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Thread: derivation of E=hf?

  1. #1 derivation of E=hf? 
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    What is the derivation for E=hf and why did experimental observation of black bodies show that quantization of light was neccessary?


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    Max Planck says he select "h" out of necessity. It don't have any derivation IMO.

    If light is not quantized, then there's no stoping to any blackbody to emmit a UV rays.... but in real life it cannot. So it appears that light is quantized to a certain energy threshold and it won't release even a single UV if energy of the blackbody's didn't reach that threshold.


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    Quote Originally Posted by msafwan View Post
    Max Planck says he select "h" out of necessity. It don't have any derivation IMO.

    If light is not quantized, then there's no stoping to any blackbody to emmit a UV rays.... but in real life it cannot. So it appears that light is quantized to a certain energy threshold and it won't release even a single UV if energy of the blackbody's didn't reach that threshold.
    but how did he know that E is proportional to f?
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    Quote Originally Posted by Naggy Doggy View Post
    [but how did he know that E is proportional to f?
    It is based on his theoretical derivation for black body radiation: Max Planck - Wikipedia, the free encyclopedia.

    It is basically a postulate (Planck postulate - Wikipedia, the free encyclopedia) that has since been confirmed repeatedly by experiment and further theoretical work.
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    Naggy: your OP question is historical in nature, see Strange's links for that. However do note this:

    "The central assumption behind his new derivation, presented to the DPG on 14 December 1900, was the supposition, now known as the Planck postulate, that electromagnetic energy could be emitted only in quantized form."

    This is perfectly correct. However this is somewhat misleading:

    "in other words, the energy could only be a multiple of an elementary unit E=hv where h is Planck's constant, also known as Planck's action quantum (introduced already in 1899), and ν (the Greek letter nu, not the Roman letter v) is the frequency of the radiation. Note that the elementary units of energy discussed here are represented by hv and not simply by h. Physicists now call these quanta photons, and a photon of frequency v will have its own specific and unique energy. The amplitude of energy at that frequency is then a function of the number of photons of that frequency being produced per unit of time."

    We can contrive the emission of single photons or single electromagnetic waves at any frequency we choose, and we can vary that frequency smoothly. That means we can vary the energy smoothly, and it can be any indiscriminate value. There are no actual elementary units of energy. Now see Planck's constant on wikipedia and note this: "Planck discovered that physical action could not take on any indiscriminate value." The action h in E=hf (aka E=hv) associated with the photon cannot take any indiscriminate value. Instead, it's the same for all photons, E=hf always applies. OK, note that the dimensionality of action can be expressed as momentum x distance. Something is the same for all photons. It isn't energy E=hf, and it isn't momentum p=hf/c. See that word amplitude in the quote above? Now go and take a look at some depictions of the electromagnetic spectrum.
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    but how did he know it was proportional to f, and not f^2, like a harmonic oscillator?
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    I don't know how Planck knew I'm afraid. I imagine it's because action has the same dimensionality as angular momentum. You can "see" the angular momentum associated with a transverse wave in this wikipedia article.
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    perhaps it was empirical evidence.
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    Quote Originally Posted by Naggy Doggy View Post
    perhaps it was empirical evidence.
    That's not too far off from the actual history. Helge Kragh, among others, has traced the story of Planck's inspiration. Planck began with Wien's spectral density equation, which was wholly empirical. Planck didn't like the impurity of such an equation, and came up with a theoretical justification for it, based on an entropy law for oscillators. E = hf fell out of that exercise. All was good until further experiments established that the Wien-Planck law was in error at long wavelengths. Planck then re-jiggered his formula to fix up that embarrassment, finally giving us the "blackbody law" as it is taught today.

    During none of this time (1899-1905, approximately) was the full import of what he had done widely recognized (by him or anyone else). Arguably, Einstein deserves the lion's share of the credit for what happened next in the story of quantum theory, with a fuller appreciation of what E = hf implied.
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    Quote Originally Posted by tk421 View Post
    Arguably, Einstein deserves the lion's share of the credit for what happened next in the story of quantum theory, with a fuller appreciation of what E = hf implied.
    My knowledge of this area of science history is fuzzy, but I assume this is a reference to the work Einstein got his Nobel prize for?
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    Quote Originally Posted by Naggy Doggy View Post
    perhaps it was empirical evidence.
    Kind of, in that to get to the bottom of E=hf you have to look to the real world. Look at some pictures of wave motion on this hyperphysics page, which is a reminder that a sine wave is associated with circular motion. Now think back to the old days of movie-making with hand-cranked cameras. I shout Lights, camera, action! and you crank the handle. There's a pen sticking out of the end of handle, and a moving scroll of paper. As you crank, the pen draws a sine wave. If you crank slow, it's a low-frequency sine wave. If you crank fast it's a high-frequency sine wave. But in both case it's the same action, and the amplitude of those sine waves is the same. The h in E=hf doesn't mean there's some elementary unit of energy, because you can vary the frequency smoothly and therefore vary the energy smoothly. What it means is that regardless of frequency the action is the same. One crank of the handle results in one wavelength, one photon, one lump of energy. It’s one “quantum” or “amount” of energy, but it can be any amount you like.
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by tk421 View Post
    Arguably, Einstein deserves the lion's share of the credit for what happened next in the story of quantum theory, with a fuller appreciation of what E = hf implied.
    My knowledge of this area of science history is fuzzy, but I assume this is a reference to the work Einstein got his Nobel prize for?
    Yes, you are right, as usual. Even though Planck "invented" the quantum of action, he got to it by such a roundabout way that no one really took notice of how revolutionary this invention was. Einstein zeroed in on that nugget and used it to explain the photoelectric effect, something that classical physics could not do. That's when people really started to pay attention, including Planck himself.

    I guess you could say that "Planck invented the quantum, while Einstein discovered it."
    Last edited by tk421; October 9th, 2012 at 09:27 AM.
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    Posts by Amanbir and responses removed to his thread.
    Disclaimer: I do not declare myself to be an expert on ANY subject. If I state something as fact that is obviously wrong, please don't hesitate to correct me. I welcome such corrections in an attempt to be as truthful and accurate as possible.

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    Quote Originally Posted by Naggy Doggy View Post
    perhaps it was empirical evidence.
    It wasn’t empirical evidence.

    Many years Planck was attracted with the
    absolutely black body problem.
    If quantum of light falls in an area of absolutely black
    body and does not radiate back, then " thermal death" comes.
    In 1900 Planck decided: there is only one way to save
    the quantum of light from ‘ thermal death’ -- it must radiate
    with unit: h=Et.
    This unit doesn’t come from any formulas or equations.
    Planck introduced this unit from heaven, from ceiling.
    Sorry. Sorry.
    I must write: Planck introduced this unit (h) intuitively.
    I must write: Planck introduced unit (h) phenomenologically.
    =.
    Socratus
    =.
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