Rotational spectra

This Presentation gives the basic idea about Rotational Spectra a topic of Atomic and Molecular Spectroscopy in Modern Physics

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 SPECTROSCO PY 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 Hetero nuclear diatomic Molecules (HCl,CO).. Vibrational Spectra Infrared Region with λ = 119mm to 0.1mm Separated by Small energy intervals Hetero nuclear diatomic Molecules (HCl,CO).. Electronic Spectra Visible and Ultraviolet region States have larger number of bands Homonuclear diatomic and Heteroatomic diatomic

6. 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.

7. 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.

8. 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:-

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

10. 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=I ω 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=0,1,2,3…… The energy of rotating molecule is ½ I and so, its energy level are specified by , E =  

11. Selection rule: For a rigid diatomic molecule the selection rule for the rotational transitions is = ( 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.. (J+1)  

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