Black body radiation formula and de broglie wavelength While deriving blackbody radiation, we assume that a standing wave of a particular wavelength can have energy $E=nh\nu$, where $\nu$ is the frequency and $n=1,2,3...$, with probability $e^{-nh\nu/k_{B}T}$. We then calculate the average energy per wavelength, but according to de Broglie there is a fixed amount of energy for a particular wavelength. I am a beginner and couldn't make sense of this. Anyone please clear up my confusion.
 A: Black body radiation is one of the experimental observations that necessitated the quantum mechanics theory.

Blackbody radiation" or "cavity radiation" refers to an object or system which absorbs all radiation incident upon it and re-radiates energy which is characteristic of this radiating system only, not dependent upon the type of radiation which is incident upon it. The radiated energy can be considered to be produced by standing wave or resonant modes of the cavity which is radiating.


This shows the calculation of the black body radiation according to the quantized hypothesis avoids the ultraviolet catastrophe.
The radiation is electromagnetic, which at the quantum level involves photons , of energy hν, where  ν is the classical light frequency.  Photons have a mass zero'
The de Broglie wave involves massive particles:

The concept that matter behaves like a wave was proposed by French physicist Louis de Broglie (/dəˈbrɔɪ/) in 1924. It is also referred to as the de Broglie hypothesis.1 Matter waves are referred to as de Broglie waves.

It is a forerunner of the probabilistic nature of quantum mechanics, what is "waving" is the probability of finding the particle of mass m at (x,y,z,t) which is mathematically expressed by the correct wavefunction for the system under observation, $Ψ^*Ψ$
You state:

but according to de Broglie there is a fixed amount of energy for a particular wavelength.

Do you mean :
$λ=h/p$
This controls the frequency of the probability wave, not the individual interaction. In the black body calculation it is the summation  of the individual interactions that generate the frequency versus intensity plot.
