Chapter 19, Problem 19.1CP

Interpretation Introduction

Interpretation:

The reason for observing pure rotational spectrum in microwave region while rotational vibrational spectrum in infrared region and not pure vibrational spectrum should be explained.

Concept Introduction:

The spectroscopy which is observed in microwave region in the electromagnetic spectrum is known as rotational spectroscopy.

Explanation of Solution

In electromagnetic spectrum; rotational spectroscopy is concerned with microwave region. The rotation of molecule occurs in the microwave region.

If a molecule consists permanent dipole moment, it is microwave active, whereas if molecule does not have permanent dipole moment or there is no interaction with microwave region, it is microwave inactive.

For example;

The heteronuclear molecule HCl is microwave active. Assume; HCl molecule to be rigid and fixed in space. So; its translational and vibrational energies are zero.

Consider only rotational energy of HCl molecule; molecule having net positive charge and net negative charge. Therefore; it carries a permanent electric dipole moment.

The selection rule for the microwave spectroscopy as follows:

Due to some net dipole moment; heteronuclear diatomic molecules are microwave active.

$\Delta J=\pm 1$

Where;

J = rotational quantum number

Rotational vibrational spectrum:

Rotational vibrational spectroscopy is also known as PQR spectrum.

Homonuclear diatomic molecules are microwave inactive and can be explained by Raman spectra.

Homonuclear diatomic molecule are IR inactive and obtained in Raman spectrum.

Raman spectroscopy is occurred when there is a change in the polarizability of molecule due to vibrational or rotational oscillations.

The selection rule for rotational vibrational spectrum as follows:

ΔJ = 0; ±2

ΔV = ±1, ±2, ±3

Where;

J = rotational quantum number

V = vibrational quantum number

So, the rotational vibrational spectrum is observed between the rotational and vibrational spectrum not in pure vibrational spectrum.