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3502_14_octo11

# 3502_14_octo11 - Chem 3502/5502 Physical Chemistry...

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Chem 3502/5502 Physical Chemistry II (Quantum Mechanics) 3 Credits Fall Semester 2010 Laura Gagliardi Lecture 14, October 11, 2010 Solved Homework We are given that the lowest microwave absorption of carbon monoxide (CO, with 12 C and 16 O specified) is 115,271,000,000 s 1 (115.271 GHz). We are asked first to compute the moment of inertia of CO. Remember that the first absorption corresponds to the 0 1 rotational transition, and the energy separation between these two levels is Δ E = h ν = 2 B where B = 2 2 I Rearranging, we have I = 2 2 B = 2 h ν = 1.0545 × 10 34 kg m 2 s -1 ( ) 2 6.6256 × 10 34 kg m 2 s -1 ( ) 115,271,000,000 s -1 ( ) = 1.456 × 10 46 kg m 2 We may compute the reduced mass for this system from the atomic masses for 12 C and 16 O μ = m 12 C m 16 O m 12 C + m 16 O = 12 × 1.66 × 10 27 kg ( ) 15.9949 × 1.66 × 10 27 kg ( ) 12 × 1.66 × 10 27 kg ( ) + 15.9949 × 1.66 × 10 27 kg ( ) = 1.138 × 10 26 kg Recalling that

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14-3 In this case, the potential energy is the Coulomb interaction between the proton and the electron, given by V = e 2 4 πε 0 r (14-2)

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3502_14_octo11 - Chem 3502/5502 Physical Chemistry...

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