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2(5)) (a) For an electron in a 2D cubic box with a side of 10 nm calculate the wavelength of the photon that would cause the transition between the ground state and the first excited state. (b) For a particle of mass m in a 2D cubic box of side L, what is the degeneracy of a state whose energy is 8.125×h2/mL2 (c) Consider an electron in a 1D box of length 2 nm in a state with n=2. Sketch the wavefunction. What is the number of nodes in this wavefunction? Determine the locations of these nodes in nm. What is the number of points of maximum probability density in this wavefunction? What are these points (determine their positions in nm)?

2(5)) (a) For an electron in a 2D cubic box with a side of 10 nm calculate the wavelength of the photon that would cause the transition between the ground state and the first excited state. (b) For a particle of mass m in a 2D cubic box of side L, what is the degeneracy of a state whose energy is 8.125×h2/mL2 (c) Consider an electron in a 1D box of length 2 nm in a state with n=2. Sketch the wavefunction. What is the number of nodes in this wavefunction? Determine the locations of these nodes in nm. What is the number of points of maximum probability density in this wavefunction? What are these points (determine their positions in nm)?

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2(5))

(a) For an electron in a 2D cubic box with a side of 10 nm calculate the wavelength of the photon that would cause the transition between the ground state and the first excited state.

(b) For a particle of mass m in a 2D cubic box of side L, what is the degeneracy of a state whose energy is 8.125×h2/mL2

(c) Consider an electron in a 1D box of length 2 nm in a state with n=2.

  1. Sketch the wavefunction.
  2. What is the number of nodes in this wavefunction? Determine the locations of these nodes in nm.
  3. What is the number of points of maximum probability density in this wavefunction? What are these points (determine their positions in nm)?
  4. What is the probability to find the electron between the two points: x = 0 nm and x = 1 nm?
  5. Calculate the energy of the electron in 1D box in a state n=2 (n = 2, L=2 nm). Express your answer in eV.
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