electrons is scattered by a crystal. b) The ejection of electrons from a metal surface illuminated by light. c) The fact that hot objects emit electromagnetic radiation. d) The fact that a rainbow consists of a continuous spectrum of colors. e) The scattering of alpha particles from gold foil. 13. As a spaceship heads directly to earth at a velocity of 0.8c, it sends a radio signal to earth. When those radio waves arrive on earth, their velocity relative to earth is: a) 0.8 c. b) √ (.8c)2 + υ2E , where υE is the velocity of the earth. c) c. d) 1.8 c. e) √ c2 + υ2E , where υE is the velocity of the earth. 14. A hydrogen atom undergoes a transition from the n = 6 to the n = 2 state by emitting a photon. According to the Bohr model of the atom, if the angular momentum is conserved, what is the angular momentum of the photon that is emitted? a) 0h̄ b) 4h̄ c) 2h̄ d) 3h̄ e) 1h̄ 3 1. The uncertainty in position of an electron in a certain state is 5× 10−10 m. The uncertainty in its momentum (in kg·m/s) must be: a) less than 10−23 b) greater than 10−23 c) less than 10−25 d) greater than 10−25 e) greater than 10−20 2. Accelerating voltages in cathode-ray-tube (CRT) TV’s are about 24.0 kV. What is the shortest wavelength of the x-rays that are produced when the accelerated electrons hit the screen. a) 0.052 nm b) 7.8nm c) 52nm d) 0.008nm e) 5.6 ×1018Hz 3. ψ(x) is the normalized wave function for a particle moving along the x axis. The probability that the particle is in the interval from x = a to x = b is given by: a) |ψ(b)|2 − |ψ(a)|2 b) ψ(b) − ψ(a) c) ∫ b a |ψ(x)| 2dx d) |ψ(b) − ψ(a)|2 e) ∫ b a ψ(x)dx 4. The wave character of electrons is best illustrated by which of the following? a) The fact that hot objects emit electromagnetic radiation. b) The ejection of electrons from a metal surface illuminated by light. c) The fact that a rainbow consists of a continuous spectrum of colors. d) The scattering of alpha particles from gold foil. e) The diffraction pattern observed when a beam of electrons is scattered by a crystal. 5. A particle is confined inside a cube of side length L, with one corner at the origin. The potential height of the walls of the cube is infinite. The normalized wave function of the particle, which is in the ground state, is ψ(x, y, z) = ( 2 L )3/2 sin πx sin πy sin πz, 0 < x, y, z < L What is the maximum value of the probability distribution func- tion for an electron in this state? a) 8 L b) ( 2 L )3/2 c) 8 L3 d) ( 1 L )3/2 e) 1 L3 6. A spaceship is moving at speed 0.70c to the right relative to earth. Standing at the rear of the ship, a woman fires a space gun, and the bullet goes forward inside the ship at a speed of 0.90c relative to the spaceship. What is the bullet’s speed as measured from earth? 0.7 c a) 0.20c b) 0.92c c) 0.54c d) 1.60c e) 0.98c 2 7. Consider an electron with the free-particle wavefunction ψ(x, t) = A exp[i(kx− ωt)]. Which of the following is false? a) the probability distribution function is independent of x. b) the energy of the electron is h̄ω. c) ψ(x, t) is not a stationary state. d) A can be chosen to be a pure imaginary number. e) the momentum of the electron is h̄k . 8. A perfectly black body at a temperature of 100◦C emits light of intensity I that has strongest intensity at wavelength λ. The temperature of the black body is now increased to 200◦C. The hotter black body now emits light most strongly at a wavelength closest to a) 0.5λ b) λ c) 1.3λ d) 0.8λ e) 2λ 9. A distant star is receding from earth at a speed such that the 434-nm emission line of hydrogen is Doppler shifted to 650 nm. At what speed is the star receding? a) 0.5c b) 0.667c c) 0.995c d) 0.9999c e) 0.383c 10. A hydrogen atom undergoes a transition from the n = 6 to the n = 2 state by emitting a photon. According to the Bohr model of the atom, if the angular momentum is conserved, what is the angular momentum of the photon that is emitted? a) 1h̄ b) 4h̄ c) 0h̄ d) 2h̄ e) 3h̄ 11. An electron is trapped in a one-dimensional infinite potential well of width 10−10 m. What is the energy of the photon emitted when the electron makes a transition from the first excited state (n = 2) to the ground state (n = 1)? a) 113 eV b) 150 eV c) 37.4 eV d) 0.062 eV e) 127 eV 12. An elementary particle with rest mass m spontaneously decays into two equal with rest masses m 3 . What are the kinetic energies of these particles? a) mc 2 6 , mc 2 6 b) mc 2 3 , mc 2 3 c) mc 2 3 , 0 d) mc 2 6 , 0 e) mc 2 3 , mc 2 6 13. A meter stick moves in the laboratory along the direction of its length with a speed of 1.2 × 108 m/sec. Its length, as seen by an observer at rest in the laboratory, is: a) 0.84 m b) 1.00 m c) 1.09 m d) 0.917 m e) 1.19 m 14. As a spaceship heads directly to earth at a velocity of 0.8c, it sends a radio signal to earth. When those radio waves arrive on earth, their velocity relative to earth is: a) 0.8 c. b) √ (.8c)2 + υ2E , where υE is the velocity of the earth. c) 1.8 c. d) √ c2 + υ2E , where υE is the velocity of the earth. e) c. 3 15. If light incident on a metallic surface is doubled in intensity, the maximum kinetic energy of electrons produced by the photoelec- tric effect will change from K to: a) K/2 b) 4K c) 2K d) K/4 e) K (no change) 16. A photon, an electron, and a baseball have the same momentum. Which has the largest de Broglie wavelength? a) all have the same wavelength b) electron c) baseball and electron d) baseball e) photon 4 7. The wave character of electrons is best illustrated by which of the following? a) The ejection of electrons from a metal surface illuminated by light. b) The scattering of alpha particles from gold foil. c) The diffraction pattern observed when a beam of electrons is scattered by a crystal. d) The fact that a rainbow consists of a continuous spectrum of colors. e) The fact that hot objects emit electromagnetic radiation. 8. A perfectly black body at a temperature of 100◦C emits light of intensity I that has strongest intensity at wavelength λ. The temperature of the black body is now increased to 200◦C. The hotter black body now emits light most strongly at a wavelength closest to a) 0.8λ b) 2λ c) λ d) 1.3λ e) 0.5λ 9. Accelerating voltages in cathode-ray-tube (CRT) TV’s are about 24.0 kV. What is the shortest wavelength of the x-rays that are produced when the accelerated electrons hit the screen. a) 0.052 nm b) 7.8nm c) 0.008nm d) 52nm e) 5.6 ×1018Hz 10. An electron is trapped in a one-dimensional infinite potential well of width 10−10 m. What is the energy of the photon emitted when the electron makes a transition from the first excited state (n = 2) to the ground state (n = 1)? a) 0.062 eV b) 150 eV c) 113 eV d) 37.4 eV e) 127 eV 11. The uncertainty in position of an electron in a certain state is 5× 10−10 m. The uncertainty in its momentum (in kg·m/s) must be: a) greater than 10−25 b) less than 10−25 c) less than 10−23 d) greater than 10−23 e) greater than 10−20 12. A hydrogen atom undergoes a transition from the n = 6 to the n = 2 state by emitting a photon. According to the Bohr model of the atom, if the angular momentum is conserved, what is the angular momentum of the photon that is emitted? a) 0h̄ b) 4h̄ c) 3h̄ d) 1h̄ e) 2h̄ 13. If light incident on a metallic surface is doubled in intensity, the maximum kinetic energy of electrons produced by the photoelec- tric effect will change from K to: a) 2K b) K/2 c) 4K d) K/4 e) K (no change) 3 14. A meter stick moves in the laboratory along the direction of its length with a speed of 1.2 × 108 m/sec. Its length, as seen by an observer at rest in the laboratory, is: a) 0.917 m b) 0.84 m c) 1.00 m d) 1.19 m e) 1.09 m 15. ψ(x) is the normalized wave function for a particle moving along the x axis. The probability that the particle is in the interval from x = a to x = b is given by: a) |ψ(b)|2 − |ψ(a)|2 b) ∫ b a ψ(x)dx c) ∫ b a |ψ(x)| 2dx d) ψ(b) − ψ(a) e) |ψ(b) − ψ(a)|2 16. Consider an electron with the free-particle wavefunction ψ(x, t) = A exp[i(kx− ωt)]. Which of the following is false? a) the energy of the electron is h̄ω. b) the probability distribution function is independent of x. c) A can be chosen to be a pure imaginary number. d) the momentum of the electron is h̄k . e) ψ(x, t) is not a stationary state. 4