A diatomic chain has force constant and a lighter ion of mass

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Lattice dynamics and thermal properties of solids · Lattice dynamics and thermal properties of solids

Condensed Matter Physics, Ch Two atoms in the cell: acoustic and optical branches

Problem

A diatomic chain has force constant K=15.0 N m−1K=15.0\ \mathrm{N\,m^{-1}} and a lighter ion of mass M1=4.00×10−26 kgM_1=4.00\times10^{-26}\ \mathrm{kg}, about the mass of a sodium ion. Estimate how large the heavier ion's mass M2M_2 must be for the frequency gap at the zone boundary to reach 1.00 THz1.00\ \mathrm{THz}, and express M2M_2 as a multiple of M1M_1.

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