Planck law

The interaction between EM radiation and matter includes experiences of everyday life. If a piece of iron is heated in the blacksmith s shop, it will turn red after a while. With further heating, the color changes to yellow. Everything heated to 6000°C will be as white as sunlight. The frequency distribution and color of the heated body depend only on its temperature. Wien had arrived at his displacement law and even derived an equation for the energy distribution, but it did not fit perfectly to very accurate measurements of energy distribution as a function of frequency. 

Equation 1.3 cannot be derived from classical physics and might be regarded as the first quantum law. With the help of Equation 1.3, Planck was able to derive the following law  

To Planck, Equation 1.3 was little more than a necessary mathematical equation. In the later quantum mechanical picture, the excitations of the black body are quantized as outgoing waves. Equation 1.3 may be derived using time-dependent quantum mechanics for the excitation process. The possible frequencies depend on the material in the case of an insulator. Planck assumed that he had a black body, meaning that all frequencies are available. AE = hv has turned out to be a general equation in quantum mechanics, holding for excitations, electrons, vibrations, fields, etc. 

---

The first and second Planck-law constants c and C9 are respectively (3.740)(10- ) (Jm )/s and (1.4388)(10- ) m K. The term clearly a function only of the product XT, is given in Fig. 5-11 which may be visualized as the monochromatic emissive power versus wavelength measured in vacuo of a black surface at 1 K discharging in vacuo. 

It is conceivable to detect amplitude and phase emitted by a celestial object at various observation sites and to correlate the results in order to create a huge interferometer (Fig. 3). Because laser can be very stable, the phase reference between lasers can be extracted at low data rate for example from the correlation of the interference signal of each laser with a high magnitude star. The main difference with communication case above is that the absolute phase of the thermal emission is meaningless only the phase correlation from site to site can be exploited. Emission of thermal source is governed by the Planck law. This law states that the probability of photon population of a mode is ... 

Since in reality there is no actual blackbody radiator (for which the Planck law applies, W), but a more realistic so-called greybody radiator (W7), the value e has been defined as the quotient W / W, where e can be given values between 0 and 1 (1 = genuine blackbody). For example, soot (e > 0.95) behaves almost like a blackbody radiator, whereas MgO behaves more like a greybody radiator. 

The Bose-Einstein distribution (1.162) may be considered to recover the Planck law of black body radiation, i.e., the photon radiation modeling, by considering the following peculiarities ... 

Using the Boltzmann-Planck law, the entropy of configuration of polymer molecules can be expressed as... 

FIG U R E 9.15 A plot of the intensity of radiation versus wavelength at different temperatures for a blackbody, assuming Planck s radiation law is correct. Predictions based on Plancks law agree with experimental measurements, suggesting a correct theoretical basis—no matter what its implications are. 

We assume that at a given wavelength the background radiation generation term has a form identical to that of the optical generation term. If we replace Pq according to the Planck law and integrate the obtained expression over all allowed... 

The next phenomenon connected with nonequilibrium methods is negative luminescence [337], also called induced absorption [338]. Actually, a semiconductor with nonequilibrium decrease of carrier concentration emits less electromagnetic radiation than it should according to the Planck law. 

---