This document discusses rotational spectra and molecular spectroscopy. It begins by explaining that molecular spectra appear as broad bands due to transitions between different molecular energy states caused by absorption, emission, or scattering of photons. It then discusses the differences between atomic and molecular spectroscopy, noting that molecular spectroscopy provides information about molecular structure, properties, and degrees of freedom. The main focus is on rotational spectroscopy, which occurs in the microwave or far-infrared region and arises from transitions between rotational energy states. This is observed in heteronuclear diatomic polar molecules with a permanent electric dipole moment. The energy levels of rotating diatomic molecules are also explained.

1. Rotational Spectra
M.sc Physics (sem-1)

2. Outline :-
When the light from the source containing a substance in molecular state
is sent into spectrometer, more or less broad wavelength regions are observed in
the spectrum. These regions are called “Bands” and the spectrum is called band
spectrum or Molecular Spectrum.
The origin of spectral lines in the molecular or atomic spectroscopy is due
to three basic phenomenon : (1). Absorption ;
(2). Emission ;
(3). Scattering of photons
Due to which the energy of the molecules changes and hence the spectral lines
arises.

3.  In the Atomic Spectroscopy, all the transitions reflects changes in the
configuration of the electrons.
 While, the Molecular Spectroscopy arises due to the change in the
configuration of electrons along with it there are also a energy states
corresponding to vibrations of the atoms as well as the whole rotations of
the molecule.
 The Molecular Spectra are more complex than the Atomic Spectra. In
contrast, the molecular spectra gives us the information on the molecular
structure and the bond strength. They also provide a variety of molecular
properties like – dipole moment, qudrapole moment, quantum numbers
characterizing all molecular degree of freedom.

4. APPLICATION OF MOLECULAR SPECTROSCOPY
 There is a wide range of applications of molecular spectra in the field of
science. Moreover, in the region of astrophysics and environmental science
for the investigation of chemical reactions as well as in the the biology to
investigate the properties of microscopic atomic and molecular objects.

5. • The Molecular Spectra can be divided into three Spectral ranges
corresponding to the different types of the transitions between the
molecular energy states :-
SPECTRA REGION STATES OBSERVED IN
Rotational Spectra Microwave or far
infrared with
λ = 0.1mm to 1cm
Separated by Small
energy intervals
Heteronuclear diatomic
Molecules (HCl,CO)..
Vibrational Spectra Infrared Region with
λ = 119mm to 0.1mm
Separated by Small
energy intervals
Heteronuclear diatomic
Molecules (HCl,CO)..
Electronic Spectra Visible and Ultraviolet
region
States have larger
number of bands
Homonuclear diatomic
and Heteroatomic
diatomic

7. • Rotational Energy Levels :-
Rotational Molecular Spectra arises from transitions between rotational
energy states and is commonly observed in the microwave or in far-infrared
region of electromagnetic spectrum.
Only the molecules that have permenant electric dipole moment can
absorb or emit the electromagnetic radiation in such transitions.
Commonly, the Rotational Spectra aries due to the absorption. For
heteronuclear diatomic molecules such as-
HF, Hcl , HBr ,CO …etc…
The main parameter due to which the rotational spectra aries is the
permenent electric dipole.

8.  As we know that ,the Electric Dipole is a measure of separation of positive
and negative charges.
 The Permanent Dipole occurs when two atoms ion a molecules have
different electronegativity that is one atom attracts electrons more than
another becoming more negative.
 Normally, this type of molecules are called the Polar Molecules.
 All the heteronuclear diatomic molecules with the unlike atoms have a
permanent dipole moment. During the motion of the molecule, the
component of dipole moment in a fixed direction changes periodically
with the frequency of rotation of molecule. Hence, the radiation is
emitted.
 Even, in the molecules with permanent dipole moment not all the
transitions between rotational states involves radiation.

9. • Rotational Spectra for Diatomic molecules:
For simplicity to understand the rotational spectra diatomic molecules is
considered over here, but the main idea apply to more complicated ones.
The simplest of all the linear molecules like : H-Cl or O-C-S (Carbon
Oxysulphide) as shown in the figure below:-

10. Masses m1 and m2 are joined by a rigid bar whose length is –
r0= r1 + r2
The molecule rotates end-over –end about a point C, the centre of
gravity: this is defined by the moment, or balancing, equation :
m1r1 = m2r2
The moment of inertia about C is defined by :
I = m1r1
2 + m2r2
2
Hence, the moment of inertia can be written as :
I = m` R2 …………….(1)
where, m` is the reduced mass.

11. The equation (1) represents that the rotation of a diatomic molecule is
equivalent to the rotation of a single particle of mass m` about an axis located at
distance R away.
The angular moment L of the molecule has the magnitude –
L=Iω
where ω is its angular velocity. Angular momentum is always quantized in
nature. If the rotational quantum number is denoted by J ,
Angular momentum L= (J(J+1)ћ J=0,1,2,3……
The energy of rotating molecule is ½ Iω2
and so, its energy level are specified by
,
E = J(J+1)ћ2
2𝐼

13. • Selection rule:
For a rigid diatomic molecule the selection rule for the rotational
transitions is
△ 𝐽 = (±1)
Rotational spectra always obtained in absorption so that each
transition that is found involves a change from some initial state of
quantum number J to next higher state of quantum number J+1..
𝜈 =
ћ
2 𝜋𝐼
(J+1)

14. THANK YOU..!!