P Q R Branches in IR Spectra
We know that each vibrational energy level of a molecule has a series of closely spaced rotational energy levels. Vibrational - rotational transitions are caused by the absorption of infra red light for which the selection rule is ΔJ = -1, 0 +1, where J and v are the rotational and vibrational quantum numbers respectively.
If ΔJ = -1, we get P Branch (Lines with frequency lower than the fundamental frequency)
If ΔJ = 0, we get Q Branch (Vibration transition occurs without being accompanied by rotational transition)
If ΔJ = +1, we get R Branch (Lines with frequency higher than the fundamental frequency)
For a diatomic molecule like HCl, we have only one fundamental vibrational mode and hence, we expect only one infrared absorptional band according to 3n − 5 rule-
3 x 2 − 5 = 1
Diatomic molecules are always linear. However, even under low resolution, it gives two bands designated as R and P bands.
The Q band is not at all expected because it is possible only when the moment of inertia I = 0 as we know that-
EJ = [h2/8π2I] J(J + 1)
ΔEJ, J = 0 only when I = 0.
Hence, it shows only ΔJ = +1 (R Branch) and ΔJ = -1 (P Branch) transition under 𝜈o → 𝜈1. These R and P bands split under high resolution due to the so many associated rotational transitions.
MCQs Branches on P Q R Bands in IR Spectra
The P, Q and R-branch in a rovibrational IR spectrum corresponds to transitions where the rotational quantum number (J) changes by ... respectively
A. ΔJ = +1, ΔJ = −1, ΔJ = 0
B. ΔJ = −1, ΔJ = +1, ΔJ = 0
C. ΔJ = −1, ΔJ = 0, ΔJ = +1
D. ΔJ = 0, ΔJ = +1, ΔJ = −1
View Answer
Option C is correct answer.
ΔJ = −1, ΔJ = 0, ΔJ = +1.
The relative intensities of the lines in the P and R branches are primarily determined by
A. The magnitude of the dipole moment change.
B. The population distribution of the rotational energy levels in the initial state.
C. The instrumental resolution of the spectrometer.
D. The type of vibrational mode (stretching or bending).
View Answer
Option B is correct answer.
The population distribution of the rotational energy levels in the initial state.
For polyatomic molecules, the presence of a Q-branch in an IR spectrum indicates a
A. Parallel band (dipole moment change parallel to the principal axis of rotation).
B. Perpendicular band (dipole moment change perpendicular to the principal axis of rotation).
C. Overtone transition.
D. Hot band.
View Answer
Option B is correct answer.
Perpendicular band (dipole moment change perpendicular to the principal axis of rotation).
In the ideal rigid rotor-harmonic oscillator model, the spacing between adjacent lines within the P-branch and R-branch is approximately
A. B
B. 2B
C. 4B
D. 𝜈̄o
View Answer
Option B is correct answer.
2B.
The spacing between lines in the P and R branches of a rovibrational spectrum is primarily influenced by
A. The vibrational frequency of the molecule.
B. The anharmonicity of the vibration.
C. The rotational constant (B) of the molecule.
D. The temperature of the sample.
View Answer
Option C is correct answer.
The rotational constant (B) of the molecule.
Which of the following statements about the Q-branch in IR spectra is generally correct for diatomic molecules?
A. It is always observed as an intense, sharp peak.
B. It is typically observed for heteronuclear diatomic molecules.
C. It is generally forbidden for diatomic molecules, except when electronic angular momentum is present.
D. It consists of lines that are widely spaced due to significant changes in rotational energy.
View Answer
Option C is correct answer.
It is generally forbidden for diatomic molecules, except when electronic angular momentum is present.
For a typical diatomic molecule like HCl, which branches are observed in its IR spectrum?
A. Only P branch
B. Only R branch
C. Both P and R branches
D. P, Q, and R branches
View Answer
Option C is correct answer.
For linear diatomic molecules, only P (ΔJ = -1) and R (ΔJ = +1) branches are observed; Q branch (ΔJ = 0) is not allowed for such molecules