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Hooke’s Law for IR spectrscopy

Hooke's Law is an equation which helps in interpreting the molecular vibrations by assuming bonds as spring having masses (atoms) at two ends. When a molecule is exposed to infrared light, the bonds between atoms can absorb specific frequencies of that light, causing the bonds to stretch, compress or bend, just like a spring. This characteristic absorption of light corresponding to certain specific vibrational frequencies helps in identifying the functional groups in that molecule and thus adding to the characterization of molecular structures.  The mathematical expression of Hooke’s law is given as follows:

ν = 1/2π√k/µ

ῡ = 1/2πc√k/µ

where:

· ν = the frequency of vibration

· ῡ = Wave number (reciprocal of wavelength)

· k = the force constant

· c = Velocity of light

· Π = Constant

· μ = reduced mass

The reduced mass of the two atoms involved in the bond is calculated as follows:

1/µ = 1/m1 +1/m2;

                                               µ = m1.m2/m1+m2

Streching frequency is directly proportional to force constant. So, Stronger bonds (multiple bonds) absorb at higher frequencies, while weaker bonds (single bonds) absorb at lower frequencies.

Streching frequency is inversely proportional to reduced mass. So, Bonds between lighter atoms (when one of the atoms is hydrogen) absorb at higher frequencies, while bonds between heavier atoms (when no hydrogen is there and both the atoms are heavier atoms) absorb at lower frequencies. 

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