Chapter 11, Problem 11C.9E

Interpretation Introduction

Interpretation:

Vibrational mode of methane that corresponds to the compression of one $\text{C-H}$ bond while the other three $\text{C-H}$ bonds stretch is whether Raman active or IR active has to be determined.

Concept Introduction:

Selection rule for vibrational spectrum:

During the vibration, the electric dipole moment of the molecule should change.

• For homonuclear molecules, the stretching motion does not cause the electric dipole moment to change and hence are infrared inactive.
• For heteronuclear molecules, the stretching motion cause the electric dipole moment to change and hence are infrared active. However, not all the modes of these molecules are infrared active.

Gross selection rule for a normal mode to be infrared activity:

A normal mode is infrared active, if the motion causes the electric dipole moment of the molecule to change.

Normal modes are independent and synchronous motion of atoms or a group of atoms that taking place in a molecule without causing the excitation of other modes.

In the vibrational transitions of gas molecules are accompanied by rotational transitions. Due to this the spectrum is split into three branches namely, Q branch $\left(\Delta J\text{ = 0}\right)$, P branch $\left(\Delta J\text{ = }-\text{1}\right)$ and R branch $\left(\Delta J\text{ = +1}\right)$.