rotational quantum number

physics

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July 13, 2026

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The rotational quantum number is a vector quantum number that defines a molecule's angular momentum as it rotates. In the gas phase, molecules are free to rotate. According to quantum mechanics, this rotational energy is quantized and depends on the rotational quantum number, denoted by J, which can take integer values (0, 1, 2, and so on). The energy is calculated using the formula E_J = J(J + 1)(h²/8π²I), where h is Planck's constant and I is the molecule's moment of inertia. Transitions between these rotational energy levels result in molecular rotational spectra, governed by specific selection rules, such as ΔJ = ±1.12

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spectroscopy
Rotational energy states
…0, 1, 2,… is the rotational quantum number. Molecular rotational spectra originate when a molecule undergoes a transition from one rotational level to another, subject to quantum mechanical selection rules. Selection rules are stated in terms of the allowed changes in the quantum numbers that characterize the energy states. For…
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…0, 1, 2,… is the rotational quantum number. Molecular rotational spectra originate when a molecule undergoes a transition from one rotational level to another, subject to quantum mechanical selection rules. Selection rules are stated in terms of the allowed changes in the quantum numbers that characterize the energy states. For…
Read More