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quiz3solution - h 2 Energy levels in an infinitely deep...

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EE 439 Name_______________________________________ Quiz 3 – Sept 23, 2008 Put your final answers on this sheet and attach any additional sheets behind. You must include your work to get full credit. Find the first two energy levels for an electron in an infinitely deep quantum well with width of 0.75 nm. Using the formula for energies in the infinitely deep well: E n = n 2 " 2 h 2 2 mL 2 = n 2 " 2 1.055 # 10 $ 34 J % s ( ) 2 2 9.11 # 10 $ 31 kg ( ) 0.75 # 10 $ 9 m ( ) 2 = n 2 1.07 # 10 $ 19 J ( ) = n 2 0.67 eV ( ) So E 1 = 0.67 eV and E 2 = 2.68 eV. Potentially useful equations and data: Square-barrier tunneling: T " 16 E U o # E ( ) U o 2 exp # 2 $ L ( ) ; $ = 2 m U o # E ( ) h 2 Energy levels in an infinitely deep quantum well:
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Unformatted text preview: h 2 Energy levels in an infinitely deep quantum well: E n = n 2 2 h 2 2 mL 2 p = h E = h # "# = c h = 6.63x10 –34 J·s = 4.14x10 –15 eV·s; h = 1.055x10 –34 J·s = 6.595x10 –16 eV·s (Planck’s constant) c = 3.0x10 8 m/s (speed of light in vacuum) k = 1.38x10 –23 J/K = 8.617x10 –5 eV/K (Boltzmann’s constant, not wave number) m = 9.11x10 –31 kg (mass of an electron) q = 1.6x10 –19 C (charge of an electron) ε o = 8.85x10 –12 F/m (free-space permittivity) 1 eV = 1.6x10 –19 J...
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