How Does Quantized Energy Affect Oscillation Amplitude?

[Quelsita]

Energy and Amplitude of Oscillation

An atom in a crystal lattice can be regarded as having a mass of 2.0E-26 kg attched to a spring. The frequency of this oscillator is 1.0E13 Hz. What is the amplitude of oscillation if the energy of oscillation is one energy quantum?

I know E=nhv, here n=1
so the energy of oscillation=> E=1h(1.0E13 Hz)= 6.626E-21 J

How does this relate to amplitude? (Energy is proportional to A^2?)
How does the mass of the atom affect this?

 

[alphysicist]

Hi Quelsita,

If it is modeled as a spring, then yes, the total energy is proportional to the square of the amplitude. But what is the explicit relationship for a spring?