WOLFRAM|DEMONSTRATIONS PROJECT

Rotation-Vibration Energy Level Transitions of a Diatomic Rotor

​
ground state quantum number
′′
J
0
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
10
joule
= 2905.6
-1
cm
This Demonstration shows the energy level transitions associated with each line observed in a rotationally resolved infrared band spectrum, in which the
v
1
←
v
0
vibrational transition is coupled with
′
J
←
″
J
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
P
branch (
Δv=+1
,
ΔJ=-1
, smaller wavenumbers, lower energy transitions) and an
R
branch (
Δv=+1
,
ΔJ=+1
, larger wavenumbers, higher energy transitions). The central gap between the
P
and
R
branches represents the forbidden
Q
branch since the
ΔJ
selection rule makes the
ΔJ=0
transitions forbidden. A
Q
branch can appear, however, if the molecule has electronic angular momentum, a well-known case being the NO molecule.