In the equation for the timedependent wave function {IL/17, t) : W(x)e*m : Aemiwl | Be*i(k$+ml keep both terms, putting A = B = \\110. The equation then describes the superposition of two matter waves of equal amplitude, traveling in opposite directions. (Recall that this is the condition for a standing wave.) (a) Find |\\Il(a:,t)l2. Mast)? = l (b) Find the positions of the nodes of this standing wave in terms of A, the de Broglie wavelength of the particle. 96: (c) Find a similar expression for the most probable locations of the particle. What are (a) the energy of a photon corresponding to wavelength 8.00 nm, (b) the kinetic energy of an electron with de Broglie wavelength 8.00 nm, (c) the energy of a photon corresponding to wavelength 8.00 fm, and (d) the kinetic energy of an electron with de Broglie wavelength 8.00 fm? (a) Number Units (b) Number Units (c) Number Units (d) Number i Units eTextbook and MediaA 1600 kg car moving at 21 m/s approaches a hill that is 26 m high and 35 m long. Although the car and hill are clearly too large to be 87-m( Up - E) treated as matter waves, determine what the equation Tze-2bl, where b = 1 , m is the mass, L is the barrier thickness, Ub - h 2 E is the energy difference and h is the Planck constant, predicts for the transmission coefficient of the car, as if it could tunnel through the hill as a matter wave. Treat the hill as a potential energy barrier where the potential energy is gravitational. Find the value of x in the expression T=ex. x = Number Units