# Blackbody radiation and Planck constant questions

1. Jul 12, 2013

### rabcarl

The way I understand it, the constant came about from experiments with black body radiation. Planck noticed that the experimental data fit the equation e=hf.

My first question: how did he come up with the equation?

My second question: why did this equation imply that light
came in packets, or quanta? This is the one I have been wondering about the most. I know that einsteins work on the photoelectric effect pretty clearly shows that light is made up of "packets" or "chunks" called photons. However, is planck's work on black body radiation enough to make the conclusion that light is quantized on its own?

As always, thanks so much for your explanations. PF has really taught me a ton about physics that I don't think i could have learned anywhere else.

2. Jul 13, 2013

### Simon Bridge

Where?

By plotting lots and lots of data and trying different models out. It wasn't random, there had already been work that introduced the idea of quantization into the physics of the very small (Millikan et al).

No - but it is suggestive. If energy is absorbed in lumps (quanta) then it seems simplest if it is also delivered in lumps - and the corpuscle theory of light had already been introduced.

The work was foundational not conclusive.

http://en.wikipedia.org/wiki/Planck_constant#Origins

Last edited by a moderator: May 30, 2014
3. Jul 13, 2013

### rabcarl

Ok, this makes more sense now. I have one more question as well. Does the quantization of light have any impact on which frequencies or wavelengths light can take on? In other words, are there an infinite amount of energies and wavelengths light can have or are there a finite number?

4. Jul 13, 2013

### Simon Bridge

The frequency of light belongs to the wave model.
Photons have energy and momentum only.
E=hf is the relationship between the energy in the particle model and the frequency in the wave model.
There does not appear to be any restriction in what energies light can have (outside conservation of energy). Very high energy-density particles, though, have a special name: matter. But you are probably wondering if quantum-mechanics effects produce gaps in the electromagnetic spectrum - which is "no". The quantization effects the probabilities.

For an extended discussion on the relationship betwen light and matter:
http://www.johnagowan.org/light.html#matter

BTW: Einsteins work was not as conclusive as it is usually presented - the effects he measured can be accounted for in a semi-classical approach which treats the field of the incoming EM wave as a perturbation on the quantized electron state. However, the perturbation theory is harder maths.

Last edited: Jul 13, 2013
5. Jul 13, 2013

### atyy

Wikipedia gives Millikan's oil drop as 1909, and Planck as 1900.

6. Jul 14, 2013

### Simon Bridge

Oh wow ... OK.
Klein, Martin J. (1961). "Max Planck and the beginnings of the quantum theory". Archive for History of Exact Sciences 1 (5): 459. doi:10.1007/BF00327765.
... gives Plank as introducing the idea of quantization.

The first part still stands ... he did it by trying lots of things out, being immersed in the field, being aware of what other people were doing. You know: science.

7. Jul 14, 2013

### SteamKing

Staff Emeritus
The first article gives a pretty detailed discussion of Planck's approach to the Black-Body problem, a little history, and the derivation of the Planck's constant itself.