What is the intensity of spectral lines in rotational spectroscopy?

The intensity of spectral lines in rotational spectroscopy is fundamentally determined by the relative probabilities of transitions between various energy levels.

Understanding Line Intensity in Rotational Spectra

In molecular spectroscopy, including rotational spectroscopy, the intensity of a specific spectral line corresponds to how strongly light is absorbed or emitted at a particular frequency or wavelength. This intensity is not uniform across all possible transitions; it depends on several factors, primarily the likelihood of a molecule transitioning from one rotational energy level to another.

Key Determinants of Intensity

According to the provided reference, a primary factor governing line intensity is the relative probability of transitions occurring between the involved energy levels. This probability is influenced by:

1. Transition Moment: This quantum mechanical quantity reflects the intrinsic likelihood of a transition occurring when a molecule interacts with electromagnetic radiation. A larger transition moment generally leads to a higher probability and thus a stronger line.
2. Population of Initial Energy Levels: The number of molecules in the initial energy state from which the transition originates plays a crucial role. Higher populations in the lower energy level involved in an absorption transition, for example, will result in more molecules absorbing light and thus a stronger line. Molecular populations are governed by the Boltzmann distribution, which describes how molecules are distributed among energy levels at a given temperature.
3. Degeneracy of Energy Levels: The number of distinct states that have the same energy also affects the population distribution and the transition probability. Rotational energy levels have a degeneracy of (2J + 1), where J is the rotational quantum number.

Insights from Rotational Raman Spectroscopy

The reference provides specific insights related to rotational Raman spectroscopy:

• Selection Rule: For rotational Raman transitions, the selection rule is typically ΔJ = ±2 for diatomic or linear molecules. The reference specifically mentions that selection rules for rotational Raman allow only J = 2 (this likely refers to the change in J, i.e., ΔJ = ±2).
• Intrinsic Transition Probability: The reference states that "The intrinsic probability for a transition of a single molecule from J = 0 to J = 2 is the same as that for a transition from J = 1 to J = 3." This highlights that, in isolation for a single molecule, certain transitions can have equal inherent likelihoods, even if they start from different initial J levels. However, the overall observed intensity will still depend on the population of the initial levels (J=0 versus J=1 in this example) and other factors like degeneracy.

Therefore, while the intrinsic probability between specific states might be equal for some transitions, the overall intensity of a spectral line in rotational spectroscopy is a composite effect, primarily determined by the relative probabilities of transitions between various energy levels, which includes factors like Boltzmann population distribution and degeneracy alongside the intrinsic transition probability.