Question

The inter-atomic spacing of a linear 1D lattice of atoms of mass 8.0 ×10^-27 kg is

5.0 Å. The force constant is 3.0×10^-2 N/m

. Calculate the maximum frequency

which can be supported by this lattice

Answer 1

The maximum frequency can be supported by such 1D lattice is

$$\omega_\text{max}=\sqrt{\frac{4C}{M}}=\sqrt{\frac{4\cdot3\cdot10^{-2}}{8.0 ×10^{-27}}}=3.87\text{ rad/s}.$$