Blackbody radiation and Planck constant questions

[rabcarl]

Ive been reading lately about the Planck constant and have been trying to learn more about it if possible.

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.

 

[Simon Bridge]

Ive been reading lately about the Planck constant

Where?

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?

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).

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?

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.

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

 

[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?

 

[Simon Bridge]

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?

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.

 

[atyy]

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).

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

 

[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.

 

[SteamKing]

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.

http://en.wikipedia.org/wiki/Planck's_law_of_black-body_radiation
http://en.wikipedia.org/wiki/Max_Planck
http://en.wikipedia.org/wiki/Rayleigh–Jeans_law

In response to your second question, the equation which Planck derived pre-supposed that energy was emitted in discrete packets. Many prior attempts had been made to explain the distribution of radiation emanating from a body as its temperature increased, notably by the physicists Wilhelm Wien, Lord Rayleigh and Jeans. The problem had originally been proposed by Kirchhoff in 1859 and Planck's attention to the matter was focussed in his attempts to create a more efficient light bulb, one which emitted the maximum amount of light for a minimum amount of electricity. Initially, in his work, Planck did not make the assumption that energy came in discrete packets, and he only gradually came around to this idea as his researches progressed. Even after he was able to produce his astounding results, and other physicists like Einstein had similar success with quantum theory, Planck remained deeply suspicious and unsettled about the quantum assumption which had made him world famous.