Black Body Radiation Curve

In summary, Plank's approach to the black-body radiation problem involved two key changes to the classical Rayleigh-Jeans approach. First, he assumed that the oscillators in the black-body cavity could only have energies that were multiples of a minimum energy, which shifted his analysis into the quantum realm. Second, he used a statistical analysis to assign the correct number of oscillators with this minimum energy to a given frequency. This approach saved Plank from the "ultra-violet catastrophe" and allowed his equation to match experimental curves. While Wien had also used a similar approach, it was Plank's inclusion of the frequency-dependent relationship between energy and frequency that made his formula a quantum breakthrough, with implications for both radiation and matter.
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According to the documents I have read, Plank made two changes to Rayleigh-Jeans approach in order to produce an equation that matched the black-body radiation, experimental curves:
1) As a mathematical convenience he assumed that the oscillators in the walls of black-body cavity could only have energies that were multiples of a minimum energy ∆E. This was ultimately described as the break-through that moved his analysis from the classical to the quantum realm.
2) He then used a statistical analysis to assign the correct number of oscillators with energy ∆E to a given frequency.
I have been through the mathematics of Planks formula, versus Rayleigh-Jeans. Plank used exactly the same relationship to determine the number of standing wave modes at a given frequency. This varied as the frequency-squared and resulted in the "ultra-violet catastrophe".
It was not the assignment of minimum energy increments that saved Plank from the same result. It was the fact that his energy increments had the relationship ∆E = hf/KT, versus Rayleigh-Jeans use of ∆E = KT.
The question is, what motivated Plank to come up with this frequency-dependent relationship for mode-energy?
 
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  • #2
Mikeal said:
According to the documents I have read, Plank made two changes to Rayleigh-Jeans approach in order to produce an equation that matched the black-body radiation, experimental curves:
1) As a mathematical convenience he assumed that the oscillators in the walls of black-body cavity could only have energies that were multiples of a minimum energy ∆E. This was ultimately described as the break-through that moved his analysis from the classical to the quantum realm.
2) He then used a statistical analysis to assign the correct number of oscillators with energy ∆E to a given frequency.
I have been through the mathematics of Planks formula, versus Rayleigh-Jeans. Plank used exactly the same relationship to determine the number of standing wave modes at a given frequency. This varied as the frequency-squared and resulted in the "ultra-violet catastrophe".
It was not the assignment of minimum energy increments that saved Plank from the same result. It was the fact that his energy increments had the relationship ∆E = hf/KT, versus Rayleigh-Jeans use of ∆E = KT.
The question is, what motivated Plank to come up with this frequency-dependent relationship for mode-energy?
There was already a catastrophic dependency in the sense that energy tended to infinity as frequencies got higher according to the classical calculations, but that was obviously not observed besides being absurd, so he came up with a relation between energy and frequency that approximated observations, he did it basically in a heuristic way, that is just trying different formulas to find the simplest that worked, even if he rejected for a long time the implications.
 
  • #3
TrickyDicky said:
There was already a catastrophic dependency in the sense that energy tended to infinity as frequencies got higher according to the classical calculations, but that was obviously not observed besides being absurd, so he came up with a relation between energy and frequency that approximated observations, he did it basically in a heuristic way, that is just trying different formulas to find the simplest that worked, even if he rejected for a long time the implications.

Thanks. The interesting thing is that Wien used a similar approach and came very close. His formula fit experimental results at wavelengths shorter than 10E06 meters and deviated only slightly at longer wavelengths. Down to 10E2 meters, you need a log-intensity scale to see it.

I'm still not sure why Plank's approach was considered a quantum-breakthrough, unless it was the fact that "h" had to be a specific value (quanta) to fit the curve?
 
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  • #4
Mikeal said:
Thanks. The interesting thing is that Wien used a similar approach and came very close. His formula fit experimental results at wavelengths shorter than 10E06 meters and deviated only slightly at longer wavelengths. Down to 10E2 meters, you need a log-intensity scale to see it.
It was precisely Wien's other formula, the displacement law(that had already been empirically validated) what demanded the frecuency dependence of the energy discrete elements E(E=hv) in the final Planck's formula.
I'm still not sure why Plank's approach was considered a quantum-breakthrough, unless it was the fact that "h" had to be a specific value (quanta) to fit the curve?
It was mostly the implications of this for both radiation(Einstein photons) and matter(Bohr "jumps" and later Schrodinger and Heisenberg full QM).
 

1. What is the Black Body Radiation Curve?

The Black Body Radiation Curve is a graph that shows the distribution of electromagnetic radiation emitted by a black body at different temperatures. A black body is an idealized object that absorbs and emits all radiation that falls on it.

2. How is the Black Body Radiation Curve calculated?

The Black Body Radiation Curve is calculated using Planck's Law, which determines the amount of radiation emitted by a black body at a given wavelength and temperature. This law takes into account the temperature of the object and the wavelength of the emitted radiation.

3. What is the significance of the Black Body Radiation Curve?

The Black Body Radiation Curve is significant because it is a fundamental concept in the field of thermodynamics and it helps to understand the distribution of energy emitted by objects at different temperatures. It has also been used to develop other important theories such as quantum mechanics and the theory of relativity.

4. How does the Black Body Radiation Curve relate to the color of objects?

The Black Body Radiation Curve is used to explain the color of objects. As the temperature of an object increases, the peak wavelength of the emitted radiation shifts towards the blue end of the spectrum. This is why hot objects appear blue or white, while cooler objects appear red or orange.

5. Can the Black Body Radiation Curve be observed in real life?

Yes, the Black Body Radiation Curve can be observed in real life. It can be seen in objects that emit a continuous spectrum of light, such as the sun or incandescent light bulbs. However, it is important to note that no object in nature is a perfect black body, so the curve is an idealized representation.

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