Planck’s theory

In 1900 Max Planck proposed a solution to the problem of black-body radiation described above. He suggested that when electromagnetic radiation interacts with matter, energy can only be absorbed or emitted in certain discrete amounts, called quanta. Planck s theory will not be described here, as it is highly technical. In any case, Planck s proposal was timid compared with the theory that followed. He supposed that quanta were only important in absorption and emission of radiation, but that otherwise the wave theory did not need to be modified. It was Einstein who took a more radical step in 1905 (the year in which he published his first paper on the theory of relativity and on several other unrelated topics). Einstein s analysis of the photoelectric effect is crucial, and has led to a complete change in the way we think of light and other radiation. 

Einstein s theory of specific heat leads to the same result. This theory connects the molecular motion in solid bodies with Planck s theory of radiation, and has been confirmed in the main by the experimental researches of Nernst and his collaborators in the last few years. Einstein assumes that the heat motion in solid bodies consists of vibrations of the atoms about a point of equihbrium, as distinct from the translational motion of the molecules which we assume for gases. The energy of these vibrations—and this is the characteristic feature of the theory, and also of Planck s theory of radiation—is always an integral multiple of a quantity of energy e, which, in turn, is the product of a universal constant (. e. a constant independent of the nature of the substance) and the frequency i/ (number of vibrations R,... 

The entropy is then equal to the entropy of an electromagnetic resonator of frequency v capable of vibrating in all three directions of space. According to Planck s theory this leads to the equation ... 

Dunitz wrote of these equations Debye s paper, published only a few months after the discovery of X-ray diffraction by crystals, is remarkable for the physical intuition it showed at a time when almost nothing was known about the structure of solids at the atomic level. Ewald described how The temperature displacements of the atoms in a lattice are of the order of magnitude of the atomic distances The result is a factor of exponential form whose exponent contains besides the temperature the order of interference only [h,k,l, hence sin 9/M]. The importance of Debye s work, as stressed by Ewald,was in paving the way for the first immediate experimental proof of the existence of zero-point energy, and therewith of the quantum statistical foundation of Planck s theory of black-body radiation. ... 

FIGURE 4.7 Experimental test of Planck s distribution for blackbody radiation. The dots represent experimental data acquired at T = 1646 K. The continuous curve represents Planck s predicted distribution, with the parameter h = 6.63 X 10 J s. Agreement between experiment and theory is spectacular, demonstrating the validity of Planck s theory and also determining the value of the previously unknown parameter/ . 

Planck s revolutionary idea about energy provided the basis for Einstein s explanation of the photoelectric effect in 1906 and for the Danish physicist Niels Bohr s atomic model of the hydrogen atom in 1913. Their success, in turn, lent support to Planck s theories, for which he received the Nobel Prize in physics in 1918. In the mid-1920s the combination of Planck s ideas about the particle-like nature of electromagnetic radiation and Erench physicist Louis de Broglie s hypothesis of the wavelike nature of electrons led to the formulation of quantum mechanics, which is still the accepted theory for the behavior of matter at atomic and subatomic levels. 

In the development of the mechanics of the atom the method of discovery has been to retain the classical mechanics as far as possible. Planck s theory of the oscillator, for example, is based on the view that the motion of the vibrating particle takes place entirely in accordance with the classical principles. Not all motions, however, with arbitrary initial conditions, i.e. values of the energy, are equally permissible certain motions, characterised by the energy values (1), occupy a preferential position in the interaction with radiation, on account of a certain inherent stability these motions constitute the stationary states. ... 

According to Planck s theory, for a given frequency, v, matter can emit or absorb energy only in whole-number multiples of hV that is,... 

G. Meyer and S. W. J. Smith pointed out that Planck s theory of liquid contact potentials (see p. 705), since the ions of KCl and KI have practically equal mobilities, shows that there should be no contact potential between their solutions, and hence a cell formed from dropping electrodes in each should have practically no e.m.f. But Meyer found 0 284 volt and Smith 0 256 to 0 262 volt. Hence part of the potential difference at the electrode depends on the anion and is not eliminated. 

That the latter process is followed by the emission of a homogeneons radiation, for which the relation between the frequency and the amount of energy emitted is the one given by Planck s theory. 

Thus, to get the frequency of a discrete spectral line, he applied Planck s theory to the energy difference between the stationary states of the oscillating electrons, not to the energy of the individual electrons themselves ... 

The constant h, known as Planck s constant, has a value of 6.63 X 10 joule-seconds (J-s). According to Planck s theory, energy is always emitted or absorbed by matter in whole-number multiples of Jw such as hv, 2hv, 3/ir, and so forth. If the quantity of energy emitted by an atom is 3hv, for example, we say that three quanta of energy have been emitted (quanta being the plural of quantum). Furthermore, we say that the allowed energies are quantized that is, their values are restricted to certain quantities. Planck s revolutionary proposal that energy is quantized was proved correct, and he was awarded the 1918 Nobel Prize in physics for his work on the quantum theory. 

A few years after Planck presented his theory, scientists began to see its applicability to a great many experimental observations. It soon became apparent that Planck s theory had wilhin it the seeds of a revolution in the way the physical... 

Planck s Quantum Theory To explain the dependence of radiation emitted by objects on wavelength, Planck proposed that atoms and molecules could emit (or absorb) energy in discrete quantities called quanta. Planck s theory revolutionized physics. 

In 1905, Albert Einstein expanded on Planck s theory by introducing the radical idea that electromagnetic radiation has a dual wave-particle nature. Light exhibits many wavelike properties, but it can also be thought of as a stream of particles. Each particle carries a quantum of energy. 

The photon density p v) can be determined from Planck s theory of light, assuming perfect blackbody behavior. Einstein introduced a proportionality constant B, now called the Einstein coefficient of stimulated absorption ... 

Planck s theory did not require the radiation field itself to be quantized, and Planck did not conclude that it is [24]. Because the radiation inside a black-body box is emitted and absorbed by the walls of the box, only the energy levels of the... 

Planck s theory removed the ultraviolet catastrophe because short wavelengths correspond to large frequencies and large energy spacings. The excited states therefore have very small populations. The result of Planck s theory is that... 

The German physicist Max Planck first formulated the theory that describes the wavelength dependence of the radiation emitted from a blackbody radiator in 1901. Planck s theory was revolutionary in its time, requiring assumptions about the quantized nature of radiation. Planck s radiation law states that the brightness of... 

Prelude to Quantum Theory—The study of electromagnetic radiation emitted from hot objects led to Planck s theory, which postulates that quantities of energy can have only certain values, with the smallest unit of energy being that of a quantum. The energy of a quantum is given by equation (8.2) = hv, where h is Planck s... 

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