Physics 107: Ideas of Modern Physics Exam 3 Nov. 30, 2005 Name ID # Section # On the Scantron sheet, 1) Fill in your name 2) Fill in your student ID # (not your social security #) 3) Fill in your section # (under ABC of special codes) Fundamental constants: c= speed of light = 3x10 8 m/s g= accel. of gravity on Earth = 10 m/s 2 G= gravitational constant = 6.7x10-11 N-m 2 /kg 2
1. A 2 2 According to Einstein, increasing the brightness of a beam of light without changing its color will increase a. the number of photons per second b. the energy of each photon c. the photon speed d. the frequency of each photon e. the wavelength of each photon Same color means same frequency. The wavelength is inversely proportional to frequency. And since the energy of each photon is hf, the energy is constant. Photons always travel at the speed of light. 3. A scientist is trying to eject electrons from a metal by shining a light on it, but none are coming out. To eject electrons, she should change the light by a. decreasing the frequency b. increasing the frequency c. increasing the intensity d. increasing the wavelength e. asking Einstein If no electrons are ejected from the metal, the incoming photon did not have enough energy. To increase the energy of the photon, the frequency should be increased (E=hf). Each photon interacts with only one electron, so increasing the intensity does not help. 4. A beta particle, gamma ray, and alpha particle all have the same momentum. Which has the longest wavelength? a. beta particle. Since wavelength =Planck s constant / momentum, b. gamma ray. Same momentum means same wavelength. c. alpha particle. d. all the same. e. depends on gamma ray energy. 5. Particular red (600 nm) and blue (300 nm) lasers both produce 10 mw of power. How do the number of photons per second from each compare? a. Both the same. b. Blue has one quarter as many as red. c. Blue has half as many as red. d. Blue has twice as many as red.. e. Blue has four times as many as red Power is energy / second, so each beam has the same energy / second coming out of the laser. The energy of each photon is hc / λ. Since each blue photon has twice the energy of each red photon, we only need half the number of blue photons / second as red photons / second. 2
6. A quantum particle in a box is in the lowest energy (ground) state. If the size of the box is decreased, the energy of the particle 3 a. becomes larger b. becomes smaller c. is unchanged d. becomes negative e. cannot be measured The energy is determined by the wavelength of the particle. In the lowest energy state, half a wavelength fits inside the box. As the box gets narrower, the wavelength fitting in must be shorter, and hence the energy higher. 7. A photon is found to have 100 ev of energy. Which answer is closest to its wavelength? a. 12000 nm b. 1200 nm c. 120 nm d. 12 nm e. 1.2 nm E = hf = hc 1240 ev # nm =, so " " (nm) 1240 ev # nm 1240 ev # nm " (nm) = = E (ev ) 100 ev =12.4 nm 8. Wave-particle duality was the first adequate explanation of which of the following properties of a hydrogen atom? a. An infinite number of possible orbits exist for the electron. b. More than one possible orbit exists for the electron. c. Only certain energies are possible for the electron. d. More than one momentum is possible for the electron. e. All of the above. 9. A particle in a box has quantum states with energies E=E o n 2, with n=1,2,3,4 and E o =1 ev. Which of these photons could in principle be absorbed? a. 1 ev b. 2 ev c. 4 ev d. 5 ev e. 6 ev A photon is absorbed when the particle jumps from a lower energy state to a higher energy state. The energy gained by the particle is provided by the photon, so the photon energy must correspond to the difference between energies of two quantum states for the particle. 2 2 The photon energy must be ( 1eV )( n final " n initial ). The only one that works is 5eV = ( 1eV )( 3 2 " 2 2 ). 3
4 10.The energy levels of a hydrogen atom are given by E = 13.6/n 2 ev. Calculate the wavelength of a photon emitted as a result of the n=3 to n=2 transition. a. 270 nm b. 150 nm c. 360 nm d. 820 nm e. 650 nm The electron loses -13.6 ev/3 2 -(-13.6 ev/2 2 )=1.89 ev This energy is carried away by the photon. The wavelength of the photon is related to its energy as " = 1240 ev # nm E (ev ) = 1240 ev # nm 1.89 ev = 656 nm 11. A quantum particle in a box is in an excited quantum state. The momentum of the particle is uncertain because a. the quantum state is a superposition of two different momenta. b. the quantum state is entangled. c. on average the particle has a momentum greater than zero. d. the particle is not in the quantum ground state. e. the particle could quantum-mechanically tunnel out of the box. 12. For the wavefunction shown below, at which point is the probability of finding the particle the smallest? a. A b. B c. C d. D e. Cannot be determined only from the wavefunction. +1 0-1 A The probability is the square of the wavefunction. The smallest probability then is zero, which occurs at B. B C D 13. The strong force acts between which of the following particles in an atom? (nucleon = proton or neutron) a. between all nucleons b. between protons only c. between neutrons only d. between a proton and a neutron only e. between protons and electrons only The strong interaction binds together protons and neutrons in the nucleus. It acts equally between two neutrons, two protons, or between neutron or a proton. 4
14. Below are three wavefunctions for a particle in a box. Which has the highest energy? 5 a. A b. B c. C d. A and B equal and highest e. B and C equal and highest A has the shortest wavelength and so the highest kinetic energy. The energy of a particle in a box is entirely energy of motion (kinetic), so A represents the particle with the highest energy. A B C 15. 14 C has 6 protons and 8 neutrons in its nucleus, and 6 electrons orbiting around the nucleus. It decays by emitting an electron from the nucleus. After the decay, it becomes a. 12 C b. 13 C c. 14 B d. 14 N e. 15 N B is the element with 5 electrons C is the element with 6 electrons N is the element with 7 electrons When 14 C emits an electron from the nucleus, a neutron in the nucleus changes to a proton in the nucleus. This keeps the number of nucleons the same, but increases the number of protons from 6 to 7 and decreases the number of neutrons from 8 to 7. Since N has 7 electrons, it has 7 protons in the nucleus. 16. A fossil bone has a 14 C : 12 C ratio that is 1/16 of the 14 C : 12 C ratio in the bone of a living animal. What is the approximate age of the fossil? ( 14 C half-life is 5,730 years). a. 11,460 years b. 17,190 years c. 22,920 years d. 45,840 years e. 91,680 years For each half-life, the 14 C : 12 C ratio decreases by a factor of two. To get to a ratio of 1/16 requires four half-lives. Since one half-life is 5,730 years, this is 4 x 5,730 yrs = 22,920 years. 5
17. 234 U has 92 protons and 234 nucleons total in its nucleus. It decays by emitting an alpha particle. After the decay, it becomes 6 a. 232 U b. 232 Pa c. 230 Th d. 230 Ra e. 234 Th U is the element with 92 electrons Pa is the element with 91 electrons Th is the element with 90 electrons Ra is the element with 88 electrons In alpa decay, the nucleus emits an alpha particle, which consists of two protons and two neutrons. So the number of nucleons goes down by four, and the number of protons goes down by two. The atomic number must then be 230, and the corresponding element is the one with 90 protons in its nucleus. 18. Nuclear fission occurs most commonly a. after nuclear fusion b. after neutron capture c. in low-mass nuclei d. after collision of two nuclei e. at extremely high temperatures The fission process is started by a heavy nucleus absorbing a neutron. It does not require high temperature, and is not related to fusion (which occurs when two low-mass nuclei collide). 19. The number of Fermions (such as electrons) that can be in a particular quantum state: a. one b. two c. any number d. any number except zero e. depends on the spin of the Fermion 20. That energy is released as a result of nuclear fission is most clearly explained as a. Daughter nuclei bound more tightly than initial nucleus b. The number of nucleons changes c. Neutrons ejected during fission can Energy induce can a only chain be reaction released if the final products have less 21. An energy band in a solid is a. A band connecting atoms in the crystal b. A region of high energy concentration in the crystal c. An energy range densely packed with quantum states d. A band of low-energy atoms in a crystal. e. A single quantum state on a group of atoms in the crystal. A fermion is a particle with half-integer spin (e.g ½, 3/2, 5/2, etc). Only one fermion can be in a particular quantum state. d. Incoming neutron transfers energy energy to the than nucleus the initial particles leading to fission. That the e. Heavy nuclei can be unstable final products have less energy can be traced to the fissioned nuclei being bound more tightly. The difference in binding energy is released as fission power. In a solid, the quantum states on each atom are altered slightly by the presence of the other atoms so that their energies are shifted. They then don t all appear at the same energy, but are spread out over a small band of energies. 6