[hamdani yusuf (OP)]

Did you not notice that I said the energy corresponded to a temperature, not that the electrons were at that temperature?

How are they correlated?
Is it proportionally? Or inversely proportional? Or another type of correlation?

I'm sure I already told you about the equipartition principle.
https://en.wikipedia.org/wiki/Equipartition_theorem
Try reading it again.
Maybe take notes if that helps you remember stuff.

Do you think that Equipartition theorem is relevant in the case of radiation and absorption by LED?

[Bored chemist]

Did you not notice that I said the energy corresponded to a temperature, not that the electrons were at that temperature?

How are they correlated?
Is it proportionally? Or inversely proportional? Or another type of correlation?

I'm sure I already told you about the equipartition principle.
https://en.wikipedia.org/wiki/Equipartition_theorem
Try reading it again.
Maybe take notes if that helps you remember stuff.

Do you think that Equipartition theorem is relevant in the case of radiation and absorption by LED?

Yes.
It's what tells you that the electrons don't have a well defined temperature.

[hamdani yusuf (OP)]

Did you not notice that I said the energy corresponded to a temperature, not that the electrons were at that temperature?

How are they correlated?
Is it proportionally? Or inversely proportional? Or another type of correlation?

I'm sure I already told you about the equipartition principle.
https://en.wikipedia.org/wiki/Equipartition_theorem
Try reading it again.
Maybe take notes if that helps you remember stuff.

Do you think that Equipartition theorem is relevant in the case of radiation and absorption by LED?

Yes.
It's what tells you that the electrons don't have a well defined temperature.

Here's a quote from the article.

Although the equipartition theorem makes accurate predictions in certain conditions, it is inaccurate when quantum effects are significant, such as at low temperatures. When the thermal energy kBT is smaller than the quantum energy spacing in a particular degree of freedom, the average energy and heat capacity of this degree of freedom are less than the values predicted by equipartition. Such a degree of freedom is said to be "frozen out" when the thermal energy is much smaller than this spacing. For example, the heat capacity of a solid decreases at low temperatures as various types of motion become frozen out, rather than remaining constant as predicted by equipartition. Such decreases in heat capacity were among the first signs to physicists of the 19th century that classical physics was incorrect and that a new, more subtle, scientific model was required. Along with other evidence, equipartition's failure to model black-body radiation?also known as the ultraviolet catastrophe?led Max Planck to suggest that energy in the oscillators in an object, which emit light, were quantized, a revolutionary hypothesis that spurred the development of quantum mechanics and quantum field theory.

I asked ChatGPT if LED can be explained by classical physics theory.

No, the functioning of LEDs cannot be fully explained using classical physics theory. Classical physics, particularly concepts from electromagnetism and thermodynamics, can describe the flow of electric current and heat generation in a simple conductor, but it falls short in explaining the specific quantum processes that occur in an LED.

Here?s why classical physics is inadequate:

1. Quantum Mechanics: The behavior of electrons in a semiconductor (which is central to how LEDs work) can only be explained by quantum mechanics. In classical physics, electrons are treated as particles with definite paths and energies. However, in an LED, the process of electron-hole recombination?which leads to the emission of photons (light)?requires understanding quantized energy levels and band theory, concepts that come from quantum physics.


2. Band Theory: Classical physics does not account for the energy band structure in semiconductors, which is essential to understanding how electrons move between the valence band and the conduction band in an LED. Quantum mechanics explains how electrons can exist in discrete energy levels within a solid, which directly leads to the emission of photons at specific wavelengths (colors of light) in LEDs.


3. Electroluminescence: The phenomenon of electroluminescence (the emission of light in response to an electric current) is inherently quantum mechanical. It involves the release of energy when an electron drops from a higher energy state to a lower energy state, a process that classical theories cannot explain in terms of photon emission.



Thus, while classical physics can describe the basic flow of current in a circuit with resistors and capacitors, the working of an LED is rooted in quantum theory. Quantum mechanics gives us the necessary framework to explain the specific behavior of particles in semiconductors and their interaction with light.

[Bored chemist]

I asked ChatGPT

Why?

[hamdani yusuf (OP)]

I asked ChatGPT

Why?

Why not?
By comparing different answers we might find a better answer to what we currently believe. If you think ChatGPT's answer is false, you can point out where it is, and how to improve it.
I asked it to check your answer about equipartition theorem.

Yes.
It's what tells you that the electrons don't have a well defined temperature.

Does equipartition theorem tell you that the electrons don't have a well defined temperature.

The equipartition theorem states that, at thermal equilibrium, the energy of a system is equally distributed among its degrees of freedom, with each degree of freedom contributing  (where  is the Boltzmann constant and  is the temperature) to the average energy. For classical systems, this works well, but electrons are quantum particles, and their behavior is governed by quantum mechanics.

Electrons, especially in solids, do not follow the equipartition theorem in the classical sense because they obey Fermi-Dirac statistics. Instead of being evenly distributed in energy, electrons fill available energy states up to the Fermi level at absolute zero, and at higher temperatures, only the electrons near the Fermi level gain significant energy. This leads to the concept of a Fermi temperature, which is very high compared to the actual temperature of the material.

Therefore, the equipartition theorem does not directly apply to electrons, and their temperature, which reflects the distribution of their energies, is defined differently from that of classical particles. In summary, electrons can have a well-defined temperature in a system (such as the electron temperature in metals), but the equipartition theorem doesn't describe their energy distribution accurately due to quantum effects.

[Bored chemist]

Does equipartition theorem tell you that the electrons don't have a well defined temperature.

These electrons have an energy of a few eV. (We know, because they emit visible light)
The electrons, atoms etc  nearby have an energy corresponding to room temperature; about 0.025 eV. (we know, because the plastic doesn't melt).
So we know that it's a (very) non-equilibrium state.
And we know that temperatures are only well defined if the equipartition theory is true

[hamdani yusuf (OP)]

These electrons have an energy of a few eV. (We know, because they emit visible light)
The electrons, atoms etc  nearby have an energy corresponding to room temperature; about 0.025 eV. (we know, because the plastic doesn't melt).

In your system,
T = room temperature = 20 C = 293 K
E = 0.025 eV = 4.005441584E-21 Joule
ΔS = 4.005441584E-21 Joule / 293 K =1.36704E-23 J/K

Where did you get these numbers from?
 

[Bored chemist]

I got them from physics.

E = kT
k = 1.380649 ? 10^-23 m2 kg s-2 K-1
T= 297
E= 4 x 10^-21 J

Strictly speaking I got the number from remembering that the energy of thermal neutrons is about 0.025eV
But that's the joy of the equipartition theory.

I could have done this calculation instead.
The speed of sound in a gas is comparable with the speed of the molecules or atoms in that gas.
I know the speed of sound in air- it's about 330 m/s
And I know that the density of air is abut 1.2 grams per litre
And I know that a mole of gas occupies about 24 litres.
And I know Avogadro's constant is about 6 x 10^23.
So I can work out that the mass of an air molecule is about 5 x 10^26 Kg

So I can calculate the energy from 1/2 M V^2
and get about 5X10^-21 Joules
And I can convert that to eV
0.031 eV.

Close enough.

I can pick any particle with a well defined temperature and if I know its energy, then I know the energy of any other particle at that temperature.
In principle, I can measure the energy of some visible light. (It's a high school expt using the photoelectric effect).
And then I can measure the spectrum of the IR emitted by my floor or wall.
And, from that, I can measure the energy of the radiation in equilibrium with the wall + floor. (It's a simple ratio; if the peak wavelength is 100 times longer then the energy is 100 times lower).

So, I can measure the energy of a typical particle.
And, using that, and the known mass of an air molecule, I can calculate the approximate speed of sound.

Clever, isn't it?

[hamdani yusuf (OP)]

Strictly speaking I got the number from remembering that the energy of thermal neutrons is about 0.025eV
But that's the joy of the equipartition theory.

What makes you think that equipartition theory is still valid to conclude that energy of thermal neutrons at room temperature is the same as electrons?

[hamdani yusuf (OP)]

I can pick any particle with a well defined temperature and if I know its energy, then I know the energy of any other particle at that temperature.
In principle, I can measure the energy of some visible light. (It's a high school expt using the photoelectric effect).
And then I can measure the spectrum of the IR emitted by my floor or wall.
And, from that, I can measure the energy of the radiation in equilibrium with the wall + floor. (It's a simple ratio; if the peak wavelength is 100 times longer then the energy is 100 times lower).

We'll need a different theory to explain the works of induction heater, microwave oven, and infrared stoves.

[Bored chemist]

What makes you think that equipartition theory is still valid to conclude that energy of thermal neutrons at room temperature is the same as electrons?

Because it's a consequence of the conservation of energy.

[Bored chemist]

We'll need a different theory to explain the works of induction heater, microwave oven, and infrared stoves.

You might; the rest of us don't.

[hamdani yusuf (OP)]

(It's a simple ratio; if the peak wavelength is 100 times longer then the energy is 100 times lower)

This only works for black body radiation.

[Bored chemist]

This only works for black body radiation.

Guess what the spectrum looks like if you apply the equipartition principle to photons...

So once again.
If that principle doesn't apply, you don't have a well defined temperature.

Did you not think about that?

Maybe, next time, at the start of your post you should add a line or two that shows that you have considered the effect of equipartition and what the outcome is.

Because I'm frankly getting tired of reminding you about it.

[hamdani yusuf (OP)]

What makes you think that equipartition theory is still valid to conclude that energy of thermal neutrons at room temperature is the same as electrons?

Because it's a consequence of the conservation of energy.

conservation of energy can still apply even when equipartition theorem doesn't hold.

[hamdani yusuf (OP)]

Guess what the spectrum looks like if you apply the equipartition principle to photons...

Ultraviolet catastrophe.

[hamdani yusuf (OP)]

So once again.
If that principle doesn't apply, you don't have a well defined temperature.

Does it imply that we can't predict where the energy will naturally flow?

[Bored chemist]

conservation of energy can still apply even when equipartition theorem doesn't hold.

Nobody suggested otherwise.

Ultraviolet catastrophe.

Was resolved by the quantisation of  em radiation- which is implicit in the use of the word "photons".

Does it imply that we can't predict where the energy will naturally flow?

No.


Do you not recognise that this sort of exchange is a very inefficient way of you learning science- especially when you fail to pay attention to important things like equipartition?

[hamdani yusuf (OP)]

conservation of energy can still apply even when equipartition theorem doesn't hold.

Nobody suggested otherwise.

What makes you think that equipartition theory is still valid to conclude that energy of thermal neutrons at room temperature is the same as electrons?

Because it's a consequence of the conservation of energy.

conservation of energy can still apply even when equipartition theorem doesn't hold.

Previously, you concluded that energy of thermal neutrons at room temperature is the same as electrons because you thought that equipartition theory is still valid in this case. You thought that its validity is a consequence of the conservation of energy.

[hamdani yusuf (OP)]

Ultraviolet catastrophe.

Was resolved by the quantisation of  em radiation- which is implicit in the use of the word "photons".

Which implies that the em radiation is not equally partitioned.