Consider a particle of mass m and energy E traveling tothe

Chapter 38, Problem 38.61

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Consider a particle of mass m and energy E traveling tothe right where it encounters a narrow potential barrier ofheight U0 and width as shown in Fig. 38-21. It canbe shown that:(i) for E < UQ, the transmission probability is and the reflection probability is R = 1 T.(ii) For E > Uq, the transmission probability is and R = 1 - T. Consider that the particle is an electron andit is incident on a rectangular barrier of height Uq = 10 eVand width = 1.0 X 1 0 10 m. (a) Calculate T and R for theelectron from E/U0 = 0 to 10, in steps of 0.1. Make a singlegraph showing the two curves of T and R as a function oiE/UQ.(b) From the graph determine the energies (E/Uq) at whichthe electron will have transmission probabilities of 10%,20%, 50%, and 80%. FIGURE 38-21 61.