Breakdown of Planck's Law under certain Conditions

[tade]

The difference between Planck's Law and the Rayleigh-Jeans' Law is, in Rayleigh Jeans, the average energy per mode is $kT$, whereas in Planck, it is $\frac{hc}{λ(e^\frac{hc}{λkT}-1)}$.

These average energy formulas are multiplied by another formula to give either Planck's Law or the Rayleigh-Jeans' Law.

This other formula is inversely proportional to $λ^4$.

Hyperphysics covers the development of this $\frac{1}{λ^4}$ formula:
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html

In it is written:

...becoming a very good approximation when the size of the cavity is much greater than the wavelength as in the case of electromagnetic waves in finite cavity.

At low temperatures, a blackbody radiates more strongly in longer wavelengths.

Does this model indicate that Planck's law breaks down when the temperature is low and the size of the blackbody cavity is small?

 

[dextercioby]

The Planck's law won't break down, no matter what.

EDIT: Well, as one case from the below comments, it can be violated, as soon as the underlying assumptions do not hold.

 

[Demystifier]

The Planck's law won't break down, no matter what.

The Plank's law is violated in led bulbs.

 

[Nugatory]

Does this model indicate that Planck's law breaks down when the temperature is low and the size of the blackbody cavity is small?

No. A cavity is only an approximation of an ideal blackbody described by Planck's law. The approximation is what's breaking down here; it doesn't work when the cavity is too small.

 

[tade]

No. A cavity is only an approximation of an ideal blackbody described by Planck's law. The approximation is what's breaking down here; it doesn't work when the cavity is too small.

Got it. Are there any formula(s) that experimental physicists use when measuring the spectra of tiny cavities?

 

[Demystifier]

Does this model indicate that Planck's law breaks down when the temperature is low and the size of the blackbody cavity is small?

One of the assumptions in the derivation of the Planck's law is that the spectrum of possible energies is continuous. But the spectrum of an atom at rest is certainly not continuous. Nevertheless, the spectrum of realistic materials is usually quasi-continuous, i.e. discrete but with such a small energy spacing that this looks negligible. However, when the temperature is low and cavity small, then it is no longer negligible, the spectrum cannot longer be considered quasi-continuous, so the Plank's law becomes badly violated.

 

[tade]

One of the assumptions in the derivation of the Planck's law is that the spectrum of possible energies is continuous. But the spectrum of an atom at rest is certainly not continuous. Nevertheless, the spectrum of realistic materials is usually quasi-continuous, i.e. discrete but with such a small energy spacing that this looks negligible. However, when the temperature is low and cavity small, then it is no longer negligible, the spectrum cannot longer be considered quasi-continuous, so the Plank's law becomes badly violated.

How small and cold does a cavity have to be before it starts deviating from Planck's law significantly?