An electron is placed in a finite well of width 1.2 nm and barrier height 1.5 eV.(a) Using Excel or some other plotting package, determine the allowed energies of the electron (in units of eV)? (Show the plot you used to solve the transcendental equation for the finite well, and indicate the intersection points that give the allowed energies.)(b) How many bound states are there?(c) What is the penetration depth (in nm) of the ground state wave function into the barrier region?(d) What is the penetration depth (in nm) of the highest energy wave function into the barrier region?(e) Provide a rough sketch of the wave functions in the finite well.(f) What are the allowed energies for an infinite well of the same width? Compare these energies in a table and in scaled diagrams of the allowed energies in the finite and infinite wells (similar to what is shown in the notes).(g) The electron is in its ground state. What is the photon energy needed to excite the electron to its first excited state for (i) the finite well and (ii) the infinite well? Compare your results. Is the infinite well a reasonable approximation to the finite well in this case?
This question was answered on: Sep 21, 2023
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