An electron is confined inside a quantum dot, which for this question can be approximated as a one-dimensional quantum box with rigid walls. The ground state has an energy of 0.024 eV. (a) Sketch the wave functions of the ground state and of at least two excited states. On each sketch, indicate the most probable locations of the electron. (b) In your own words, explain why the energy of the ground state of the system is larger than zero. (c) Calculate the length of the quantum dot. (d) What wavelength of photon is needed to cause a transition from the ground state to the first excited state? (e) Is the wavelength of 51.7 μm observed in the spectrum of the quantum dot? Explain your answer. Experiments on the quantum dot show that it can actually be ionized by any light with a wavelength shorter than 450 nm. Thus the walls of the quantum dot can no longer be treated as rigid. (f) Using this information, estimate how many quantum states there are in the quantum dot and explain your reasoning. (g) Estimate how far the ground state wave function of the electron in the quantum dot penetrates the wall. Explain your answer. A beam of electrons traveling in the x-dimension with velocity vx = 4.1 × 105 m s^−1 is perpendicularly incident on a circular aperture of diameter 50 nm in a thin silicon membrane in the yz-plane. (h) Explain what you would expect to observe in this experiment in the context of the Heisenberg Uncertainty Principle.