Question

1. Consider an electron in a rigid box of length L = 1nm. You are not required to know how to solve the Schrödinger equation, but just need to know that En = n^2 * h^2 / (8mL^2) a. What are the energies for the first three energy levels? b. If the length of the box is doubled, what happens to the energies? c. For the n=3 state, determine, by examining the graphs of the probability density, if the probability of finding the particle in the left one-third of the box is less than, equal to, or greater than 1/3. d. If the electron in the ground state absorbs a photon of 412nm wavelength, which energy level will the electron be elevated to? e. If the box is not rigid any more and the potential energy at the boundary drops from infinity to 3.5 eV, how many bound states would you expect? What is the penetration distance of the electron in the ground state (the ground state energy in this finite potential well is roughly 0.252 eV)? f. Does the penetration distance become larger or smaller for the n=2 and n=3 states?

          1. Consider an electron in a rigid box of length L = 1nm. You are not required to know how to solve the Schrödinger equation, but just need to know that En = n^2 * h^2 / (8mL^2)
a. What are the energies for the first three energy levels?

b. If the length of the box is doubled, what happens to the energies?

c. For the n=3 state, determine, by examining the graphs of the probability density, if the probability of finding the particle in the left one-third of the box is less than, equal to, or greater than 1/3.

d. If the electron in the ground state absorbs a photon of 412nm wavelength, which energy level will the electron be elevated to?

e. If the box is not rigid any more and the potential energy at the boundary drops from infinity to 3.5 eV, how many bound states would you expect? What is the penetration distance of the electron in the ground state (the ground state energy in this finite potential well is roughly 0.252 eV)?

f. Does the penetration distance become larger or smaller for the n=2 and n=3 states?

1. Consider an electron in a rigid box of length L = 1nm. You are not required to know how to solve the Schrödinger equation, but just need to know that En = n^2 * h^2 / (8mL^2)
a. What are the energies for the first three energy levels?

b. If the length of the box is doubled, what happens to the energies?

c. For the n=3 state, determine, by examining the graphs of the probability density, if the probability of finding the particle in the left one-third of the box is less than, equal to, or greater than 1/3.

d. If the electron in the ground state absorbs a photon of 412nm wavelength, which energy level will the electron be elevated to?

e. If the box is not rigid any more and the potential energy at the boundary drops from infinity to 3.5 eV, how many bound states would you expect? What is the penetration distance of the electron in the ground state (the ground state energy in this finite potential well is roughly 0.252 eV)?

f. Does the penetration distance become larger or smaller for the n=2 and n=3 states?

Added by Patrick J.

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