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455sample_exams_Exam_1 - Chemistry 455 A Autumn 1998...

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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 n th Bohr orbit for a nucleus of atomic number “Z” is E = - Z 2 m e 4 /(8 ε o 2 h 2 n 2 ) We are approximating μ by m = electron mass. (15 points) Using the formula above, derive the general “Rydberg- Balmer” formula: 1/ λ = Z 2 R ( 1/n 2 - 1/m 2 ) and arrive at an explicit expression for the Rydberg constant R, in terms of the fundamental constants, h,e,c,m, π , ε ο …… (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.
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