Quantized energy and 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?

 

[baba89]

I would like to clarify that the concept of quantized energy and amplitude is a fundamental principle in quantum mechanics. It states that energy can only exist in discrete, specific amounts, rather than being continuous. This is known as energy quantization.

In the context of the given scenario, the energy of oscillation is one energy quantum, which means it is the minimum amount of energy that can exist for this particular system. This energy is proportional to the amplitude of oscillation, as stated by the equation E=nhv, where n is the quantum number, h is Planck's constant, and v is the frequency. This means that as the energy increases, the amplitude of oscillation also increases.

Furthermore, the mass of the atom attached to the spring does not directly affect the amplitude of oscillation. However, it does affect the frequency of the oscillator, as stated by the equation f=1/(2π√(m/k)), where m is the mass, and k is the spring constant. This means that a heavier atom will have a lower frequency and therefore a smaller amplitude of oscillation compared to a lighter atom with the same energy of oscillation.

In summary, the concept of quantized energy and amplitude is crucial in understanding the behavior of systems on a quantum level. The energy of oscillation is directly related to the amplitude of oscillation and is affected by the mass of the system.