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The selection rules for the appearance of P branch in the rotational-vibrational absorption spectra of a diatomic molecule within rigid rotor- harmonic oscillator model are
- a)Δν = ± 1 and ΔJ = ± 1
- b)Δν = + 1 and ΔJ = + 1
- c)Δν = + 1 and ΔJ = - 1
- d)Δν = - 1 and ΔJ = - 1
Correct answer is option 'C'. Can you explain this answer?
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The selection rules for the appearance of P branch in the rotational-v...
The selection rules for the appearance of P branch in the rotational-vibrational absorption spectra of a diatomic molecule within the rigid rotor-harmonic oscillator model are as follows:
1. Change in rotational quantum number: The P branch occurs when there is a change in the rotational quantum number, ΔJ, of the molecule. In the P branch, ΔJ = 1, meaning that the rotational quantum number increases by one unit.
2. Change in vibrational quantum number: The P branch also requires a change in the vibrational quantum number, Δv, of the molecule. In the P branch, Δv = 0, meaning that the vibrational quantum number remains the same.
3. Parity selection rule: The P branch occurs for transitions that involve a change in the parity of the molecule, where parity refers to the symmetry of the wavefunction. In the P branch, the initial and final states of the molecule must have opposite parity.
4. Absorption of energy: The P branch occurs when the molecule absorbs energy from the incident radiation, resulting in an upward transition to a higher energy state. This corresponds to a peak in the absorption spectrum.
Overall, the P branch in the rotational-vibrational absorption spectra of a diatomic molecule within the rigid rotor-harmonic oscillator model represents transitions that increase the rotational quantum number by one unit, with no change in the vibrational quantum number, involving states of opposite parity, and resulting in absorption of energy.
1. Change in rotational quantum number: The P branch occurs when there is a change in the rotational quantum number, ΔJ, of the molecule. In the P branch, ΔJ = 1, meaning that the rotational quantum number increases by one unit.
2. Change in vibrational quantum number: The P branch also requires a change in the vibrational quantum number, Δv, of the molecule. In the P branch, Δv = 0, meaning that the vibrational quantum number remains the same.
3. Parity selection rule: The P branch occurs for transitions that involve a change in the parity of the molecule, where parity refers to the symmetry of the wavefunction. In the P branch, the initial and final states of the molecule must have opposite parity.
4. Absorption of energy: The P branch occurs when the molecule absorbs energy from the incident radiation, resulting in an upward transition to a higher energy state. This corresponds to a peak in the absorption spectrum.
Overall, the P branch in the rotational-vibrational absorption spectra of a diatomic molecule within the rigid rotor-harmonic oscillator model represents transitions that increase the rotational quantum number by one unit, with no change in the vibrational quantum number, involving states of opposite parity, and resulting in absorption of energy.
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The selection rules for the appearance of P branch in the rotational-v...
- The rigid rotor-harmonic oscillator model is an approximation used to describe the vibrational and rotational behavior of diatomic molecules.
- The selection rules for vibrational transitions in an absorption spectroscopy are Δv = +1 (v is the vibrational quantum number). This is because absorption of energy leads to a rise in the vibrational level of the molecule.
- For the rotational transitions, the absorption of a photon can cause a molecule to start rotating or to rotate faster, implying an increase in rotational energy level (ΔJ = +1), where J is the rotational quantum number.
- The P branch corresponds to a rotational transition where ΔJ = -1 (the molecule slows down in rotation).
- So, considering both vibrational (Δv = +1) and rotational transitions (ΔJ = -1, for the P branch), the correct selection rules are:
The correct answer is: Δν = + 1 and ΔJ = - 1
The selection rules for the appearance of P branch in the rotational-vibrational absorption spectra of a diatomic molecule within rigid rotor- harmonic oscillator model are Δν = + 1 and ΔJ = - 1
The selection rules for the appearance of P branch in the rotational-vibrational absorption spectra of a diatomic molecule within rigid rotor- harmonic oscillator model are Δν = + 1 and ΔJ = - 1
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