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Questions and Answers
What is the formula for the eigenvalues of a rigid rotor in terms of the rotational quantum number J?
What is the formula for the eigenvalues of a rigid rotor in terms of the rotational quantum number J?
- $E_J = \frac{\hbar^2}{2I}J(J+1)$ (correct)
- $E_J = \frac{\hbar^2}{2I}(J-1)^2$
- $E_J = \frac{\hbar^2}{2I}(J-1)(J+1)$
- $E_J = \frac{\hbar^2}{I}(J^2+J)$
In spectroscopy, what unit is preferred for reporting the energy levels EJ of a rigid rotor?
In spectroscopy, what unit is preferred for reporting the energy levels EJ of a rigid rotor?
- Joules
- eV
- cm^-1 (correct)
- Watts
What is the formula for the rotational constant B in terms of the moment of inertia I and the rotational quantum number J?
What is the formula for the rotational constant B in terms of the moment of inertia I and the rotational quantum number J?
- $B = \frac{\hbar}{8\pi^2Ic}(J-1)(J+1)$
- $B = \frac{\hbar}{8\pi^2Ic}J(J+1)$ (correct)
- $B = \frac{\hbar}{8\pi^2Ic}J^2$
- $B = \frac{\hbar}{8\pi^2Ic}J$
What are the selection rules for the rotational transition in a rigid rotor?
What are the selection rules for the rotational transition in a rigid rotor?
In the case of absorption of electromagnetic radiation, what is the spacing between adjacent lines in the rotational spectrum of a rigid rotator?
In the case of absorption of electromagnetic radiation, what is the spacing between adjacent lines in the rotational spectrum of a rigid rotator?
What is the bond length for the molecule C≡O?
What is the bond length for the molecule C≡O?
In the non-rigid rotor model, how does the new term in the rotational energy equation affect the energy levels?
In the non-rigid rotor model, how does the new term in the rotational energy equation affect the energy levels?
What condition must a molecule satisfy to be microwave active?
What condition must a molecule satisfy to be microwave active?
Which classification applies to molecules based on the relative values of principal moments of inertia?
Which classification applies to molecules based on the relative values of principal moments of inertia?
What effect does rotation have on the bond in a non-rigid rotor model?
What effect does rotation have on the bond in a non-rigid rotor model?
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Study Notes
Rigid Rotor
- The eigenvalues of a rigid rotor are a function of the rotational quantum number J.
- The energy levels EJ of a rigid rotor are typically reported in units of cm⁻¹.
- The rotational constant B is given by the formula B = ħ / (4πcI), where I is the moment of inertia and ħ is the reduced Planck constant.
Rotational Transition Selection Rules
- The selection rules for rotational transitions in a rigid rotor are ΔJ = ±1.
Rotational Spectrum
- The spacing between adjacent lines in the rotational spectrum of a rigid rotor is 2B.
Molecular Properties
- The bond length for the molecule C≡O is 113 pm.
Non-Rigid Rotor Model
- In the non-rigid rotor model, a new term is added to the rotational energy equation, causing the energy levels to be affected.
- Rotation causes an increase in the bond length in a non-rigid rotor model.
Microwave Activity
- A molecule must have a permanent electric dipole moment to be microwave active.
Moment of Inertia Classification
- Molecules can be classified as prolate (Ia > Ib > Ic), oblate (Ia < Ib ≤ Ic), or spherical (Ia = Ib = Ic) based on the relative values of their principal moments of inertia.
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