PH214_2008SPRING_EXAM3_PROFSOLN_[0]

# PH214_2008SPRING_EXAM3_PROFSOLN_[0] - Ph 214 Spring 2008...

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Ph 214, Spring 2008 Exam # 3 Multiple Choice Name: SOLUTIONS N.B. A question with a next to the number is one of the Fve ”trivial” questions. Questions 1 and 2 : A car of rest length 5 meters passes through a garage of rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage’s rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time. 1. [4 pts] The velocity of the car in the garage’s rest frame is (A) 0 . 8 c 2. [4 pts] Which of the following statements is the best response to the question, ”Was the car ever inside the closed garage?” (E) There is no unique answer to the question, as the order of the door openings and closings depends on the reference frame. 3. [4 pts] The solution to the Schr¨ odinger equation for the ground state of hydrogen is ψ 0 = 1 r πa 3 0 exp r/a 0 , where a 0 is the Bohr radius and r is the distance from the origin. Which of the following is the most probable value for r ? (D) a 0 4. [4 pts] Blue light of wavelength λ = 480 nm is most strongly re±ected o² a thin Flm of oil on a glass slide when viewed near normal incidence. Assuming that the index of refraction of the oil is 1 . 2 and that of the glass is 1 . 6, what is the minimum thickness of the oil Flm (other than zero) ? (B) 200 nm 2 t = λ oil 5. [4 pts] A free particle with initial kinetic energy E and de Broglie wavelength λ enters a region in which it has potential energy V . What is the particle’s new de Broglie wavelength? (E) λ (1 V/E ) 1 / 2 6. [4 pts] A charged particle oscillates harmonically along the x axis as shown in the Fgure. The radiation from the particle is detected at a distant point P , which lies in the xy plane. The electric Feld at P is in the (C) xy -plane and has a maximum amplitude at θ = 90 1

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Ph 214, Spring 2008 Exam # 3 Multiple Choice Name: SOLUTIONS 7. [4 pts] Let Ψ n ( x,t ) represent the normalized n th eigenfunction of the one- dimensional harmonic oscillator p V ( x ) = 1 2 2 0 x 2 P . If Ψ( x,t ) is a normalized superposition state given by the linear combination Ψ( x,t ) = 1 14 Ψ 1 ( x,t ) + 2 14 Ψ 2 ( x,t ) + 3 14 Ψ 3 ( x,t ). What is the expectation value of energy a E A for this superposition state? (E)
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PH214_2008SPRING_EXAM3_PROFSOLN_[0] - Ph 214 Spring 2008...

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