I'm trying to understand how black body radiation works. I already understand that it is an ideal system that absorbs all radiation that makes contact with it. What I do not understand what happens after it absorbs all wavelengths of radiation. Does it give it back off? Does it keep the energy within it, raising its own temperature? Can radiation escape from a black body? Also, in regards to the ultraviolet catastrophe, why can't a finite body give off an infinite amount of energy? Thanks.
i just ask what elements make that body black and go from there but other don't look at the causality behind the experiment
First off, ignore the second post. Bishadi is taking a *long* vacation from this site. What happens with a black body is that the radiation emitted at any point in time depends on the temperature of the body and nothing else. What happens right after that instant in time depends on temperature then. If the body absorbs more radiation than it emits its temperature will rise, and this will in turn make it emit more radiation. Regarding the ultraviolet catastrophe, infinities and singularities are indicative of a problem with the model. A finite-sized object that radiated an infinite amount of energy would instantaneously cool to absolute zero. This doesn't happen. The model that led to the ultraviolet catastrophe was flawed. The problem at the turn of the prior century was to show how/why that model was flawed.
k Please Register or Log in to view the hidden image! Ok, if I'm understanding this correctly, a black body will emit radiation, but this radiation is only dependent on the temperature and nothing else such as the atoms that make up the black body? I see, it does make sense that if an object radiated an infinite amount of energy, it would cool down to absolute zero (lose all its energy). I am still puzzled as to why Planck's theory of discrete energy led to a solution to the ultraviolet catastrophe. I'm trying but not seeing a link between discrete energy and showing that classical mechanics was wrong in predicting what would happen to a black body when exposed to increasingly smaller wavelengths. Thanks, I'm beginning to understand this. Please Register or Log in to view the hidden image!
Correct. A black body is an idealization. That real objects are made up of atoms and molecules that have excitation modes means that there is no such thing as a true black body. (Cavity radiators can however come very close to following ideal curve.) In a sense, it didn't. Planck's 1901 paper does not even mention Rayeigh-Jeans law. It does however mention Wein's law. Planck was trying to come up with a better model than Wein's law. Wein's law was purely empirical and did not explain behaviors at low frequencies. Planck's first came up with a simple but ad hoc modification to Wein's law that accomplished this goal. This initial model was still empirical. Very shortly after that initial concept, Planck developed a motivation for this empirical law by assuming a very early model of quantization. It was after the fact that people (particularly Einstein and Ehrenfest) realized that Plank's law resolves the ultraviolet catastrophe. The ultraviolet catastrophe results from erroneously applying the equipartition principle. Planck's model generates a non-uniform probability distribution; equipartition amongst frequencies simply does not apply.
The basic idealization of a blackbody is a closed metal box with an empty cavity on the inside. If the blackbody were a perfect absorber and emitter, any radiation energy in the cavity which hits the walls would be completely absorbed and then spat back out into the cavity. Thus no energy would escape, and the box would look black from the outside (assuming you're not shining a light of your own on it). In practice there are no blackbodies, but there are good approximations, and originally they would poke a little hole in the wall to peek inside and see how much energy was given off at every frequency. Planck's assumption changes the maths used to calculate the frequency distribution of the blackbody radiation. In the original Rayleigh-Jeans classical derivation of blackbody radiation, the only thing that made a difference between different frequencies of light was that there are more ways to emit high frequency light than low frequency, because there are more ways to fit it into the box. Otherwise, it's equally easy for light to be radiated at any frequency, because the amount of energy needed can be dropped by just reducing the amplitude of the radiation waves. With Planck's correction, there's a minimum amplitude at which light can be emitted (equivalent to 1 photon) and so it takes an increasing amount of energy to radiate at higher frequencies, eliminating the ultraviolet catastrophe.
You are right. Planck solved the ultraviolet catastrophe as you say, buy determining that photons are like little buckets that have to be filled before they can be emitted. At the ultraviolet end of the spectrum, where it was noted that no photons were emitted, i.e. the "catastrophe", Planck determined that photons are emitted in discrete amounts, i.e. quantized. He found the formula for "h" by trial and error and arrived at the formula that avoided the catastrophy, showing that the energy of a photon equals the frequency times "h".
Except Planck did not solve the ultraviolet catastrophe. He doesn't reference the Rayleigh-Jeans equation in his 1901 paper. The apparent problem wasn't even noticed until 1905, amd the term "ultraviolet catastrophe" was coined until 1911. Saying that Planck solved a problem that he did not address is a bit of a stretch, one unfortunately oft repeated in physics texts. A PhysicsWorld article on the subject: http://physicsworld.com/cws/article/print/373 Thomas Kuhn in Black-Body Theory and the Quantum Discontinuity: 1894-1912 makes the case that Planck is not the father of quantum mechanics. Planck's 1901 theory was, for the most part, a classical theory.
Rayleigh and Wien both were working on the problem of the blackbody radiation curve vs. the conventional understanding of continuously increasing frequency. Both published formulas that were flawed in the years before Planck discovered the formula for “h”. He was actively working on the problem during the same period of time. Though it is well recorded history that the term “ultraviolet catastrophe” didn’t come into use until later as you advise us, it is not true that Planck was not aware of their formulas and the fact that Rayleigh’s only fit the curve at the lower end and Wien’s formula fit at the high end of the frequencies, but neither explained the whole blackbody radiation curve. As for who was the father of quantum theory I guess you are saying it wasn’t Planck after all. My latest college physics book (purchased at a used book story for $3, not for a course I was taking and I’m not implying that) is the 6th edition of College Physics by Serway/Faughn, almost a hundred years after Kuhn said that. And still they are saying that Planck’s theory key point, the quantized energy states, marked the birth of quantum theory.
You can find Planck's 1900 and 1901 papers all over the internet. Here are a couple of English translations: On an Improvement of Wien's Equation for the Spectrum, http://web.ihep.su/dbserv/compas/src/planck00/eng.pdf On the Law of Distribution of Energy in the Normal Spectrum, http://bourabai.kz/articles/planck/planck1901.pdf Their is no mention of Rayleigh, or Jeans, or their law, equipartition in those papers. The black body radiation at high frequencies was well-known at the time. That is what Wein's law describes. You will see plenty of references to Wein's law in those papers. The ultraviolet catastrophe results from Rayleigh-Jeans theory, which was developed four or five years after Planck published his papers. Thomas Kuhn wrote Black-Body Theory and the Quantum Discontinuity: 1894-1912 in 1987. Do you not know who Thomas Kuhn is?
Is this a correct statement summing up the solution to the catastrophe? Plank showed that because energy is discrete, higher frequencies would require more photons. Because photons aren't infinite, the classical dilemma (ultraviolet catastrophe) was solved.
Higher frequencies do not require more photons. It is just that a black body is much less likely to emit high frequency photons. Black body radiation is not equipartitioned.
I don't understand why a black body is much less likely to emit high frequency photons. What I basically don't understand is why a curve shows up in the graph. It has to do with something about discrete energy, but I don't understand how discrete energy has anything to do with it. I sort of understood the bucket analogy, but was that for frequency or intensity? I apologize, I do not understand physics vocabulary such as equipartitioned. I'm taking a high school level physics class and they haven't taught us this word yet. :-/
The point is the energy of a photon depends on it's frequency - the higher the frequency, the higher the energy of the photon.
This makes sense, however, why doesn't an infinitely large frequency cause a black body to reach an infinitely large temperature? The solution to the graph of the ultraviolet catastrophe appears to drop to zero as frequency increases.
You seem to know this but the curve drops off as the frequency increases because fewer and fewer photons are emitted as the energy required to “fill the next higher frequency bucket” increases. When the output of higher frequency photons stalls, in order to get the next photon at the next higher frequency, you have to add more energy to the blackbody. Obviously there comes a point where you don’t have enough energy to add to the black body to fill the next higher bucket. That is why there is no catastrophe; unless you have an infinite source of energy to play with, which you don’t AFAIK. The energy required for the next higher bucket is the frequency of that photon times the constant “h”, Planck’s constant. The discovery of “h”, the quantum increment, is what some say initiated Quantum Theory.
Is the energy required to fill the next higher frequency bucket exponential? If so, why is E=hf a linear curve? If the energy required to emit more photons in linear, then why does the curve drop off as frequency increases? This is where most of my problems in understanding are coming from. So because an infinite frequency required infinite energy, and you can't have infinite energy, the catastrophe is solved? If so, why did people before Planck think there was a problem in the first place? (did they think they could reach infinite frequencies without infinite energy?) Why am I having such trouble understanding something I'm sure many people find so simple? Please Register or Log in to view the hidden image! Btw, this question is on my phyics homework. The question was: "Describe what blackbody radiation is and how Max Planck solved its problem."
This is the right forum to ask those questions and I'm sorry not to be the one who is best to answer but someone will. Yes, the frequency is not continuous, it is quantum, and the energy to emit a photon at each frequency is "h" times the frequency. Each increment in frequency takes a greater amount of energy to emit a photon than it did at the previous lower frequency. The drop off of the curve or stalling of photon emissions as the frequency goes up is a matter of energy, and as you move higher in frequency, each photon carries more energy. No, they noticed that the curve dropped off and eventually stalled and didn't know that the emissions were quantized with each increment requiring a greater amount of energy. Don't beat yourself up. Someone will say something and the light will go on Please Register or Log in to view the hidden image!.
Thanks to everyone who helped me! I answered "describe what blackbody radiation is and how max planck solved its problem" by saying: A black body is an ideal system that absorbs all radiation. A black body emits radiation based only on its temperature. Max Planck solved a problem called the ultraviolet catastrophe where classical physics predicted that as light of increasing frequency where shone on a black body, its temperature would increase exponentially to infinity. Planck solved this by showing that energy is discrete. Higher frequencies of photons would require more energy, and because energy isn't infinite, the catastrophe was solved.
