ENEE 313, Spr. ’09 Quiz II - Feb 11, 2009Name:1. Consider the two infinite potential wells, displayed in the figures b e low.Left: Infinite potential well, size L. Right: In-finite potential well, size 3L.For the potential well on the left, where there are infinite barriers at x = 0 and x = L and withV (x) = 0 in between, we solved the time-independent (TI) SWE in class to find the TI wavefunctionand average energy of each state n asψn(x) =r2Lsin(nπLx) ; En= n2¯h2π22mL2(1)(a) (6 pts.) For the potential well on the right, by inspection, write the TI wavefunction and averageenergy of each s tate n. Note that the only difference is L being widened to 3L.(b) (4 pts.) Compare the ground state energies (n=1) for the two cases. Comment on what wouldhappen to the lowest allowable energy if the well size was widened infinitely.Turn around for the second question.12. (5 pts.) The energy levels of the orbits in the Bohr model of the hydrogen atom are given byEn=1n2−q4me2(4π0)2¯h2(2)What is the wavelength of the photon required to excite an electron from n=1 to n=3 in terms ofthe constants q, me, 0, ¯h and c (the speed of light)? Remember that photon energy is given byEph= hν, where ν = c/λ is the frequency, λ is the wavelength, and ¯h =
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