Rotational Spectroscopy

Introduction to spectroscopy: part 2


Rotational spectroscopy electromagnetic radiation lies in the microwave region (λ = 30cm – 3mm) of the electromagnetic radiation spectrum.

 Rotational spectroscopy is applicable only for the molecules with a dipole moment.

 Samples are usually in gaseous state.
Rigid diatomic molecules;


A general equation can be derived using Schrödinger equation for a rigid rotor.

 Planck's constant = 6.626 × 10-34 m2 kg / s






Normally Energy is given in the term of ṽ



Selection Rules for a rigid rotor




Needs a permanent dipole moment. only polar molecules can give a pure rotational spectrum.

 Only #1 type transitions can be used for rotational spectra. #2 can not be used.









Spacing between Energy Levels


The Energy gap between two energy levels is given by the equation which is derived below.




The table 01: Rotational Energy levels




Spectral lines:

Moment of Inertia 

Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. It appears in the relationships for the dynamics of rotational motion. The moment of inertia must be specified with respect to a chosen axis of rotation.
(Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html)


Questions:

 1. What is the degeneracy of the rotational energy level with J = 4 for a heteronuclear diatomic molecule?

2.The A rotational constant of a phosphorus pentafluoride, PF5, molecule is 3.566 Hz. Calculate the lengths of the equatorial P-F bonds.

3. The rotational constant of ICl is 0.1142 cm-1. Calculate the bond length of the molecule. 
Answers








introduction to spectroscopy; part 03 ( vibrational spectroscopy)

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