Are energy levels in a Debye solid equivalent to particles?

In summary, the conversation discusses the derivation of the Debye model and the relationship between the density of states at a specific frequency and the total number of photons at that frequency. The participants clarify that the total number of phonons at a frequency is not the same as the total number of energy levels at that frequency, and that each energy level can hold multiple photons. The density of states at a frequency is represented by dN(\nu) in the expression.
  • #1
Karthiksrao
68
0
Dear all,

In the wiki article about Debye solid :
https://en.wikipedia.org/wiki/Debye_model , in the section 'Another derivation', below Eq. 6, the following statement is provided:
382bf6a9a1564fd0f9e1ea0af7e89d19.png


Here, I understand the right hand side, which is nothing but the density of states/modes at the frequency \nu.

I fail to understand how this can be equated to the total number of photons (particles) Sigma n_i

Is each mode/state equivalent to a particle ?

Thanks!
 
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  • #2
It's not the total number of phonons but just the total number of phonons with frequency ## \nu ##. For a given frequency you can have different energies associated (Ei) and for each energy level you have some number of phonons (ni).
 
  • #3
oh yes, I did actually have in mind total number of photons with frequency \nu.

So just to clear things up, at every frequency \nu, there are many energy levels corresponding to 1 h \nu, 2 h \nu, 3 h \nu, etc.
Each of these energy levels is populated by photons. If you add up the number of photons distributed in all these energy levels, I am unable to visualize why this sum comes out to be just equal to the number of energy levels at frequency \nu (or the density of states at frequency \nu) represented by dN(\nu) in the expression. Can't each energy level hold more than one photon ? That doesn't seem right.
 

1. What is a Debye solid?

A Debye solid is a theoretical model used to describe the behavior of solids at low temperatures. It assumes that the atoms in a solid are arranged in a regular lattice and vibrate around their equilibrium positions. The model also takes into account the fact that at low temperatures, the vibrations of the atoms are quantized and can only have certain discrete energies.

2. How does the Debye solid model differ from the classical model?

The classical model of solids assumes that the atoms are in continuous motion and can have any energy. However, the Debye solid model takes into account the discrete energy levels of the atoms at low temperatures, resulting in a more accurate description of the behavior of solids at these temperatures.

3. What is the Debye temperature?

The Debye temperature is a characteristic temperature for a solid, calculated from the speed of sound in the material and the density of the atoms. It represents the temperature at which the vibrations of the atoms in the solid become significant and the classical and Debye models start to deviate.

4. How does the Debye solid model explain heat capacity?

The Debye solid model can be used to explain the heat capacity of a solid at low temperatures. It predicts that the heat capacity will decrease as the temperature is lowered and will approach a value of zero at absolute zero. This is in contrast to the classical model, which predicts that the heat capacity will remain constant at all temperatures.

5. What are some limitations of the Debye solid model?

While the Debye solid model provides a more accurate description of solids at low temperatures compared to the classical model, it has some limitations. For example, it assumes that the atoms in the solid are arranged in a regular lattice, which may not be the case for all materials. It also does not take into account the effects of defects or impurities in the solid, which can affect its behavior at low temperatures.

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