Chemistry 455 A Autumn 1998 Reinhardt, Gibbons and Caralombous No Calculators of any type may be used on this exam! Each student may have one (1) handwritten 5 by 8 inch note card. Note that all answers must be supported by “work clearly shown”, or a an explicit explanation in words of how the result was arrived at! Exam #1.v.1 (100 points) Name: _________________________________________ UW ID#:_______________________________________ Signature: ______________________________________ Points Problem #1______________________ Problem #2______________________ Problem #3______________________ Total _____________________
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Problem #1. 20 points. The Bohr atom. This problem is from your homework. The energy of an electron in the nthBohr orbit for a nucleus of atomic number “Z” is E = - Z2m e4/(8 εo2h2n2) We are approximating μby m = electron mass. (15 points) Using the formula above, derive the general “Rydberg- Balmer” formula: 1/ λ = Z2R ( 1/n2- 1/m2) and arrive at an explicit expression for the Rydberg constant R, in terms of the fundamental constants, h,e,c,m,π,εο…… (5 points) State in words how and why you have used the Bohr-Einstein frequency relation in your derivation. Hint, it might be helpful to draw an energy level diagram.