Chem_442_Hour_Exam_1_Answer_Key - Chem 442 Hour Exam #1....

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Chem 442 Hour Exam #1. November 8, 2008 Each problem is worth 20 pts. Exam total = 100 pts. Answer Key 1) a)Calculate λ for an electron beam traveling at 1X10 -6 times the speed of light. 6.626 34Js 2.42 6m = 2420 nm (9.11 31kg)(1 6)(3 8m/s) E E EE E λ == −− b)If this were a beam of photons and assuming the threshold energy for lithium is 2.301eV, would the incident radiation have enough energy to eject an electron from a sheet of lithium? 0 1 0 1 11 00 2.301 3.687 19 3.687 19 5.57 14 6.626 34 38 1.24 14 ; (6.626 34 )(1.24 14 ) 8.22 20 2.42 6 (or E >E ) so an electron would not be ejected eV E J E EJ vE s s cE m s s E h v E J s E s Em vv φφ φ => = = = = = > E J No, an incident photon beam does not have sufficient energy to over come the lithium metal’s work function. c)However, this is not a photon beam, it is an electron beam. Now, does the electron beam have enough kinetic energy to eject an electron when it collides with the surface of lithium metal? Why or why not. KE = 1/2mv 2 12 ? 1 (9.11 31 )((1 6)(3 8 )) 4.0995 26 2 4.0995 26 3.69 19 KE KE E kg E E ms E J = =− −< No, an incident electron beam will not eject an electron from lithium either because the kinetic energy of the beam is less than the work function of the solid. 2) For the Harmonic Oscillator, V(x) = ½ kx 2 for - ∞≤ x ≤∞ . However in this problem, the potential energy has the following form: 2 () f o r x 0 1 f o r 0< x 2 Vx k x = ∞≤ = ≤∞ a) Qualitatively explain why the odd Harmonic wavefunctions are eigenfunctions for the Hamiltonian with this potential energy function.
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All of the odd Harmonic wavefunctions obey the relation that ( 0) 0 n x ψ = = , for n-odd.
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This note was uploaded on 05/10/2011 for the course CHEM 442 taught by Professor Mcdonald,j during the Spring '08 term at University of Illinois, Urbana Champaign.

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Chem_442_Hour_Exam_1_Answer_Key - Chem 442 Hour Exam #1....

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