An electron is trapped in an octahedral hole in a closest packed array of aluminum atoms (assume they behave as uniform hard spheres). In this situation the energy of the electron is quantized and the lowest-energy transition corresponds to a wavelength of 9.50 nm. Assuming that the hole can be approximated as a cube, what is the radius of a sphere that will just fit in the octahedral hole? Reference Exercise 148 in Chapter 12 for the energy equation for a particle in a cube.
Energy equation in exercise 148 chapter 12

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