Harmonic oscillator
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The document discusses the harmonic oscillator model of molecular vibration. It explains that atoms in molecules periodically displace from their equilibrium positions, changing bond lengths and angles in a simple harmonic motion. This periodic motion results in changes to the vibrational and rotational energy levels. The harmonic oscillator model treats vibrating diatomic molecules as simple harmonic oscillators that obey Hooke's law, where a restoring force is proportional to the displacement from the equilibrium position. The frequency of this periodic motion is known as the vibrational frequency. Quantum mechanical equations like the Schrödinger equation can calculate the allowed vibrational energies.
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Harmonic oscillator
- 1. Harmonic Oscillator Dr. S. Vidhya Assistant Professor Department of Chemistry Holy Cross College (Autonomous) Tiruchirappalli.
- 2. Molecular Vibration The atoms in the molecules tends to displaced from the equilibrium position, as a result the bond length and bond angle changes periodically. As a result of periodic motion the vibrational and rotational energy level changes.
- 3. Fundamental Modes of Vibration
- 4. The simple Harmonic Motion Vibrating diatomic molecule is a Simple Harmonic Oscillator Model Atoms in molecules executes vibratory motion along with bond length and bond angle changes periodically is called Simple Harmonic motion A body that executes simple harmonic oscillation or motion is called Harmonic Oscillator
- 5. Hooke’s Law When a particle is displaced from the equilibrium position , a force start acting in its opposite direction in order to relate its equilibrium position.
- 6. Vibrational frequency The frequency of the periodic motion is known as a vibration frequency.
- 7. Vibrational Energy Equation The Schrodinger equation are used to calculate the allowed vibrational energies of a particular system.
- 8. Selection Rule The Vibrational energy levels are equally spaced
- 9. Zero point energy Fundamental Absorption band
- 10. Summary