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314-SampleProblems-F201000002

314-SampleProblems-F201000002 - excited state n = 4 w hat...

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1. A semiconductor laser diode emits monochromatic radiation at 620 nm. If the laser output is 10 mW, calculate the number of photons emitted per second. Suppose the laser beam is incident on a fluorescent substance w hich converts each photon into a new photon of 0.5 eV energy, calculate the w avelength and pow er level of the radiation coming out of the fluorescent material. How do you account for the pow er loss? 2. A certain organic dye molecule has six so-called B -electrons that may be considered as free electrons in a 1-dimensional potential w ell of length L = 1 nm. Assume that at each allow ed energy level there can only be tw o electrons w ith opposite spins (Pauli Exclusion Principle). (a) Sketch the probability densities for the states occupied by these six B -electrons. Sketch and label also the corresponding energy levels. (b) What is the total energy of these six electrons in their ground states? [Caution: Pauli Exclusion Principle]. (c) If one of these electrons is to be excited from its ground state n = 3 to the first
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Unformatted text preview: excited state n = 4, w hat is the w hat is the w avelength of absorbed light for this transition? Is it in the visible range? Can you say anything about the color of the dye molecule from this piece of information? (d) Indicate how you w ill calculate the net charge w ithin the region 0 < x < 0.2 nm, assuming all these electrons are in their ground states. Do not do the actual calculation. 3. An electron w ave travelling in the positive x-direction is incident on the rectangular potential barrier show n: (a) Write (do not solve) the Schrödinger’ s equation in the three regions. (b) What is the nature of the solution (travelling w ave, standing w ave, decaying w ave) in the three regions? (c) Neglecting reflection at x = W, solve the equation in region II and show that [ R (W) / R ((0)] = exp -(14.5). (d) Using the result of (c), calculate the tunnel transmission probability [ R (W) / R ((0)] . 2...
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