3502_14_octo12_LG

# 3502_14_octo12_LG - Chem 3502/5502 Physical Chemistry...

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Chem 3502/5502 Physical Chemistry II (Quantum Mechanics) 3 Credits Fall Semester 2009 Laura Gagliardi Lecture 14, October 12, 2009 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 = h 2 2 I Rearranging, we have I = h 2 2 B = h 2 h ! = 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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