Planck quantization

Max Planck Quantized energy Energy is released from atoms in discrete packets, or quanta... 

Understand how particles and waves differ and how the work of Planck (quantization of energy) and Einstein (photon theory) changed thinking about it ( 7.1) (EPs 73-7.5)... 

Electromagnetic radiation in thermal equilibrium within a cavity is often approximately referred to as the black-body radiation. A classical black hole is an ideal black body. Our own star, the Sun, is pretty black A perfect black body absorbs all radiation that falls onto it. By Kirchhoff s law, which states that a body must emit at the same rate as it absorbs radiation if equilibrium is to be maintained , the emissivity of a black body is highest. As shown below, the use of classical statistical mechanics leads to an infinite emissivity from a black body. Planck quantized the standing wave modes of the electromagnetic radiation within a black-body cavity and solved this anomaly. He considered the distribution of energy U among A oscillators of frequency... 

Modern physics dates from Planck s proposal that en ergy IS quantized which set the stage for the develop ment of quantum mechanics Planck received the 1918 No bel Prize in physics... 

In the course of his research on electromagnetic waves Hertz discovered the photoelectric effect. He showed that for the metals he used as targets, incident radiation in the ultraviolet was required to release negative charges from the metal. Research by Philipp Lenard, Wilhelm Hallwachs, J. J. Thomson, and other physicists finally led Albert Einstein to his famous 1905 equation for the photoelectric effect, which includes the idea that electromagnetic energy is quantized in units of hv, where h is Planck s con-... 

Studies of black-body radiation led to Planck s hypothesis of the quantization of electromagnetic radiation. The photoelectric effect provides evidence of the particulate nature of electromagnetic radiation. 

Bohr knew of the work of Planck and Einstein. What if the energies of electrons in an atom were not continuous What if they could only take on certain values What if atoms were quantized, just as blackbody oscillators and light that struck a metal plate were. The challenge was how to apply quantum ideas to the atom. 

The constant h and the hypothesis that energy is quantized in integral multiples of hv had previously been introduced by M. Planck (1900) in his study of blackbody radiation. In terms of the angular frequency a> deflned in equation (1.2), the energy E of a photon is... 

But it was Max Planck who shattered the paradigm of the steadiness of nature. He showed that atoms could not absorb energy in all forms and quantities, but only in so-called quanta, that is, in defined amounts. Thus, electrons jump, as we explain it today, from one energy level to another. Natura saltat Albert Einstein s theory was even more groundbreaking space and time form a continuum, matter and energy, in contrast, are quantized, essentially "grainy", so to speak. In this case, nature cannot but jump. 

Here g, go, Tu, e, and h are respectively the conductance, the quantum of conductance equal to 77.48 microsiemens, the transmission through channel i, the electronic charge, and Planck s constant. The idea that conductance can be quantized is a remarkably new one compared with ohmic behavior - Fig. 6 shows experiments that directly demonstrate quantization of transport in atomic gold wires. 

In order to understand these observations it is necessary to resort to quantum mechanics, based on Planck s postulate that energy is quantized in units of E = hv and the Bohr frequency condition that requires an exact match between level spacings and the frequency of emitted radiation, hv = Eupper — Ei0wer. The mathematical models are comparatively simple and in all cases appropriate energy levels can be obtained from one-dimensional wave equations. 

The settling of certain particular amplitude depends on the initial conditions. When the motion becomes stationary the amplitude s value practically does not depend on the wave s intensity when the latter changes over a significant range above a certain threshold value. This is reminiscent of Einstein s explanation of the photoelectric effect using Planck s quantization hypothesis. In this case the absorption is also independent of the incoming wave s intensity. Besides, the absorbed... 

The colour of a chromophore depends on the way its valence-shell electrons interact with light, i.e. its colour depends on the way it absorbs photons. Photons are absorbed during the promotion of an electron between wave-mechanically allowed (i.e. quantized) energy levels. The magnitude of the energy required to achieve this, E, is given by the Planck equation, as follows ... 

Einstein (1907) applied equation 3.32 (originally conceived by Planck for the quantization of electromagnetic energy) to the quantization of particle energy, describing the internal energy of a solid composed of Nq atoms as... 

The energy of the radiation absorbed or emitted is quantized according to Planck s equation (Eqn. 1.1). These quanta are known as photons, the energy of which is proportional to the frequency of the radiation. 

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