Question

At room temperature in a solid, atoms oscillate typically at a frequency of 10^13 Hz. Consider the case of copper (1mol is 0.064kg and has 6.02 x 10^23 atoms). Suppose that while all the other atoms are at rest, one atom has this frequency and estimate the effective spring constant of the "atomic spring".

Answer 1

I think you need some more information here, i.e., bulk modulus and atomic spacing.

Answer 2

Just treat it like a regular spring and use Hook's Law

\[\omega = \sqrt{k/m}\]

Now you need to know m which can be found by using the molar mass and number of atoms. Just find the mass of one copper atom, and plug it into the above.