4. a) Given that B=58000 MHz and ilde{ u}=2160.0 cm$^{-1}$ for CO, calculate the frequencies of the first three lines of the R and the P branches of the vibration-rotation spectrum of CO in the harmonic oscillator-rigid rotor approximation. (b) Using the information above, sketch the rotational-vibrational spectra of CO in wavenum- bers, including each of the peaks that you have computed. Label the P, Q, and R-branches and the x-axis. Label the peaks according with the rotational quantum numbers. For example, you might label a peak as J = 0 $ ightarrow$ J = 2. Also give the relevant vibrational quantum numbers.
Added by Kiara E.
Close
Step 1
First, we need to find the rotational constant B in wavenumbers (cm⁻¹). We are given B in MHz, so we need to convert it to cm⁻¹ using the speed of light (c) in cm/s: B (cm⁻¹) = B (MHz) * 1 MHz / (c (cm/s)) B (cm⁻¹) = 58000 MHz * 1 MHz / (3.0 * 10^10 cm/s) B Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 95 other Chemistry 101 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The first three lines in the R branch of the fundamental vibration-rotation band of H35Cl have the following frequencies in cm^-1: 2906.25 (0), 2925.78 (1), 2944.89 (2), where the number in parentheses is the J values for the initial level. What are the values of ν̃e, B̃'v, B̃''v, B̃e and α̃e using the harmonic oscillator – rigid rotor approximation?
Sri K.
4. For the 12C32$ molecule, the following millimeter wave pure rotational transitions have been observed (in MHz): Transition v = 0 U = 1 v = 2 J = 1-0 48 990.978 48 635.977 48 280.887 J = 2-1 97 980.950 97 270.980 96 560.800 J = 3 2 146 969.033 145 904.167 144 838.826 J = 4-3 195 954.226 194 534.321 193 113.957 (a) For each vibrational level, derive a set of rotational constants by fitting the data. (6) From the results of (a), derive an expression (by fitting) for the vibrational dependence of B. (c) From Bo, calculate ro; from Be, calculate Te-
Consider the CO molecule as a diatomic rigid rotor with a bond length of 1.12A. The reduced mass of the system is obtained from the atomic masses of C and O. The rotational energies are defined in terms of B (the rotational constant) and J (the rotational quantum number). If ?1 and ?2 denote the frequency of the first rotational resonance lines for the molecules 12 C16 O and 13 C18 O respectively, their ratio ?1 /? 2 is approximately 1. 1.5 2. 1.1 3. 0.9 4. 1.01
Recommended Textbooks
Chemistry: Structure and Properties
Chemistry The Central Science
Chemistry
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD