PH 253 Midterm: ph253_S13_Exam_1_SOLN
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Ph 253 exam i solutions: an electron and a proton are each accelerated starting from rest through a potential di erence of 10. 0 million volts (107 v). Find the momentum (in mev/c) and kinetic energy (in mev) of each, and compare the results with the classical expectation. Each particle has a charge |q| = e, and when accelerated through a potential di erence of v changes its potential energy by e v. This must equal the change in kinetic energy of the particle. Thus, k = e v = 107 ev = 1. 6 10 12 j for both. From this, we can use the relativistic kinetic energy expression to nd the velocity, and from that the momentum. The algebraic expressions are the same for both - the only di erence between the two cases is the particle mass. K = q v = ( 1) mc2 q v mc2 + 1 p = mv = mr1 .