Physics 2D Winter 2015: Final Exam 1 Version A Closed book. No work needs to be shown for multiple-choice questions. You may use a calculator. All values are in SI units unless explicitly stated otherwise. 1) Due to the Hubble expansion of the universe, a distant galaxy is moving at a velocity of 0.99c away from the earth. At what wavelength will the Lyman alpha line (n=2 goes to n=1) from that galaxy’s Hydrogen be observed on earth? a. 121.5 nm b. 8.61 nm c. 1715 nm d. 657 nm e. None of the above. 2) An astronaut makes a round trip to a star 10 light years away. He goes with a velocity of 0.6c then immediately turns around and comes back with the same velocity. How many years has he aged when he returns to the earth? a. 33.3 years b. 18.4 years c. 26.7 years d. 20 years e. none of the above 3) An electron is accelerated from rest through a voltage of 2.5 million Volts. What is the electron’s momentum? a. 3.15 MeV/c b. 3.11 MeV/c c. 0.511 MeV/c d. 3.07 MeV/c e. none of the above 4) The origins of two inertial frames coincide at t=0. The K’ frame moves relative to the K frame at a velocity of 0.5c in the +x direction. In the K frame, a proton is at rest. What is the momentum 4-vector of the proton in the K’ frame? a. (938.3, 472, 0, 0) MeV/c b. (1083, 542, 0, 0) MeV/c c. (1083, -542, 0, 0) MeV/c d. (938, -472, 0, 0) MeV/c e. none of the above 5) The photocurrent of a photocell is cut off by a retarding potential of 1.6 V for radiation of wavelength 450 nm. Find the work function for the material. a. 4.36 eV b. 2.76 eV c. 1.6 eV d. 1.16 eV e. none of the above 6) The classical calculation of blackbody radiation by Rayleigh and Jeans had what problem with experiment. a. There was a small disagreement in the Wien displacement law b. Rayleigh-Jeans predicted an infinite rate of radiation in strong disagreement with the data. c. The total output of a BB was off by a factor of about 2 d. The data showed radiation was proportional to T4 while the calculation showed a smaller dependence on temperature. e. None of the above. Physics 2D Winter 2015: Final Exam 2 7) A Tungsten filament is heated to 2200 degrees Kelvin. At what wavelength will the maximum amount of radiation be emitted? a. 656 nm b. 1022 nm c. 1.32 µm d. 1.55 mm e. none of the above 8) If the intensity is turned down in a 2 slit diffraction experiment so that there is only one photon in the detector at a time, what will the observed distribution of photons be after enough time to accumulate measurements? a. The sum of the distributions from slit 1 and slit 2 b. The normal 2 slit diffraction pattern c. The sum of the electric fields from the two slits d. There is no pattern e. none of the above 9) It is observed that α particles with kinetic energies of 8 MeV and higher, incident on Al foil, do not obey Rutherford’s scattering formula for angles very near 180 degrees. What is the nuclear size of Aluminum from this observation? a. 4.68 X 10-15 m b. 4.68 X 10-12 m c. 4.68 X 10-16 m d. 4.62 X 10-14 m e. none of the above 10) Light from excited Hydrogen atoms is observed with a wavelength of 4.05 microns. What atomic transition could this light come from? a. From n=7 to n=6 b. From n=6 to n=5 c. From n=5 to n=4 d. From n=4 to n=3 e. none of the above 11) Calculate the de Broglie wavelength of a proton that is accelerated through a potential difference of 5 million Volts. a. 253 nm b. 253 fm c. 12.8 nm d. 5.3 fm e. None of the above. 12) An electron is in a 1D box with length of 2 nm. Find the energy of the 2nd excited state. a. 1.13 eV b. 0.094 eV c. 0.376 eV d. 0.846 eV e. None of the above. 13) A Hydrogen atom in the 3D state is put into a magnetic field. Including the Fine Structure and the splitting in the field, into how many energy states will the 3D state be split? a. 2 b. 5 c. 10 d. 18 e. None of the above. Physics 2D Winter 2015: Final Exam 3 14) Which of the following spin states of two electrons is symmetric under interchange? (Assume the first of two arrows is the spin state of electron 1 and the second is the state of electron 2.) a. ↑↓-↓↑ b. ↑↓ c. ↓↓ d. all of the above e. none of the above. 15) The Helium first excited state has one electron in the 1s state and the other electron in the 2s state. (Recall that the big effect on the energies of the states is the Coulomb repulsion between the two electrons). Which state below is (one of) the first excited state(s) of Helium? a. ψ1s ! r( 1)ψ2s ! r( 2 ) χ+ (1) χ+ (2) b. 1 2 ψ1s ! r( 1)ψ2s ! r( 2 ) +ψ2s ! r( 1)ψ1s ! r( 2 ) ! ” # $χ+ (1) χ+ (2) c. 1 2 ψ1s ! r( 1)ψ2s ! r( 2 ) +ψ2s ! r( 1)ψ1s ! r( 2 ) ! ” # $ χ+ (1) χ− (2) − χ− (1) χ+ (2) ! ” # $ d. 1 2 ψ1s ! r( 1)ψ2s ! r( 2 ) −ψ2s ! r( 1)ψ1s ! r( 2 ) ” # $ % χ+ (1) χ− (2) + χ− (1) χ+ (2) ” # $ % e. 1 2 ψ1s ! r( 1)ψ2s ! r( 2 ) −ψ2s ! r( 1)ψ1s ! r( 2 ) ” # $ % χ+ (1) χ− (2) − χ− (1) χ+ (2) ” # $ % 16) What is the main reason that the atomic shell model works well? a. The periodic table shows that elements from the same column have similar chemical properties. b. Closed shells are tightly bound, spherically symmetric, and have total angular momentum 0. c. Hund’s rule maximizes the number of unpaired electrons. d. The Coulomb repulsion between electrons is small. e. None of the above. 17) The H2 molecule is bound together by electrons in the 1s state, shared between the atoms. What can be the spin state of the 2 electrons? a. 1 2 χ+ (1) χ− (2) + χ− (1) χ+ (2) ” # $ % b. χ+ (1) χ+ (2) c. χ− (1) χ− (2) d. 1 2 χ+ (1) χ− (2) − χ− (1) χ+ (2) ” # $ % e. a, b, and c 18) Energy bands and band gaps in solids are derived from: a. The covalent bonds between atoms. b. Ionic bonds between atoms. c. Doping of the crystal. d. Translation symmetry in the regular structure. e. None of the above. 19) Which statement about the PN junction in a diode is false? a. Electrons from the N region diffuse across the junction into the P region. b. An electric field is created in the region of the junction. c. In the region around the junction, there are very few holes in the P region. Physics 2D Winter 2015: Final Exam 4 d. There is a voltage drop across the junction that opposes current in the forward direction of the diode. e. None of the above. 20) The half-life of 131I is 8.04 days. The safe level of this isotope in drinking water is considered to be 100 Becquerels per liter. If the water supply around a reactor disaster has an activity of 500000 Bq per liter, what is the minimum time one must wait for the water to be safe? a. 6530 days b. 1.44 X 105 days c. 92.9 days d. 98.8 days e. None of the above. 21) At t=0, a Harmonic Oscillator with mass m and classical angular frequency ω is in the state � = ! ! �! � − �! � , where un is the nth energy eigenstate of the HO. What is the wave function at a later time t? a. � = ! ! �! � �!!!”# − �! � �!!”# b. � = ! ! �! � + �! � c. � = ! ! �! � �!!”# − �! � �!!!!”/! d. � = ! ! �! � − �! � �!!”# �!!!!”/! e. none of the above 22) At t=0, a Harmonic Oscillator with mass m and classical angular frequency ω is in the state � = ! ! �! � − �! � , where un is the nth energy eigenstate of the HO. What is the expected value of x, 〈x〉, at a later time t? a. − ℏ !” cos �� b. ℏ !” cos �� c. ℏ !” sin �� d. ℏ !!” sin �� e. − ℏ !!” cos �� 23) 238U decays by α emission followed by β – emission followed again by β – emission. What isotope is the product of this decay chain? a. 234Th b. 234Ra c. 234U d. 236Th e. 235Pa 24) What type of symmetry is the basis for Electromagnetic, Strong, and Weak forces in Quantum Field Theory? a. Rotation symmetry b. Parity symmetry c. Translation symmetry d. Gauge symmetry. e. Time symmetry Physics 2D Winter 2015: Final Exam 5 25) About what fraction of the mass-energy density of the universe is made up of normal matter that we see on earth, like photons, electrons, protons, neutrons, atoms, and nuclei (excluding neutrinos)? Ch16Q1 a. 5% b. 25% c. 65% d. 0% e. 0.5% 26) We see almost no antimatter in the universe but believe that a lot of antimatter was produced in the big bang. Why do we see matter but not antimatter? a. In the early universe the was a lot of matter and antimatter but there about 1.0000000001 times more mater. After matter and antimatter annihilated, only matter was left. b. Gravity is repulsive between matter and antimatter so part of the universe is made out of matter and part antimatter. Our galaxy is matter. c. All the antimatter went backward in time and disappeared into the big bang. d. Over the age of the universe, the antimatter changed into matter. e. Maybe someone used up all the antimatter propelling starships. 27) What is inflation in the early universe? a. After the explosion, everything was moving outward inflating the size of the universe. b. Very soon after the big bang, the space-time expanded in size by a factor of e60 in something like 10-33 seconds. c. Atoms, molecules, galaxies, and everything grew bigger as the universe got older. d. Due to the dark energy, the universe expands faster and faster. e. When the emperor printed too much imperial currency, it lost value quickly. 28) Fraternal twins Speedo and Notso travel to a planet 20 light years from the earth. Speedo’s spaceship moves at 0.95c relative to the earth and Notso travels at the relatively slow speed of 0.8c. How will the twins differ in age when both have arrived at the planet? (We assume rapid acceleration and deceleration.) a. Speedo will be 8.43 years younger than Notso. b. Speedo will be 6.57 years younger than Notso. c. They will be the same age. d. Speedo will be 4.48 years younger than Notso. e. None of the above. 29) A distant galaxy is moving at a velocity of 0.99c away from the earth. At what wavelength will the Lyman alpha line from that galaxy’s Hydrogen be observed on earth? a. 121.5 nm b. 8.61 nm c. 1714 nm d. 657 nm e. None of the above. 30) A proton is accelerated in a Van de Graff with a potential difference of 1000 MeV. What will the final momentum of the proton be? a. 1696 MeV/c b. 1370 MeV/c c. 1000 MeV/c d. 1939 MeV/c e. None of the above. Physics 2D Winter 2015: Final Exam 6 31) A Lorentz transformation to a velocity of 0.5c in the z direction is viewed in 4-dimensional Minkowski space as a: a. A rotation about the t axis through tanh-1(0.5) b. A rotation in the x-t plane through tanh-1(0.5) c. A rotation about the x axis through tanh-1(0.5) d. A translation in the x direction by tanh-1(0.5) e. None of the above. 32) A rechargeable AA battery with a mass of 50 grams can supply 1.2 Watts to a LED for 2 hours. 50% of its power is delivered electrically while an additional 50% is lost to heat in the battery. What is the difference in mass between the charged and totally discharged battery? a. 1.51 X 10-17 kg b. 3.04 X 10-9 kg c. 1.92 X 10-13 kg d. 2.95 X 10-6 kg e. None of the above. 33) A material has a work function of 3.5 eV. What is the cutoff wavelength for the photoelectric effect. a. 169 nm b. 221 nm c. 1340 nm d. 354 nm e. None of the above. 34) The classical Rayleigh-Jeans calculation of black-body radiation had what problem with measurements. a. There was a small disagreement in the Wien displacement law b. Rayleigh-Jeans predicted an infinite rate of radiation in strong disagreement with the data. c. The total output of a BB was off by a factor of about 2 d. The data showed radiation was proportional to T4 while the calculation showed a smaller dependence on temperature. e. None of the above. 35) Calculate the potential energy in the ground state of Hydrogen given the Radial wavefunction R10. a. -27.2 eV b. -13.6 eV c. -6.8 eV d. +6.8 eV e. None of the above. 36) Use the uncertainty principle to estimate the potential energy in the ground state of the harmonic oscillator. a. ℏω/4 b. ℏω/2 c. -ℏω/4 d. -ℏω/2 e. None of the above. 37) Calculate the de Broglie wavelength of a proton that is accelerated through a potential difference of 5 million Volts. Physics 2D Winter 2015: Final Exam 7 a. 253 nm b. 253 fm c. 12.8 nm d. 5.3 fm e. None of the above. 38) An atom in an excited state 2.4 eV above the ground state has a mean lifetime of 3 nanoseconds. What is the uncertainty in the energy of the photon in a transition to the ground state? a. 3.4 X 10-27 eV b. 9.2 X 10-16 eV c. 2.1 X 10-9 eV d. 1.1 X 10-7 eV e. None of the above. 39) For the first excited state of the Helium atom: a. The spin state is antisymmetric under interchange. b. The spin state is symmetric under interchange. c. The space state is symmetric under interchange. d. All the (1s)(2s) combinations are degenerate. e. None of the above. 40) The n=3 states in the Hydrogen atom are split by the spin-orbit and other relativistic effects lumped together as the Hydrogen fine structure (see ΔEfine). With the fine structure corrections, how many different energies will the n=3 states have (in the absence of a B field)? a. 18 b. 3 c. 9 d. 2 e. None of the above. 41) For the ground state of atoms in the periodic table, Hund’s rule says to first fill each ml state with a spin up electron then, when there are no more states in the shell without a spin up electron, to continue filling with spin down electrons. Why is this rule correct? a. This maximizes the number of unpaired electrons so that the spatial state is antisymmetric for all these pairs. b. This maximizes the number of unpaired electrons so that the spin-spin interaction gives the smallest contribution. c. This makes the spin state antisymmetric under interchange d. This is a rule to help us count states. e. None of the above. 42) For an electron in the 4d shell, what is the expected value of L2? a. 2ℏ2 b. 4ℏ2 c. 2ℏ d. 6ℏ2 e. None of the above. Physics 2D Winter 2015: Final Exam 8 43) Consider the original Stern-Gerlach experiment in which the magnetic moment of silver atoms is entirely due to the spin of a single valence electron. What is the difference in energy between the two spin states of the electron in a 1 T magnetic field? a. 5.08 X 10-5 eV b. 1.16 X 10-4 eV c. 1.77 X 10-1 eV d. 13.6 eV e. None of the above. 44) Eight identical electrons are put into a cubic box of side 0.1 nm. What is the ground state energy for the eight electrons? a. 1.58 X 103 eV b. 2.25 X 102 eV c. 6.77 X 102 eV d. 66.1 eV e. None of the above. 45) From the optical absorption spectrum of a semiconductor, the longest wavelength of photons absorbed is 3 micrometers. What is the band gap in this semiconductor? a. 0.26 eV b. 6.1 eV c. 2.30 eV d. 0.413 eV e. None of the above. 46) What is the radius for 235U? a. 7.40 fm b. 4.11 fm c. 255 fm d. 1.20 fm e. None of the above. 47) What radio frequency will cause transitions between spin states for free neutrons in a 2 T magnetic field. (µneutron = -1.91 µn) a. 5.75 X 108 Hz b. 5.82 X 107 Hz c. 4.34 X 106 Hz d. 9.12 X 105 Hz e. None of the above. 48) The half-life of 131I is 8.04 days. The safe level of this isotope in drinking water is considered to be 100 becquerels per liter. If the water supply around a reactor disaster has an activity of 300000 bq per liter, what is the minimum time one must wait for the water to be safe? a. 6530 days b. 1.44 X 105 days c. 92.9 days d. 0.611 days e. None of the above. Physics 2D Winter 2015: Final Exam 9 49) If a nuclear reactor has an electrical output of 1.21 GigaWatts, which represents only 30% of the fission power of the reactor due to inefficiency, how much 235U is used per year of running? (Assume a net energy of 208 MeV per fission and a 235U mass of 235 u.) a. 106 kg b. 6.34 kg c. 0.97 kg d. 33.9 kg e. None of the above. 50) Due to the Hubble expansion of the universe, a distant galaxy is moving at a velocity of 0.99c away from the earth. At what wavelength will the Lyman alpha line (n=2 goes to n=1) from that galaxy’s Hydrogen be observed on earth? Ch1P7P15 Ch4P12 a. 121.5 nm b. 8.61 nm c. 1714 nm d. 657 nm e. None of the above. 51) A material has a work function of 2.1 eV. What is the cutoff wavelength for the photoelectric effect? Ch3P15 a. 169 nm b. 221 nm c. 590 nm d. 354 nm e. None of the above. 52) The classical calculation of black-body radiation by Rayleigh and Jeans had what problem with experiment. Ch3Concept a. There was a small disagreement in the Wien displacement law b. Rayleigh-Jeans predicted an infinite rate of radiation in strong disagreement with the data. c. The total output of a BB was off by a factor of about 2 d. The data showed radiation was proportional to T4 while the calculation showed a smaller dependence on temperature. e. None of the above. 53) A proton is accelerated in a Van de Graff through a potential difference of 4 million Volts. What will the final momentum of the proton be? Ch5P7 Ch2P11 a. 4.12 MeV/c b. 86.6 MeV c. 4.12 kg m/s d. 86.6 MeV/c c e. 938.7 MeV/c 54) An atom in an excited state 2.4 eV above the ground state has a mean lifetime of 3 nanoseconds. What is the uncertainty in the energy of the photon in a transition to the ground state? Ch5P32 a. 3.4 X 10-27 eV b. 9.2 X 10-16 eV c. 2.1 X 10-9 eV d. 1.1 X 10-7 eV Physics 2D Winter 2015: Final Exam 10 e. None of the above. 55) Calculate the expected value of the potential energy in the ground state of Hydrogen given the Radial wavefunction R10. Ch8P24 a. -27.2 eV b. -13.6 eV c. -6.8 eV d. +6.8 eV e. None of the above. 56) For the first excited state of the Helium atom: Ch9Q25Q26 a. The spin state is antisymmetric under interchange. b. The spin state is symmetric under interchange. c. The space state is symmetric under interchange. d. All the (1s)(2s) combinations are degenerate. e. None of the above. 57) The n=4 states in the Hydrogen atom are split by the spin-orbit and other relativistic effects lumped together as the Hydrogen fine structure (see ΔEfine). With the fine structure corrections, how many different energies will the n=4 states have (in the absence of a B field)? Ch9P12P13Q11-13 a. 12 b. 3 c. 4 d. 8 e. None of the above. 58) For the ground state of atoms in the periodic table, Hund’s rule says to first fill each ml state with a spin up electron then, when there are no more states in the shell without a spin up electron, to continue filling with spin down electrons. Why is this rule correct? Ch9Concept a. This maximizes the number of unpaired electrons so that the spatial state is antisymmetric for all these pairs, thus lowering Coulomb repulsion. b. This maximizes the number of unpaired electrons so that the spin-spin interaction gives the smallest contribution. c. This makes the spin state antisymmetric under interchange d. This is a rule to help us count states. e. None of the above. 59) Consider the original Stern-Gerlach experiment in which the magnetic moment of silver atoms is entirely due to the spin of a single valence electron. What is the difference in energy between the two spin states of the atom in a 1 T magnetic field? Ch9P6 a. 5.08 X 10-5 eV b. 1.16 X 10-4 eV c. 1.77 X 10-1 eV d. 13.6 eV e. None of the above. 60) What radio frequency will cause transitions between spin states for free neutrons in a 1.2 T magnetic field. (µneutron = -1.91 µn) Ch13P4 a. 5.75 X 108 Hz Physics 2D Winter 2015: Final Exam 11 b. 5.82 X 107 Hz c. 4.34 X 106 Hz d. 3.50 X 107 Hz e. None of the above. 61) The half-life of 131I is 8.04 days. The safe level of this isotope in drinking water is considered to be 100 becquerels per liter. If the water supply around a reactor disaster has an activity of 500000 bq per liter, what is the minimum time one must wait for the water to be safe? Ch13P22 a. 6530 days b. 1.44 X 105 days c. 92.9 days d. 98.8 days e. None of the above. 62) If a nuclear reactor has an electrical output of 1.21 GigaWatts, which represents only 30% of the fission power of the reactor due to inefficiency, how much 235U is used per year of running? (Assume a net energy of 208 MeV per fission and a 235U mass of 235 u.) Ch14P25 Ch2 a. 106 kg b. 6.34 kg c. 0.97 kg d. 33.9 kg e. None of the above. 63) The Mars colony’s radar, which is used to track spaceships in the area, has a frequency of 6.2 GHz. A spaceship leaving the colony is detected and the reflected wave has a frequency of 5.1 GHz. What is the velocity of the spaceship? Q1 Ch1P18 a. 0.0296c toward mars b. 0.396c toward mars c. 0.148c toward mars d. 0.193c away from mars e. 0.096c away from mars 64) At t=0, a Harmonic Oscillator with mass m and classical angular frequency ω is in the state � = ! ! �! � − �! � , where un is the nth energy eigenstate of the HO. What is the wavefunction at a later time t? Q3 Ch6P37 a. � = ! ! �! � �!!!”# − �! � �!!”# b. � = ! ! �! � + �! � c. � = ! ! �! � �!!”# − �! � �!!!!”/! d. � = ! ! �! � − �! � �!!”# �!!!!”/! e. none of the above 65) A Hydrogen atom is in the n=3 state. If a measurement of J2 is made, what are the possible outcomes? Q3 Ch8P10P13 a. 0, 2ħ2 , 6ħ2 b. 0, 2ħ2 , 6ħ2 , 12ħ2 c. 3 4 !2 , 15 4 !2 , 35 4 !2 d. -6ħ2 , -2ħ2 , 0, 2ħ2 , 6ħ2 Physics 2D Winter 2015: Final Exam 12 e. − 5 2 !, − 3 2 !, − 1 2 !, 1 2 !, 3 2 !, 5 2 ! 66) A proton moves at a speed of 0.7c. Calculate its total energy. Ch2P8 a. 1314 MeV b. 938.9 MeV c. 375.1 MeV d. 172100 MeV e. 0.772 MeV 67) A hydrogen atom initially at rest in the n=4 state decays to the ground state with the emission of a photon. Estimate the kinetic energy of the recoiling atom. Ch4P24 Ch2 a. 0.0866 eV b. 2.44X10-4 eV c. 4.62X10-6 eV d. 8.66X10-8 eV e. 7.79X10-8 eV 68) The band gap in Germanium is 0.72 eV. When used as a photon detector, roughly how many electronhole pairs can be made by a 3 keV photon that loses all its energy in the crystal? Ch12P a. 1.06 X103 b. 1.06 X106 c. 2084 d. 8334 e. 4167 69) For the low Z elements, the stable nuclei tend to have an approximately equal number of protons and neutrons. Explain why this is so. Ch14Q2 a. The neutron is more massive than the proton and decays into a proton. b. The highest probability is for the two numbers to about equal. c. The force between a proton and a neutron is stronger than the force between two neutrons or between two protons. d. The Coulomb repulsion favors more neutrons. e. As we add more protons or neutrons, the energy levels fill up and extra particles must go into higher energy states, but protons and neutrons are not identical so by keeping them equal, they go into the lowest E states possible and the attractive strong force between them increases Binding Energy. 70) What type of symmetry is the basis for Electromagnetic, Strong, and Weak forces in Quantum Field Theory? Ch15Q9 a. Rotation symmetry b. Parity symmetry c. Translation symmetry d. Gauge symmetry. e. Time symmetry 71) About what fraction of the mass-energy density of the universe is made up of normal matter that we see on earth, like photons, electrons, protons, neutrons, atoms, and nuclei (excluding neutrinos)? Ch16Q1 a. 5% Physics 2D Winter 2015: Final Exam 13 b. 25% c. 65% d. 0% e. 0.5% 72) We see almost no antimatter in the universe but believe that a lot of antimatter was produced in the big bang. Why do we see matter but not antimatter? Ch16Q10 Ch15 a. In the early universe the was a lot of matter and antimatter but there about 1.0000000001 times more mater. After matter and antimatter annihilated, only matter was left. b. Gravity is repulsive between matter and antimatter so part of the universe is made out of matter and part antimatter. Our galaxy is matter. c. All the antimatter went backward in time and disappeared into the big bang. d. Over the age of the universe, the antimatter changed into matter. e. Maybe someone used up all the antimatter propelling starships. 73) What is inflation in the early universe? Ch16Q14 a. After the explosion, everything was moving outward inflating the size of the universe. b. Very soon after the big bang, the space-time expanded in size by a factor of e60 in something like 10-33 seconds. c. Atoms, molecules, galaxies and everything grew bigger as the universe got older. d. Due to the dark energy, the universe expands faster and faster. e. When the emperor printed too much imperial currency it lost value quickly.