Solid State Neumarical Practice part1

commutation of operator part 3

CSIR NET DEC 2018 solution (spectroscopy problem)

msc part 1 sem1n2

Number of Fundamental Vibrations

The IR spectra of polyatomic molecules may exhibit more than one vibrational
absorption bands. The number of these bands corresponds to the number of
fundamental vibrations in the molecule which can be calculated from the degrees
of freedom of the molecule. The degrees of freedom of a molecule are equal to
the total degrees of freedom of its individual atoms. Each atom has three degrees
of freedom corresponding to the three Cartesian Coordinates (x, y and z) necessary
to describe its position relative to other atoms in the molecule. Therefore, a
molecule having n atoms will have 3n degrees of freedom. In case of a nonlinear
molecule, three of the degrees of freedom describe rotation and three
describe translation. Thus, the remaining (3n - 3 - 3) = 3n - 6 degrees of

freedom are its vibrational degrees of freedom or fundamental vibrations, because

Total degrees of freedom (3n) = Translational + Rotational

+ Vibrational degrees of freedom


In case of a linear molecule, only two degrees of freedom describe rotation
(because rotation about its axis of linearity does not change the positions of the
atom) and three describe translation. Thus, the remaining (3n - 2 - 3) = 3n - 5
degrees offreedom are vibrational degrees offreedom or fundamental vibrations.
The number of vibrational degrees of freedom for the linear carbon dioxide
molecule can be calculated as follows:
Number of atoms (n) = 3
Total degrees of freedom (3n) = 3 x 3 = 9
Rotational degrees of freedom = 2
Translational degrees of freedom = 3
Therefore, vibrational degrees of freedom = 9 - 2 - 3 = 4
Since each vibrational degree of freedom corresponds to a fundamental vibration
and each fundamental vibration corresponds to an absorption band, for carbon
dioxide molecule there should be four theoretical fundamental bands.

Similarly, for a non-linear molecule ethane (C2H6), the vibrational degrees of
freedom can be calculated as:
Number of atoms (n) = 8
Total degrees of freedom (3n) = 3 x 8 = 24
Rotational degrees of freedom = 3
Translational degrees of freedom = 3
Hence, vibrational degrees of freedom = 24- 3- 3 = 18
Thus, theoretically there should be 18 absorption bands in the IR spectrum of
ethane.

In case of benzene (C6H6), the number of vibrational degrees of freedom can
be calculated as follows:
Number of atoms (n) = 12
Total degrees of freedom (3n) = 3 x 12 = 36
Rotational degrees of freedom = 3
Translational degrees of freedom = 3

Therefore, vibrational degrees of freedom = 36 - 3 - 3 = 30

Woodward-Fieser rules for calculating absorption maximum in conjugated dienes

folllowing chart is given 

some example are solved

18 electrone rule
It can be stated as "central metal atom keeps on accepting electrons from the ligands till it possess 18 valency electrons.


The following chart  is about contribution of electron by ligands 

Here some example are shown