Question

Consider an electron in a one-dimensional box as a model of a quantum dot. Suppose the box has width 0.7 nm. For this problem, absorption of light and subsequent relaxation connect two states (i andj) with a difference in energy, AEi E - E. (a) Calculate AEsi and AE2I for luminescence from excited energy levels to the ground state. Convert the energies to the corresponding wavelengths of light, λ31 and λ21. (b) Find the wavelength of light that corresponds to Ehalf 0.5 AE21. (c) For what size of box (of width L) is the transition from n = 2 to n = 1 equal to Ehalf?

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3 -19 - -21XlO Jou 19t9 2. 31 al

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