Question

5. [10% 01 For the linear diatomic lattice in FIG. 2. Draw arrows on the atoms to indicate the motion of the atoms in the acoustic mode and optical mode of vi- brations.

Answer 1

In linear diatomic lattice, there are two modes of vibration : The optical mode and the Acoustic mode .

Let the anion has mass m and amplitude of oscillation A and the cation has mass M and amplitude of oscillation B.

Then ,

For optical mode :

The ratio of amplitude comes out to be

( negative sign is indicating that they will oscillate in opposite direction of each other )

or,   

This can be shown as

For acoustic mode :

The ratio of amplitude comes out to be

or,  

Hence, the amplitude for both the atom will remain same and they both will oscillate in same direction .

From the above results motion of the atoms can be shown as :

For optical mode :

NOTE : In this diagram amplitude of vibration is not considered. For amplitude please refer to the diagram mentioned earlier.

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