# I Breakdown of Planck's Law under certain Conditions

1. Oct 31, 2016

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:

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?

2. Oct 31, 2016

### 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.

Last edited: Oct 31, 2016
3. Oct 31, 2016

### Demystifier

The Plank's law is violated in led bulbs.

4. Oct 31, 2016

### Staff: Mentor

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.

5. Oct 31, 2016

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

6. Oct 31, 2016

### Demystifier

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.

7. Oct 31, 2016