Planck’s quantum

Contrary to the impression that one might have from a traditional course in introductory calculus, well-behaved functions that cannot be integrated in closed form are not rare mathematical curiosities. Examples are the Gaussian or standard error function and the related function that gives the distribution of molecular or atomic speeds in spherical polar coordinates. The famous blackbody radiation cuiwe, which inspired Planck s quantum hypothesis, is not integrable in closed form over an arbitiar y inteiwal. 

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. 

Bohr s planetary atomic model proved to be a tremendous success. By utilizing Planck s quantum hypothesis, Bohr s model solved the mystery of atomic spectra. Despite its successes, though, Bohr s model was limited because it did not explain why energy levels in an atom are quantized. Bohr himself was quick to point out that his model was to be interpreted only as a crude beginning, and the picture of electrons whirling about the nucleus like planets about the sun was not to be taken literally (a warning to which popularizers of science paid no heed). 

In 1913 Niels Bohr proposed his atomic theory with the help of the line spectrum of hydrogen atoms and Planck s quantum theory. His postulates can be summarized as follows ... 

All conclusions, drawn before the importance of Planck s quantum of action was appreciated, were strictly qualitative. Introduction of the quantum condition was Bohr s innovation, and it could have been more effectively combined with Nagaoka s stable orbits, rather than with electrodynamically unstable orbits. Whereas Bohr s was a one-electron theory, Nagaoka proposed a model for all atoms, with electrons spread across a set of concentric rings. Developing this into a quantum model remains an intriguing possibility. 

Niels Bohr incorporated Planck s quantum concept into Rutherford s model of the atom in 1913 to explain the discrete frequencies of radiation emitted and absorbed by atoms with one electron (H, He+, and Li2+). This electron is attracted to the positive nucleus and is closest to the nucleus at the ground state of the atom. When the electron absorbs energy, it moves into an orbit further from the nucleus and the atom is said to be in an electronically excited state. If sufficient energy is absorbed, the electron separates from the nucleus entirely, and the atom is ionized ... 

Action. This technical term is a historic relic of the 17th century, before energy and momentum were understood. In modern terminology, action has the dimensions of energyxtime. Planck s constant has those dimensions, and is therefore sometimes called Planck s quantum of action. Pairs of measurable quantities whose product has dimensions of energyxtime are called conjugate quantities in quantum mechanics, and have a special relation to each other, expressed... 

Thinking Critically Explain how Einstein utilized Planck s quantum concept in explaining the photoelectric effect. 

Explain Planck s quantum concept as it relates to energy lost or gained by matter. (5.1)... 

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)... 

The new era in physics started in 1900 with a young German physicist named Max Planck. While analyzing the data on radiation emitted by solids heated to various temperatures, Planck discovered that atoms and molecules emit energy only in certain discrete quantities, or quanta. Physicists had always assumed that energy is continuous and that any amount of energy could be released in a radiation process. Planck s quantum theory turned physics upside down. Indeed, the flurry of research that ensued altered our concept of nature forever. 

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... 

Briefly explain Planck s quantum theory and explain what a quantum is. What are the units for Planck s... 

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... 

A similar argument applies when v is slowly varied by some other external influence. Since the harmonic oscillator is mathematically equivalent to a pendulum with an infinitely small amplitude of oscillation, Wjv is constant in that case also Planck s quantum 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. 

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