Relationship between Planck Distribution and Quantization of Energy

In summary, the Planck Distribution explains the UV catastrophe by showing that the energy emitted by a black body has discrete values. This is related to the equation E=nhv, where n represents the discrete energy values. Quantum electrodynamics limits the number of modes that can exchange energy, leading to Planck's radiation law and a finite total radiation energy, solving the problem of the UV catastrophe.
  • #1
HelpMeGodWithPhysics
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I got stuck with the correlation between Planck Distribution and Quantization of Energy.
I came to understand that Planck Distribution is necessary to explain UV catastrophe. With that necesity in the background, the distribution equation eventually suggests that the energy emitted by black body has discret values. But I wonder how that's related to E=nhv. I understand that "n" also implies the discrete energy values but how does "n" ultimately contribute to deriving distribution equation? I might need a mathematical explanation.
 
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HelpMeGodWithPhysics said:
the distribution equation eventually suggests that the energy emitted by black body has discret values

No, it doesn't. A black body emits a continuous range of frequencies (energies).

HelpMeGodWithPhysics said:
I wonder how that's related to E=nhv

Where are you getting the ##n## from?
 
  • #3
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As indicated, to me, it sounds like this experiment shows that energy is quantized or has discrete amounts when it's tranferred and Planck Distribution is an explanation for that.
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  • #4
The crucial point is that radiation in a cavity comes to thermal equilibrium through interaction with the walls of the cavity. Kept at constant temperature, the radiation must come to thermal equilibrium at this temperature, which means that the rate of absorption and emission of radiation energy are the same. In the classical picture each mode of the radiation field (i.e., the solution of Maxwell's equation harmonic in time with (angular) frequency ##\omega##) can exchange any quantity of energy, but this leads to the validity of the equipartition theorem, i.e., each mode would contain on average ## k T## of energy, which clearly leads to the UV catastrophe since you have infinitely many modes.

According to QT (i.e., in this case quantum electrodynamics) each mode can only exchange an integer number of energy portions of the size ##\hbar \omega##, i.e., you can excite only an integer number of "photons" of each mode. Together with the Bose nature of photons, which is due to the integer spin of 1 of the em. field, you get Planck's radiation law, which leads to a finite total radiation energy ##\propto T^4##, i.e., it solves the problem with the UV catastrophe.
 
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  • #5
vanhees71 said:
i.e., each mode would contain on average ## k T## of energy, which clearly leads to the UV catastrophe since you have infinitely many modes.

(i.e., in this case quantum electrodynamics) each mode can only exchange an integer number of energy portions of the size ##\hbar \omega##, i.e., you can excite only an integer number of "photons" of each mode.

So is it safe to say that according to QT, it limits the number of mode that can exchange energy rather than allowing infinite number of mode of energy exchange so that the total radiation energy becomes finite rather than infinite?
 

FAQ: Relationship between Planck Distribution and Quantization of Energy

1. What is the Planck Distribution?

The Planck Distribution, also known as the Planck's Law, is a mathematical formula that describes the distribution of energy emitted by a blackbody at different wavelengths. It was developed by German physicist Max Planck in 1900 and is a fundamental concept in the field of quantum mechanics.

2. How does the Planck Distribution relate to quantization of energy?

The Planck Distribution is closely related to the concept of quantization of energy, which states that energy can only exist in discrete, quantized units rather than being continuous. Planck's Law explains that the energy emitted by a blackbody is not continuous, but rather consists of discrete packets or "quanta" of energy. This was a groundbreaking discovery that laid the foundation for the development of quantum mechanics.

3. What is the significance of the Planck Distribution in modern physics?

The Planck Distribution is significant because it provided the first evidence that energy is quantized, or exists in discrete units rather than being continuous. This challenged the classical physics notion of continuous energy and led to the development of quantum mechanics, which has revolutionized our understanding of the microscopic world and has numerous practical applications in fields such as electronics, materials science, and telecommunications.

4. How is the Planck Distribution used in practical applications?

The Planck Distribution has a wide range of practical applications, particularly in fields such as thermodynamics and spectroscopy. It is used to calculate the energy emitted by objects at different temperatures, which is important in understanding the behavior of stars and other celestial bodies. It is also used in the design of electronic devices, such as LED lights and solar cells, and in the analysis of atomic and molecular spectra.

5. Are there any limitations to the Planck Distribution?

While the Planck Distribution is a powerful tool in understanding the behavior of energy at the microscopic level, it has its limitations. It assumes that the blackbody emitting the energy is in thermal equilibrium, meaning that it is at a constant temperature. This is not always the case in real-world scenarios, so the Planck Distribution may not accurately predict the energy distribution in certain situations. Additionally, it does not take into account the effects of relativity, which are important at high energies and velocities.

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