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Modern physics 2330 Incomplete Exam. Time: Two Hours The Islamic University of Gaza Department of Physics .........................................: الرقم الجامعي....................................................................:االسم ============================================================= Q1 Indicate (√ ) for true statement and (× ) for false statement. 1- ( ) According to the special theory of relativity, interaction between objects in nature propagates with infinite speed. 2- ( ) An event is determined by the location where, and by the time at which occurs. 3- ( ) According to classical mechanics, a moving clock runs slower than one at rest. 4- ( ) The number, strength, and exact position of the lines in the spectrum of an element depend only upon temperature. 5- ( ) According to de Broglie, the electron of the Bohr atom forms a standing h wave around the nucleus with . p 6- ( ) Davisson-Germer experiment (1927) is a direct experimental proof that the electron charge is, e=1.6x10-19C. 7- ( ) Classical mechanics is a special (limiting) case of relativistic mechanics. 8- ( ) The Heisenberg uncertainty principle states that, position and conjugate momentum can not be measured simultaneously with any degree of accuracy. 9- ( ) A wave packet is a superposition of many plane waves. 10- ( ) In classical mechanics the state of a particle is fully determined by its wavefunction x . Q2 Explain in details the Davisson-Germer experiment. Q3 Discuss both Rutherford and Bohr atomic models. Q4 Show that the group velocity of the matter wave particle v g is the same as the particle speed v. E (Hint: you may need the relations, v p , E p 2 c 2 m 2 c 4 , and the p relativistic energy and momentum respectively are, E mc 2 , p mv ) Q5 Consider a 200 gram object in a box 10 m on a side, moving with a speed of 3 m/s along x-axis. Show that the spread of velocities caused by the uncertainty principle does not have measurable consequences for macroscopic object. Q6 A particle is described by the wave function L L x , for x A cos x 2 2 L 0, otherwise. a) Determine the normalization constant A. b) What is the probability that the particle will be found between L x 0 and x if a measure of its position is made. 4