Bell shape like of Planck's distribution

[Entanglement]

As a high schooler, what I can deduce from Planck's distribution's bell shape is that the majority of the atoms of a body above 0k possesses a certain K.E which is the average K.E which leads to the presence of a peak point in the distribution. While the minority posses higher or lower K.E which leads to the decrease of intensity of radiation for longer or shorter wavelengths than that of the peak point. And as the temperature of the body increases the K.E energy possessed by the majority increases so the peak point moves to a higher frequency, I think the explanation is related to maxwell-boltzman distribution to a great extent. All of what I said is just my deductions, at school we are not given explanations for what we study, and we don't have enough knowledge about the topics to deduce the explanations on our own, I'm keen on understanding every point, so I hope anyone on the forum to correct what I mentioned about the bell shape and give me a good explanation, thanks in advance.

 

[Jilang]

The Plank distribution can be derived from the Boltzmann distribution. You get from the second to the first by assuming that the energy is quantised - i.e. Existing in little packets.
http://disciplinas.stoa.usp.br/pluginfile.php/48089/course/section/16461/qsp_chapter10-plank.pdf

 

[Entanglement]

You get from the second to the first by assuming that the energy is quantised - i.e. Existing in little packets.

What is meant by energy is quantized ?

 

[Jilang]

Planck's postulate was that the energy of oscillators comes in discrete packets given by:
E=nhv
Where n is an integer, h is Plancks constant and v is the frequency of the oscillator. By applying this to the classical distribution for states he arrived at the Planck distribution.

 

[Entanglement]

Planck's postulate was that the energy of oscillators comes in discrete packets given by:
E=nhv
Where n is an integer, h is Plancks constant and v is the frequency of the oscillator. By applying this to the classical distribution for states he arrived at the Planck distribution.

You mean we mean that he assumed the Particle nature of light ?

 

[Jilang]

He didn't quite go that far. Einstein is given credit for that.

 

[Entanglement]

He didn't quite go that far. Einstein is given credit for that.

But at least he assumed that the light is quantized to photons.

 

[Entanglement]

Planck's postulate was that the energy of oscillators comes in discrete packets given by:
E=nhv
Where n is an integer

N is number of oscillators ?

 

[Jilang]

But at least he assumed that the light is quantized to photons.

No, I don't think he went that far. It was a mathematical trick that gave the right answer.

 

[Jilang]

N is number of oscillators ?

No, it is just an integer. The number of oscillators is given by the Boltzmann distribution.