Unformatted text preview: energy level arrangement for a three‐level laser. Indicate which (spontaneous) transitions must be fast and which must be slow in order to make an efficient laser. 14 of 20 l) (4 pts) Sketch the band diagrams for the two semiconductors. Shade states filled at 0 K. GaAs (Egap = 1.42 eV) and Si (Egap=1.1 eV) m) (2 pts) Can GaAs absorb a photon of energy 1.2 eV by promoting an electron from the valence band to the conduction band? Why or why not? n) (2 pts) Can Si absorb this same photon? Why or why not? 15 of 20 2010, Exam 2 Problem 1 – Quantum Mechanics [____/28 pts] a) [4 pts] Cite an experiment or observation that shows that light behaves like a flux of particles. b) [4 pts] Cite an experiment or observation that shows that electrons behave as waves. c) [6 pts] A silicon photodiode is a light detector that converts incoming light power (Watts) into a current signal (Amps). A certain photodiode has an area of 3.14 cm2 and a conversion factor (responsivity) of 1.2 A/W across the entire spectrum from ultraviolet to infrared. If we measure the light from the sun as it is setting one evening with this photodiode and get a current of 2 mA, what is the total intensity (in W/m2) reaching us from the sun? 16 of 20 d) [4 pts] The sun appears red‐orange as it is setting so treat the light from the sun you just calculated as having only a single wavelength of 750 nm. How many photons hit the pupil of your eye per second at sunset if it has an area 0.5 cm2? e) [4 pts] What is the probability of finding an electron at the position x=L/2 if it is in an infinite square well of length L and its quantum number n is even? f) [2 pt] Does this probability change with time (yes or no)? g) [4 pts] Give the equations for the momentum and for the energy of a photon in terms of the wavelength . 17 of 20 2010 Exam 2, Problem 3 b) [3 pts] What is the dispersion relation (k) for a photon in vacuum? c) [4 pts] What is the dispersion relation (k) for an electron having purely kinetic energy in vacuum? d) [6 pts] A laser pulse can be described as a wavepacket of EM radiation. If a pulse from a frequency‐
doubled Nd:YAG laser (a high‐power green laser) is travelling through vacuum and is 10 ns in duration, what is the bandwidth in wavelength ( of the plane waves that went into making the pulse? Use the classical wave mechanics analog coming from the properties of Fourier transforms: ΔΔ 2 Hints: Don’t use Heisenberg’s uncertainty relation – this is not a quantum problem. Remember how to correctly relate the differentials and via the dispersion relation. 18 of 20 Constants me = 9.11 x 10‐31 kg e = ‐1.602176 x 10‐19 C kb = 1.38065 x 10‐23 J K‐1 = 8.6173 x 10‐5 eV K‐1 R = 8.314472 J K‐1 mol‐1 o = 8.854 x 10‐12 F m‐1 o = 4x 10‐7 N A‐2 c = 2.99792458 x 108 m s‐2 h = 6.62606896 x 10‐34 J s ħ = 1.054571628 x 10‐34 J s 1 eV = 1.602176 x 10‐19 J 1 Å = 10‐10 m mproton = 1.672621 x 10‐27 kg AMU = 1.660539 x 10‐27 kg NA = 6.0221415 x 1023 mol‐1 s = 5.670 x 10‐8 W m‐2 K‐4 Helpful Identities 2 2 2 19 of 20 2 2 2 1 20 of 20...
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