Einstein-Planck quantum theory

Classical and Quantum Mechanics. At the beginning of the twentieth century, a revolution was brewing in the world of physics. For hundreds of years, the Newtonian laws of mechanics had satisfactorily provided explanations and supported experimental observations in the physical sciences. However, the experimentaUsts of the nineteenth century had begun delving into the world of matter at an atomic level. This led to unsatisfactory explanations of the observed patterns of behavior of electricity, light, and matter, and it was these inconsistencies which led Bohr, Compton, deBroghe, Einstein, Planck, and Schrn dinger to seek a new order, another level of theory, ie, quantum theory. 

The expressions in (3.72) and (3.73) are valid only for monatomic ideal gases such as He or Ar, and must be replaced by somewhat different expressions for diatomic or polyatomic molecules (Sidebar 3.8). However, the classical expressions for polyatomic heat capacity exhibit serious errors (except at high temperatures) due to the important effects of quantum mechanics. (The failure of classical mechanics to describe the heat capacities of polyatomic species motivated Einstein s pioneering application of Planck s quantum theory to molecular vibrational phenomena.) For present purposes, we may envision taking more accurate heat capacity data from experiment [e.g., in equations such as (3.84a)] if polyatomic species are to be considered. The term perfect gas is sometimes employed to distinguish the monatomic case [for which (3.72), (3.73) are satisfactory] from more general polyatomic ideal gases with Cv> nR. 

The development of quantum theory, particularly of quantum mechanics, forced certain changes in statistical mechanics. In the development of the resulting quantum statistics, the phase space is divided into cells of volume hf. where h is the Planck constant and / is the number of degrees of freedom. In considering the permutations of the molecules, it is recognized that the interchange of two identical particles does not lead to a new state. With these two new ideas, one arrives at the Bose-Einstein statistics. These statistics must be further modified for particles, such as electrons, to which the Pauli exclusion principle applies, and the Fermi-Dirac statistics follow. 

Solvay s desire to submit his work on the fundamental principles what he called gravito-materialitique to the attention of Europe s leading physicists prompted Nernst to envision an international conference on the current problems of kinetic theory of matter and the quantum theory of radiation. The idea struck an immediate responsive chord in Solvay s mind, and he charged Nernst to explore it further with Planck, Lorentz, Einstein, and the other prominent physicists. Nernst was quick to pursue the idea immediately on his return from Brussels to Berlin. 

Planck s explanation of the blackbody radiation curves (1900 [4]) and Einstein s explanation of the facts of the photoelectric effect (1905 [7]) indicated that the flow of energy in physical processes did not take place continuously, as had been believed, but rather jerkily, in discrete jumps, quantum by quantum. The contributions of Planck and Einstein were the signal developments marking the birth of quantum theory and the transition from classical to modem physics. 

By employing the quantum theories of Planck and Einstein, Compton was able to describe light as both a particle and a wave, depending upon the way it was tested. While this may seem paradoxical, it remains an acceptable model for explaining the phenomena associated with light and is the dominant theory of our time. 

Schrodinger, Heisenberg and Dirac. The remainder of this chapter will describe the early contributions to the quantum theory by Planck, Einstein and Bohr. 

Further work on similar types of cells has been carried out, in which not only is use made of the Nernst Theorem but likewise of the Einstein theory of atomic heat of solids (as modified by Nernst and Lmdemann) This will be taken up after we have discussed Planck s Quantum Theory of radiation and Einstein s application of it to the heat capacity of solids (Vol. Ill)... 

In 1905, only five years after Planck presented his quantum theory, Albert Einstein used the theory to solve another mystery in physics, the photoelectric effect, a phenomenon in which electrons are ejected from the surface of certain metals exposed to light of at least a certain minimum frequency, called the threshold frequency (Fignre 7.5). The number of electrons ejected was proportional to the intensity (or brightness) of the light, but the energies of the ejected electrons were not. Below the threshold frequency no electrons were ejected no matter how intense the light. 

The photoelectric effect conld not be explained by the wave theory of light. Einstein, however, made an extraordinary assumption. He snggested that a beam of light is really a stream of particles. These particles of light are now called photons. Using Planck s quantum theory of radiation as a starting point, Einstein deduced that... 

Identify the following individuals and their contributions to the development of quantum theory Bohr, de Broglie, Einstein, Planck, Heisenberg, Schrbdinger. 

Einstein f succeeded in giving a qualitative explanation of this behaviour by applying Planck s quantum theory to the oscillations of atoms about their equilibrium position. If this hypothesis be applied to each individual atom, and it be assumed that if v is the oscillation frequency of the atom, the latter can only take up the quantum c = hv, or a whole multiple of it, we obtain... 

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. 

By consideration of Planck s formula W0=Av, Einstein was led to interpret phenomena of another type in terms of the quantum theory, thus giving rise to a new conception of this equation which has proved very fruitful. The phenomenon in question is the photoelectric effect. If light of frequency v falls on a metallic surface,4 electrons are set free and it is found that the intensity of the light influences... 

Another application of this idea occurs in a new derivation of Planck s radiation formula this is duo to Einstein, and has given effective support to the ideas of the quantum theory and in particular to Bohr s frequency condition. 

It is commonly accepted that the old quantum theory era spans from the birth of Planck s quantum hypothesis to the formulation of Schrodinger s equation. This section describes the old quantum theory in three parts the failure of classical mechanics, the birth of the quantum theory, and the completion of wave mechanics.5 8) This century obviously began with the birth of quantum theory. Many researchers appeared on the scene of quantum theory at the time, but we remember mostly the contributions of four researchers Max Planck (1901), Albert Einstein (1905), Niels Bohr (1913), and de Broglie (1923). Then Schrodinger proposed the new wave equation to conclude the age of the old quantum theory. Heisenberg established matrix mechanics and formulated the uncertainty principle. 

We have compared the birth of quantum theory to a drama written and acted by Planck, Einstein, Bohr, and de Broglie. Indeed they inherited a critical mind with a deep insight into the quantum theory and they pursued continuously the development of this concept. From their research in that fertile period of time, we can study the inner workings of their considerations as human beings. Taking advantage of the failure of classical mechanics, they created a new concept. In the formation process of the quantum theory, they never denied the system of classical physics. The new physical system which they constructed included classical physics and grew to such a scale that it exerted a tremendous influence upon all science fields for nearly a century. 

Despite its successes, Bohr s theory did not resolve the fundamental issues that lie at the heart of the quantum theory of Planck and Einstein What is behind the quantization of oscillators and atoms What happens when a system changes its state, resulting in the creation of a photon How can the generated photon behave like a particle under certain conditions and like a wave under other conditions ... 

To explain the photoelectric effect, Einstein assumed that the radiant energy striking the metal surface behaves like a stream of tiny energy packets. Each packet, which is like a particle of energy, is called a photon. Extending Planck s quantum theory. 

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