IGNOU PHE 13 2026 - The frequency of the longitudinal optical phonon for at the

Question

The frequency of the longitudinal optical phonon for $\text{NaCl}$ at the centre of the first Brillouin zone is $5\text{ rad s}^{-1}$ . Calculate the interatomic force constant for this material. (The atomic weight of $\text{Na} = 23$ and $\text{Cl} = 37$ )

29 Jan 2026

Answer :

Word Count : 175

The interatomic force constant (k) is related to the frequency of the optical phonon by the formula for a diatomic linear lattice: [ \omega = \sqrt{\frac{2k}{\mu}} ] where (\mu) is the reduced mass of the two atoms: [ \mu = \frac{m_\text{Na} m_\text{Cl}}{m_\text{Na} + m_\text{Cl}} ] The atomic masses are: [ m_\text{Na} = 23 , \text{u} = 23 \times 1.66 \times 10^{-27} , \text{kg} = 3.818 \times 10^{-26} ,

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