Increases in Rotational Energy shows Absorption Spectrum in Molecular Spectroscopy

Introduction:
Molecular spectroscopy deals with the study of the interaction of electromagnetic radiation with molecules and provides insight into the electronic, vibrational, and rotational states of molecules. Absorption spectroscopy is a technique used to measure the absorption of electromagnetic radiation by a molecule. When a molecule absorbs radiation, it transitions from its ground state to an excited state, and the energy difference between these states corresponds to the frequency of the absorbed radiation. In this context, the rotational energy of a molecule plays a crucial role in determining its absorption spectrum.

Rotational Energy and Absorption Spectrum:
The rotational energy of a molecule is given by the expression E = J(J+1)h^2/2I, where J is the quantum number associated with the rotational energy, h is Planck's constant, and I is the moment of inertia of the molecule. As the rotational energy of a molecule increases, the energy difference between rotational states becomes larger, and the molecule can absorb radiation of higher frequency. This absorption leads to the appearance of peaks in the absorption spectrum of the molecule, known as rotational transitions.

Selection Rules:
The selection rules for rotational transitions are ΔJ = ±1, where ΔJ is the change in the quantum number associated with the rotational energy. This means that for a molecule to undergo a rotational transition, it must absorb or emit radiation with a frequency corresponding to the energy difference between rotational states, and the frequency of the absorbed or emitted radiation must be such that ΔJ = ±1.

Conclusion:
In summary, the rotational energy of a molecule plays a crucial role in determining its absorption spectrum in molecular spectroscopy. As the rotational energy of a molecule increases, the energy difference between rotational states becomes larger, and the molecule can absorb radiation of higher frequency, leading to the appearance of peaks in the absorption spectrum of the molecule. The selection rules for rotational transitions specify the conditions under which a molecule can absorb or emit radiation corresponding to the energy difference between rotational states.