How Does Quantized Energy Affect Oscillation Amplitude?

AI Thread Summary
The discussion centers on the relationship between quantized energy and oscillation amplitude in a spring-mass system, specifically an atom in a crystal lattice. The energy of oscillation is calculated using E=nhv, resulting in 6.626E-21 J for one energy quantum. It is noted that energy is proportional to the square of the amplitude (A^2), prompting questions about the explicit relationship for a spring. Additionally, the impact of the atom's mass on amplitude is raised, indicating that mass plays a role in determining oscillation characteristics. Understanding these relationships is crucial for analyzing oscillatory systems at the quantum level.
Quelsita
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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?
 
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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?
 

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