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MIDTERM EXAM – I [July 10, 2000] Department of Physics University of Cincinnati Course: Phy. 276 (“Modern Physics for Engineers”) Name: ____________________________ S.S.N: ________________ [Please answer all the questions] Problem 1: (40 points) With respect to an inertial frame S, a subatomic particle X is found to decay spontaneously into two particles, A and B, each of rest energy 100 MeV. The particles fly off in opposite directions, each with equal speed relative to S. The rest energy of X is 400 MeV. (a) What was the speed of X relative to S? Justify your answer. (10 points) (b) What is the total (relativistic) energy of A in S? (10 points) (c) Find the speed of A relative to S. (10 points) (d) What is the kinetic energy of B in S? (10 points) Problem 2: (20 points) A Lincoln Continental is twice as long as a VW Beetle, when they are at rest. As the Continental overtakes the VW, going through a speed trap, a (stationary) policeman observes that they both have the same length. The VW is going at half the speed of light. How fast is the Lincoln going? (Leave your answer in terms of ‘c’) Problem 3: (40 points) In a Compton scattering experiment, a 0.065 nm x-ray photon scatters off an electron at 60° to its initial direction. (h/mec = 0.00243 nm) (a) What is the wavelength of the scattered photon? (15 points) (b) Find the energy of the incident photon and the energy of the scattered photon. (10 points) (c) What is the energy gained by the electron? (15 points)