Smallest amount of vibrational energy

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In summary, the equation E = 1/2 h√(ks/m) can be used to calculate the smallest amount of vibrational energy that can be added to a system, specifically a quantum harmonic oscillator. The smallest amount of energy that can be added is \hbar\omega.
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LocalStudent
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Would I use the equation E = 1/2 h√(ks/m) to work out what the smallest amount of vibrational energy that I can add to a system?
 
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LocalStudent said:
Would I use the equation E = 1/2 h√(ks/m) to work out what the smallest amount of vibrational energy that I can add to a system?
If you are referring to a quantum harmonic oscillator, such as the vibration of a diatomic molecule, the energy levels are:

[tex]E_n = \hbar\omega(n+\frac{1}{2})[/tex]

where [itex]\omega = \sqrt{k/\mu}[/itex], μ being the reduced mass of the system and k being the spring constant.

So the smallest amount of energy it can have is the zero energy level: [itex]E_0 = \hbar\omega/2[/itex]. The smallest amount of energy that can be added would be [itex]\hbar\omega[/itex].

AM
 
  • #3
Thanks Andrew :)
 

1. What is the smallest amount of vibrational energy?

The smallest amount of vibrational energy is known as a quantum of energy, which is the minimum amount of energy that can be emitted or absorbed by a system.

2. How is the smallest amount of vibrational energy measured?

The smallest amount of vibrational energy, or quantum of energy, is typically measured in units of joules (J) or electron volts (eV).

3. What is the significance of the smallest amount of vibrational energy?

The smallest amount of vibrational energy is significant because it is the fundamental unit of energy in the quantum world, and it plays a crucial role in understanding the behavior of atoms and molecules.

4. Can the smallest amount of vibrational energy be divided into smaller units?

No, the smallest amount of vibrational energy, or quantum of energy, cannot be divided into smaller units. It is a discrete, indivisible unit of energy.

5. How does the smallest amount of vibrational energy relate to temperature?

The smallest amount of vibrational energy is directly related to the temperature of a system. As the temperature increases, the amount of vibrational energy also increases, leading to more energetic and faster-moving particles.

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