Rotation-Vibration Energy Level Transitions of a Diatomic Rotor

ground state quantum number

′′

view all transitions

color code:

P branch (ΔJ = -1)

R branch (ΔJ = +1)

P branch transition energy

no transition

R branch transition energy

ΔE = 5.7718×

-20

joule

= 2905.6

-1

This Demonstration shows the energy level transitions associated with each line observed in a rotationally resolved infrared band spectrum, in which the

←

vibrational transition is coupled with

′

←

″

rotational transitions. For a diatomic molecule the vibrational and rotational energy levels are quantized and the selection rules are

Δv=±1

(vibration) and

ΔJ=±1

(rotation). Only transitions that meet the selection rule requirements are allowed, and as a result discrete spectral lines are observed, as shown in the bottom graphic. The position of a spectral line corresponds to the energy difference between the initial and final states of the transition. These energy level transitions from the ground to excited rotation-vibration states are shown in the top graphic. The spectrum consists of a

branch (

Δv=+1

ΔJ=-1

, smaller wavenumbers, lower energy transitions) and an

branch (

Δv=+1

ΔJ=+1

, larger wavenumbers, higher energy transitions). The central gap between the

and

branches represents the forbidden

branch since the

ΔJ

selection rule makes the

ΔJ=0

transitions forbidden. A

branch can appear, however, if the molecule has electronic angular momentum, a well-known case being the NO molecule.

Details

This Demonstration utilizes molecular constants of the molecule

HCl

and the infrared spectrum is simulated at a temperature of 200 Kelvin.

HCl

molecular constants:

= 2990.946

-1

= 52.8186

-1

= 10.59341

-1

= 0.30718

-1

= 5.3194E-04

-1

The intensity of the observed spectral lines reflects the dependence on the thermal population of the initial rotational energy levels and the dependence on the quantum number

, not on the magnitude of the corresponding transition energy.

Note: the

axis on the energy level diagram (top graphic) is arbitrary. The arrows indicating transitions in the top graphic are spread out for clarity and so that their positioning lies directly above the corresponding transition wavenumber in the spectrum below (bottom graphic).

References

[1] P. Atkins and J. de Paula, Physical Chemistry, New York: Oxford University Press, 2006.

[2] G. Herzberg, Molecular Spectra and Molecular Structure I. Spectra of Diatomic Molecules, Princeton, New Jersey: D. Van Nostrand Company, Inc., 1950.

[3] K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules, New York: Van Nostrand Reinhold Company, 1979.

[4] Diatomic Constants for HCl. webbook.nist.gov/cgi/cbook.cgi?ID=C7647010&Units=SI&Mask=1000# Diatomic (NIST Chemistry WebBook. webbook.nist.gov/chemistry).

External Links

Spectroscopy (ScienceWorld)

Vibration Spectra (ScienceWorld)

Rotation Spectra (ScienceWorld)

Selection Rules (ScienceWorld)

Rovibronic Infrared Spectrum of a Rigid Diatomic Rotor

Absorption Spectroscopy

Temperature-Dependent Rotational Energy Spectrum

Rotational-Vibrational Spectrum of a Diatomic Molecule

Permanent Citation

Whitney R. Hess, Lisa M. Goss

"Rotation-Vibration Energy Level Transitions of a Diatomic Rotor"
http://demonstrations.wolfram.com/RotationVibrationEnergyLevelTransitionsOfADiatomicRotor/
Wolfram Demonstrations Project
Published: March 7, 2011