## Calculation Of Force Constant

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# Calculation of Force Constant

Taking the simple case where a diatomic molecule may be considered as a simple harmonic oscillator i.e. an oscillator in which the resorting force(F) is directly proportional to the displacement , in accordance with Hook’s we have

Where x is the displacement and is equal to the distance to which the atoms have been stretched (R) minus equilibrium distance between the atoms (Re) i.e. x=R-Re k in equation is called force constant. Thus if x=1 cm, k=-F . Hence

Where is the reduced mass of the system.

To calculate k, equation can be rewritten as follows:

Where m

For more help in

**F = -kx**Where x is the displacement and is equal to the distance to which the atoms have been stretched (R) minus equilibrium distance between the atoms (Re) i.e. x=R-Re k in equation is called force constant. Thus if x=1 cm, k=-F . Hence

**force constant**may be defined as the restoring force per unit displacement (or per cm) of a harmonic oscillator. It is found to be related to the equilibrium vibration frequencyaccording to equationWhere is the reduced mass of the system.

To calculate k, equation can be rewritten as follows:

Where m

_{1}and m_{2}are the masses of the oscillating atoms.For more help in

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