- Please Answer Parts C D And E 1 (54.45 KiB) Viewed 63 times
please answer parts c d and e .
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please answer parts c d and e .
please answer parts c d and e .
1. (a) An electron is moving in a thin metal wire of length L. State a quantum mechanical model for this system. Explain your reasoning. (b) Using your model, compute the ground-state energy of the electron for L = 1 cm. Calculate the probability of finding the electron in the region 0 < x < 0.25 cm Sketch this probability on a suitable graph. (c) The length of the wire is now reduced to L=0.1 nm. Compute the 3 lowest energies of the electron. Sketch these energies on an energy level diagram. Find the wavelengths of the photons emitted when the electron makes transitions from the n= 3 energy level. (d) Given that the initial wave function of the electron in the wire is (x,0) = Ax, 0 SXSL Determine the constant A. Hence, find '(x, t). (e) Calculate the probability that the electron is in the energy level E1, Ez and Ez.
1. (a) An electron is moving in a thin metal wire of length L. State a quantum mechanical model for this system. Explain your reasoning. (b) Using your model, compute the ground-state energy of the electron for L = 1 cm. Calculate the probability of finding the electron in the region 0 < x < 0.25 cm Sketch this probability on a suitable graph. (c) The length of the wire is now reduced to L=0.1 nm. Compute the 3 lowest energies of the electron. Sketch these energies on an energy level diagram. Find the wavelengths of the photons emitted when the electron makes transitions from the n= 3 energy level. (d) Given that the initial wave function of the electron in the wire is (x,0) = Ax, 0 SXSL Determine the constant A. Hence, find '(x, t). (e) Calculate the probability that the electron is in the energy level E1, Ez and Ez.