1. BLACKBODY RADIATION A “blackbody” is an object that absorbs 100% of all the EM radiation incident on it. Normally, what we think is black, is not exactly black. For instance, one of the “blackest” things one can think of, SOOT, absorbs only about 95% of impinging light. A much better example of a blackbody is here: You think it’s a pizza? NO! This is the SUN! This is not a joke – the Sun does absorb almost all radiation reaching its surface. For instance, starlight. However, as far as EM radiation is concerned, the Sun is pri- marily an emitter, not an absorber, RIGHT? Yes, right, but the above definition does not exclude that a blackbody radiates energy out, RIGHT? Right! In fact, most of them do. Is a WIRE RING a blackbody?NO, of course not, this is not a true absorption

2. BLACKBODY RADIATION (2) Re-radiation of absorbed energy: a blackbody MUST radiate out energy, because if it only absorbed energy, its temperature would keep increasing all the time… So, when a blackbody is in equilibrium with the ambient world, and no energy is taken away from it by cooling, (e.g. by blowing cold air on it), then the amount of energy radiated in a time unit is equal to the amount of energy deposited by the impinging radiation. The RADIATION of energy by blackbodies started intriguing scientists by the end of the XIX century. They needed blackbodies that they could study in their labs. Sun has one disadvantage for the scientist: It is not a good object for experimenting. Shining light on it, or changing its temperature may pose a problem… Then someone go an idea: “Open windows always look black!” And it is how a cavity, a nearly-perfect model of a blackbody,was Invented.

3. Spectacular examples of thermal radiation Cooler lava stops glowing, as you can see – does it mean that only very hot bodies radiate energy? Answer: Not only very hot! It is our eyes that are not sensitive to wavelengths longer than those corresponding to RED light (i.e., 700 nm) – light from the longer wavelength region is called “infrared radiation”.

5. BLACKBODY RADIATION (3) Why started the radiation emitted by hot bodies intriguing scientists? They started to measure the WAVELENGTH SPECTRUM of the light emitted by various blackbody models. The measurements revealed one amazing fact: Namely, that the SHAPE of the spectrum is essentially the same for all blackbodies, regardless of their size and chemical composition of the cavity walls. What only matters, is the TEMPERATURE

6. Step One: Stretch the vertical scale by a factor 2 5 = 32 Step Two: “Squeeze” the wavelength scale by a factor of 2 Note: after these two rescaling steps, The shape of the 2000 K spectrum is exactly the same as that of the 4000K spectrum What does it mean: “the shape is essentially the same”? Suppose that two measurements of the wavelength spectrum from the same blackbody were made, one at 2000 K and the other at 4000K.

7. Conclusion from the preceding slide: All wavelength spectra from blackbodies are described by one “universal” function. The results of studies of blackbody radiation made it clear to the XIX-century physicists that the spectrum shape is described by a new unknown law of physics. It became a major challenge for them to derive its mathematical form.

8. BLACKBODY RADIATION, continued Before the end of the XIX century, two empirical laws were formulated. The results indicated that the position of the spectrum maximum in wavelength scale is inversly proportional to the blackbody temperature. This is expressed by the so-called Wein’s Displacement Law: The total power I radiated by a surface unit of a blackbody is given by the So-called Stefan-Boltzmann Law: However, several attempts of deriving the functional form of the spectrum shape – all on the grounds of classical physics, i.e, the only theory that Existed at that time – ended with failures. And finally the solution was found! By a German physicist Max Planck. He announced his findings at a seminar on December 19, 1900. Just 12 days before the end of the XIX century. That day quantum physics was born!

9. Planck’s revolutionary concept A standard approach to the blackbody problem is to consider the state of equilibrium between the EM field filling a cavity, and the cavity walls. According to the famous Maxwell’s theory, electromagnetic (EM) radiation can be emitted or absorbed by oscillating electric dipoles. Where are the dipoles in a blackbody? Well, atoms or molecules in the cavity walls can act as such oscillating dipoles. They can “take away” electromagnetic energy from the EM field, or “return it” to the field. In equilibrium, the amount of energy absorbed by all dipoles and the amount re-radiated per time unit are equal. Max Planck used the above assumption – as others who attempted to solve the problem before him did. However, Plank additionally assumed that the energy can only be absorbed or re-emitted in discrete “bundles” (portions? quantities?). Consider a “Dollar Store” in which all prices are $1, $2, $3… No cents! Suppose that YOU are the EM field. You can only add $1, $2, $3 … to the owners pocket ( = cavity in our example), or, if you return some of the items purchased, you may get back $1, $2, $3…. No cents!

10. Planck’s revolutionary approach (continued) Planck’s thinking went along a similar line as in our “Dollar store example”. He called the discrete quantities of energy “QUANTA”. He assumed that The energy of a single “quantum” of EM radiation with frequency ν is proportional to that frequency, i.e., E=hν, where h is a constant. In fact, Planck used that assumption as a “mathematical trick” – His only intention was to find a way to facilitate the calculations, but he did not expect that ANY NEW PHYSICS WOULD EMERGE from it. Actually, IT DID EMERGE! The equation that Planck derived, viz.: was found to agree with the results of experiments remar- kably well! “Remar- kably” is not enough to say – “sensatio- nally” is perhaps a better word. The result was so surprising that many physicists could not believe it reflected physical reality. Including Max Planck himself.

11. Planck’s revolutionary approach (continued) Planck for a long time was not fully convinced that “quanta” are real, not just a mathematical illusion. He continued working on the problem, trying to find a way to obtain the same result without introducing discrete quanta. Only after about twenty years, when experimental evidence supporting the existence of energy quanta amassed, he reluctantly accepted them, those “brainchildren he himself fathered”. But what is the conclusion that emerges from that “blackbody story”? Does Planck’s result resolve whether light has a wave-like nature, or particle-like nature? The answer is NO. Even though Planck introduced quanta to his the- ory, only the “oscillators” comprising the blackbody were “quantized” in his approach, whereas the EM radiation field was assumed to be a “continuum”. Two more times the blackbody radiation problem was attacked using different initial assumption than those Planck had used (Einstein, 1917, and Bose & Einstein, 1924). In both cases light was assumed to consist of discrete particle-like photons. Both approaches produced exactly the same result as In Planck’s study (and, as a “byproduct”, each led to a major discovery). CONCLUSION? All work done on the blackbody problem showed that Both assumptions – that light is a continuous wave, or that it consists of particle-like photons – lead to the same result. ERGO, they do not resolve the dilemma.

12. CONCLUSION? All work done on the blackbody problem showed that either assumption – that light is a continuous wave, or that it consists of particle-like photons – leads to the same result. ERGO, they do not resolve the dilemma. RATHER, the results obtained in all blackbody radiation studies support our thinking of light as of an entity having a “dual nature”. Below, there is a link that calculates the blackbody spectrum at a given Temperature that can be varied. You can check, for instance, that the spectrum of light radiated by the Sun (T  5500 K) has its maximum in the yellow-green wavelength region. Therefore, it may not be accidental that plants are green, and that our eyes are most sensitive to light from this very region. Blackbody Radiation Applet Copyright 2001 The McGraw-Hill Companies, Inc. Blackbody radiation – closing comments