WOLFRAM|DEMONSTRATIONS PROJECT

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.