Phy63S09-Exam2 - Physics 63L Exam 2 Spring 2009 Name Closed...

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Unformatted text preview: Physics 63L Exam 2 Spring 2009 Name: _________________________ Closed book; no notes. Exam 2 A. MULTIPLE CHOICE Circle the best answer (5 points each): Recitation Section:______ 1. Which of the following experimental results provides evidence that electrons have spin 1/2? a. Compton effect. b. Davison Germer experiment. c. Measurements of the spectrum of sodium vapor. d. Both a. and c. e. Both b. and c. 2. In an experiment, different wavelengths of light, all able to eject photoelectrons, shine on a freshly prepared (oxide-free) zinc surface. Which statement is true? a. b. c. d. e. The number of photoelectrons emitted per second is independent of the intensity of the light for all the different wavelengths. The number of photoelectrons emitted per second is directly proportional to the frequency for all the different wavelengths. For each wavelength present, all photoelectrons are emitted with a single quantized value of kinetic energy that depends on wavelength. The maximum kinetic energy of the photoelectrons is proportional to the intensity of the light and independent of the frequency. The maximum kinetic energy of the photoelectrons has a linear relationship with the frequency for each wavelength present. 1 Physics 63L Exam 2 Spring 2009 3. An electron is in the ground state of the H atom such that its energy is −13.6eV . How many distinct quantum states are there that possess this energy? a. b. c. d. e. 1 2 4 8 16 4. An electron with kinetic energy of 5 eV is incident on a rectangular tunneling barrier of height 10 eV with a thickness d and has a probability of ¼ to tunnel through the barrier. If the barrier length is doubled to thickness 2d then the tunneling probability becomes: a. b. c. d. e. 1/8 1/16 1/32. ¼, unchanged. Not enough information given to make a unique determination. 2 Physics 63L Exam 2 Spring 2009 B. TRUE/FALSE Circle the best answer (3 points each): 1. The Davison-Germer experiment involves the diffraction of x-rays by crystalline material. TRUE FALSE 2. An electron and a photon both have energy 3 eV. Then, the electron de Broglie wavelength must be shorter than the wavelength of the photon. TRUE FALSE 3. The best materials for slowing down neutrons have relatively small A values. TRUE FALSE 4. In beta decay, the emitted beta particle has a continuous range of kinetic energies up to a maximum value. TRUE FALSE 3 Physics 63L Exam 2 Spring 2009 22 points PROBLEM C-1. (a) A proton (mp= 1.67 X 10-27 kg) is confined in a onedimensional box of length L. Derive an expression – in terms of L, mp , and for the minimum kinetic energy that this proton must have due to the Uncertainty Principle. Assume that the box is large enough so that you can safely neglect relativistic effects. (b) Evaluate this energy (in eV units) when L = 1 fm = 10-15 m. (c) Consider now an electron (me = 9.11 X 10-31 kg), confined to the same onedimensional box with L = 1 fm. Find the minimum energy for this case, again neglecting relativistic effects. (d) Use your result of part (c) to estimate the velocity of the electron. What does your result say about the assumption that relativistic effects are negligible for the electron in the box? 4 Physics 63L Exam 2 Spring 2009 24 points PROBLEM C-2 Two electrons (each of mass m and spin ½) are sitting in a onedimensional simple harmonic oscillator potential U ( x ) = mω 2 x 2 2 . In the problem below we will neglect the repulsive Coulomb interaction between the electrons. (a) What is the minimum total energy – equivalently, the ground state energy - for the entire two particle system? Express your answer in terms of and ω . (b) For the minimum energy state of part (a), sketch the spatial wavefuction(s) that the individual electrons are sitting in. Also, you should specificy the spin quantum number ms for each electron. 5 Physics 63L Exam 2 Spring 2009 (C-2 continued on next page) C-2 continued (c) What is the energy of the first-excited state of the two-particle system. What is the degeneracy of this state; in other words, how many distinct quantum states have this same energy? (d) An external magnetic field B is now applied to this system. This causes the firstexcited state energies to split according to different ms values. Based on this observation, what is the new first-excited state energy? (e) If B is large enough, show that the first excited state from part (d) can actually have a lower energy than the original ground state energy from part (a). Find an expression for the value of B for which this transition occurs. 6 Physics 63L Exam 2 Spring 2009 22 points PROBLEM C-3 Write a short essay describing and contrasting the following three types of actual and/or proposed nuclear-based power generation: fission, D-T fusion, and aneutronic fusion. For each of the three processes, provide a specific example of the nuclear reaction involved. Which of these processes have so far demonstrated “break even” operation. Please limit your comments to one page. 7 Physics 63L Exam 2 Spring 2009 A. B. C-1 C-2 C-3 total 8 ...
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