# The Drude model can be used to estimate the force constants, vibrational frequencies, and related properties...

###### Question:

The Drude model can be used to estimate the force constants,
vibrational frequencies, and related properties in metals. We use a
crude model to describe the vibration of a single ion in a monovalent metal:
The ion is assumed to be a positive point charge in a spherical unit cell that is
filled with electrons of the appropriate density n. All the rest of the crystal is
ignored. (a) Consider a small displacement of the ion from the center of the
unit cell. Show that the restoring force is proportional to the magnitude of the displacement. Hint: Use Gauss’ law to calculate the force. (b) What is the
vibrational frequency for a single ion of sodium? (c) Performa crude estimate
of the speed of sound in sodium, and compare your result to the experimental
value of 3200 ms−1.

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