Advanced Topic 966 of 1102 Analytical, Lab & Spectroscopy
Rigid Rotor Model
A quantum model for molecular rotation giving microwave spectra.
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In-depth explanation of Rigid Rotor Model
The rigid rotor model treats a diatomic molecule as two masses held at a fixed separation, and its rotational energy levels are E_J = J(J+1) h^2/(8 pi^2 I), where J is the rotational quantum number and I is the moment of inertia. The spacing between adjacent levels increases with J, and the selection rule delta J equal to plus or minus 1 governs allowed transitions. In a microwave spectrum the absorption lines are equally spaced by 2B, where B is the rotational constant, so the spacing gives the moment of inertia and hence the bond length. Only molecules with a permanent dipole moment show pure rotational spectra. Centrifugal distortion causes small deviations at high J.
Going deeper: Rigid Rotor Model
Key ideas: Rotational constant B = h/(8 pi^2 c I), with I = mu r^2. Spectral lines at wavenumbers 2B(J + 1), spaced by 2B, so r = sqrt(h/(8 pi^2 c mu B)). Population of level J is proportional to (2J + 1) exp(minus E_J/kT), so the strongest line is at J near sqrt(kT/2B) minus 1/2. Isotopic substitution changes I and shifts lines, which allows determination of bond lengths to high accuracy.
Common mistakes and connections: Students use the total mass instead of the reduced mass, or forget the 2J + 1 degeneracy. Homonuclear diatomics (H2, N2) have no pure rotational spectrum because no dipole, but show rotational Raman lines. Real molecules stretch as they spin, shrinking line spacing at high J. Related to microwave spectroscopy, moment of inertia and Boltzmann distribution.
Visualization of Rigid Rotor Model
Rotational energies J(J+1)B spread out with J, so adjacent allowed lines are equally spaced by 2B, from which CO bond length is found. The interactive lesson shows this as a live animation or chart.
Worked example and use case
The microwave spectrum of carbon monoxide gives a line spacing from which the C-O bond length is calculated.
Frequently asked questions about Rigid Rotor Model
What is Rigid Rotor Model?
A quantum model for molecular rotation giving microwave spectra.
Is Rigid Rotor Model a beginner, intermediate or advanced topic?
Rigid Rotor Model is a advanced topic in Analytical, Lab & Spectroscopy. It builds on beginner and intermediate topics, so review those first if needed.
What should I learn before Rigid Rotor Model?
Study these earlier topics in Analytical, Lab & Spectroscopy first: Born-Oppenheimer Approximation, Particle in a Box, Harmonic Oscillator Model.
What comes after Rigid Rotor Model?
The next topics in Analytical, Lab & Spectroscopy are Molecular Symmetry and Group Theory in Chemistry.
Can I practise Rigid Rotor Model with quizzes?
Yes. The interactive lesson includes a self-check question on Rigid Rotor Model, and the Analytical, Lab & Spectroscopy quiz draws on every topic in this area.
Where Rigid Rotor Model fits in Analytical, Lab & Spectroscopy
Rigid Rotor Model is topic 90 of 99 in Analytical, Lab & Spectroscopy.