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Midterm 1 F98 solutions

Modern Physics

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file:///C|/Documents%20and%20Settings/Linda%20Grauer/My%20Doc...20HEP-H2/PHY251%20Sp01/Phy251%20Fa98/PHY251_M1_F98solutn.html Name: PHYSICS 251 - Midterm I Wednesday Oct 14, 1998 I. Short answer problems: (60 points) a. List and/or name: (16 points) i. An important set of equations that showed c = 1 / √εμ , and foreshadowed Einstein's Special Theory of Relativity. Maxwell's equations for electro-magnetism incorporated the existence of electro- magnetic waves propagating in vacuo with speed c . ii. A significant experiment that led directly to Einstein's Special Theory of Relativity. The Michelson-Morley experiment, which proved the non-existence of the aether as medium for the propagation of electro-magnetic waves, and showed that c was independent of the reference frame. iii. Three historic experiments that gave strong evidence for the particle character of light (light quanta or photons). a. The photo-electric effect; photons being absorbed only in quantized packages. b. Compton scattering of light off electrons; as if photons were simple particles. c. Planck's law of black-body radiation; quantized character of electro- magnetic wave absorption and re-emission by the walls. iv. Three experiments or experimental observations that are clear evidence for the wave character of sub-atomic particles (e.g. electrons). a. Electron diffraction (Davisson-Germer experiment). b. Tunneling of particles through classically forbidden regions; the explanation for radio-active decay of nuclei with the emission of alpha particles. c. The existence of discrete (quantized) energy levels in atoms, which can only be explained using the wave character of electrons. b. A muon has a mean lifetime (in its own rest frame) τ 0 = 2.2×10 -6 s. Calculate the mean distance it will travel in the lab, when its speed is v = 0.95 c . (4 points) The muon, viewed in the laboratory, will have a mean lifetime which is dilated by the factor γ : τ = γτ 0 = 2.2×10 -6 s / [1 - (0.95 c / c )²] = 3.20× 2.2×10 -6 s = 7.0 μ s. c. Prove that dE / dp = v , with for E the relativistic expression for the total energy of a particle file:///C|/Documents%20and%20Settings/Linda%20Gra...251%20Sp01/Phy251%20Fa98/PHY251_M1_F98solutn.html (1 of 6) [2/5/2008 11:41:30 AM]
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