Planck Postulate

10 Key excerpts on "Planck Postulate"

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  Let There Be Light: The Story Of Light From Atoms To Galaxies (2nd Edition)

  The Story of Light from Atoms to Galaxies

  • Alex Montwill, Ann Breslin(Authors)
  • 2013(Publication Date)
  • ICP

    (Publisher)

  Still, there was a heavy price to pay: Planck had to make the assumption that an electric oscillator can have only certain energies, which are an integral number of quantum units hf . Up to then, an inherent understanding in natural philoso-phy was that there are no restrictions on the possible values of physical entities. The suggestion that nature is not continuous was so revolutionary that Planck was afraid to publish his hypothesis, which was not generally accepted until 1913, when Niels Bohr used quantum theory in his radical model of atomic structure. Physicists were reluctant to abandon long-established beliefs, with some notable exceptions, such as Albert Einstein, who in 1905 had developed the concept of quantization even further in his theory of the photoelectric effect.* To follow this chapter in detail, some knowledge of basic mechanics and thermodynamics is helpful but, even without it, you should enjoy following Planck’s footsteps to one of the most fundamental discoveries in the history of physics. 11.1 Emission of energy by radiation How does matter emit electromagnetic energy? Matter consists of atoms and molecules containing positively charged protons and negatively charged electrons. There is always electrical activity, even in an electrically neutral piece of matter, because of atomic oscillators whose motion becomes more rapid with increasing temperature. As predicted by Maxwell, and verified by Hertz in 1888, oscillating charges emit electromagnetic waves and in the process lose energy and slow down. The hot surface cools down by radiating light into the space around it. Eventually, thermal equilibrium is established when the average energy emitted per second is balanced by the radiation absorbed. * Some years later, when the consequences of the quantum theory became apparent, Einstein also began to have misgivings.

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  100 Years Of Planck's Quantum

  • Ian Duck, E C George Sudarshan(Authors)
  • 2000(Publication Date)
  • World Scientific

    (Publisher)

  With this supporting evidence he does declare that the theory must be correct in general, and with absolute validity. In a longer paper almost a year later [4], Planck showed - following his first paper Chapter I. Planck Invents the Quantum 15 of the same title - that the new energy distribution was stationary, but made no further interpretation or even any specific mention of the quantum. And again in 1902 [5] in a long discussion of the nature of white light, although he emphasized the outstanding problem of the interpretation of the nature of spectral lines, he made no mention of the energy-quantum. In 1943: • • • there arose the all-important problem, to assign this remarkable constant a physical meaning. • • • But the nature of the energy-quantum remained unclear. And finally: For many years I continued to do further research, trying somehow to fit the action quantum into the system of classical physics. But it seems to me that this is not possible. §1-4. Planck's Discovery as Prolog. In the remainder of this book we collect and discuss principal landmark con-tributions to the discoveries of quantum theory which sprang directly - if at first slowly and reluctantly - from Planck's invention of the energy quantum. We have chosen to follow a fundamental but rather narrow path leading from Planck to Einstein, Bohr, and de Broglie; then to the formulations of quantum mechanics due to Heisenberg, Born and Jordan, and to Schrodinger, and to Dirac. Then we enter into the interpretation of quantum mechanics, again following original contributions, here of Born, Heisenberg, and Bohr. Then we vault forward to contemporary contributions from Bell and Aspect and others, originating in the Einstein-Podolsky-Rosen paradox. We complete our account of the first one hundred years of Planck's h-quantum with an introduction to recent advances in the theory of measurement and de-coherence.

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  Physical Constants

  • (Author)
  • 2014(Publication Date)
  • Orange Apple

    (Publisher)

  Einstein's explanation for these observations was that light itself is quantized; that the energy of light is not transferred continuously as in a classical wave, but only in small packets or quanta. The size of these packets of energy, which would later be named ________________________ WORLD TECHNOLOGIES ________________________ photons, was to be the same as Planck's energy element, giving the modern version of Planck's relation: Einstein's postulate was later proven experimentally: the constant of proportionality between the frequency of incident light ( ν ) and the kinetic energy of photoelectrons ( E ) was shown to be equal to the Planck constant ( h ). Atomic structure A schematization of the Bohr model of the hydrogen atom. The transition shown from the n =3 level to the n =2 level gives rise to visible light of wavelength 656 nm (red), as the model predicts. Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model. In classical electro-dynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies E n where R ∞ is an experimentally-determined constant (the Rydberg constant) and n is any integer ( n = 1, 2, 3, …). Once the electron reached the lowest energy level ( n = 1), it could not get any closer to the nucleus (lower energy). This approach also allowed Bohr to account for the Rydberg formula, an empirical description of the atomic spectrum of hydrogen, and to account for the value of the Rydberg constant R ∞ in terms of other fundamental constants.

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  General Physics Electromagnetism Optics

  • Pierluigi Zotto, Sergio Lo Russo, Paolo Sartori(Authors)
  • 2022(Publication Date)
  • Società Editrice Esculapio

    (Publisher)

  Moreover, no classical explanation can justify the discrete nature of emission and absorption spectra of solids, which are expected to be continuous as it occurs for gases and liquids. Also in this case it must be assumed that only discrete frequencies are possible. Furthermore, X-ray production can be classically explained as radiation emitted by a charge being decelerated in a material (the so called bremsstrahlung phenomenon) but it shows a production thresh- old which cannot exist in classical theory. So different situations are all solved by introducing energy quantisation, whose amount is determined by a constant, h, called Planck constant, which is indeed the same in all cases. This agreement cannot be casual and therefore it makes sense to presume that a radical change in the perspective under which physical phenomena are described is needed. The hypothesis assumed by Einstein in order to solve the photoelectric effect puzzle is rather strong: in fact, Planck presumed that the quantisation occurs during an energy ex- change between the inner standing wave and the material walls, so it is still possible to as- sume that something misses in the description of the radiation-matter interaction, but, on the contrary, Einstein’s assumption implies that the wave, i.e. the electromagnetic field which constitute it, is, in its turn, quantised. Besides, Planck solution of blackbody radiation requires that the available energies are discrete energy levels nhν, while, on the contrary, photons carry exactly energy hν. The incompatibility between the two assumptions is solved by one step further, i.e. by giving up also Boltzmann statistics. A photon gas must be considered instead of a standing wave and Bose-Einstein statistics must be introduced to replace the classical one. The nature of light becomes, according to Einstein hypothesis, corpuscular; interference and diffraction phenomena highlight, on the contrary, its undulatory nature.

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  Theoretical Concepts in Physics

  An Alternative View of Theoretical Reasoning in Physics

  • Malcolm S. Longair(Author)
  • 2020(Publication Date)
  • Cambridge University Press

    (Publisher)

  I now knew for a fact that the elementary quantum of action played a far more significant part in physics than I had originally been inclined to suspect and this recognition made me see clearly the need for the introduction of totally new methods of analysis and reasoning in the treatment of atomic problems. 12 Indeed, it was not until after about 1908 that Planck fully appreciated the quite fundamental nature of quantisation, which has no counterpart in classical physics. His original view was that the introduction of energy elements was 383 15.5 Planck and the Physical Significance of h a purely formal assumption and I really did not give it much thought except that no matter what the cost, I must bring about a positive result. 13 This quotation is from a letter by Planck to R.W. Wood written in 1931, 30 years after the events described in this chapter. I find it a rather moving letter and it is worthwhile reproducing it in full. October 7 1931 My dear colleague, You recently expressed the wish, after our fine dinner in Trinity Hall, that I should describe from a psychological viewpoint the considerations which had led me to propose the hypothesis of energy quanta. I shall attempt herewith to respond to your wish. Briefly summarised, what I did can be described as simply an act of desperation. By nature I am peacefully inclined and reject all doubtful adventures. But by then I had been wrestling unsuccessfully for six years (since 1894) with the problem of equilibrium between radiation and matter and I knew that this problem was of fundamental impor- tance to physics; I also knew the formula that expresses the energy distribution in the normal spectrum. A theoretical interpretation therefore had to be found at any cost, no matter how high. It was clear to me that classical physics could offer no solution to this problem and would have meant that all energy would eventually transfer from matter into radiation.

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  Thirty Years that Shook Physics

  The Story of Quantum Theory

  • George Gamow(Author)
  • 2012(Publication Date)
  • Dover Publications

    (Publisher)

  Fig. 5. If, according to Planck’s hypothesis, the energy corresponding to each frequency v must be an integer of the quantity hv, the situation is quite different from that shown in the previous diagram. For example, for v = 4 there are eight possible vibration states, whereas for v = 8 there are only four. This restriction reduces the number of possible vibrations at high frequencies and cancels Jeans’ paradox.

  It has been said that there are “lies, white lies, and statistics,” but in the case of Planck’s calculations the statistics turned out to be well-nigh true. He had obtained for energy distribution in thermal radiation spectrum a theoretical formula that stood in perfect agreement with the observation shown in Fig. 2 .

  While the Rayleigh-Jeans formula shoots sky high, demanding an infinite amount of total energy, Planck’s formula comes down at high frequencies and its shape stands in perfect agreement with the observed curves. Planck’s assumption that the energy content of a radiation quantum is proportional to the frequency can be written as:

  where v (the Greek letter nu) is the frequency and h is a universal constant known as Planck’s Constant, or the quantum constant. In order to make Planck’s theoretical curves agree with the observed ones, one has to ascribe to h a certain numerical value, which is found to be 6.77 × 10−27 in the centimeter-gram-second unit system.¶

  The numerical smallness of that value makes quantum theory of no importance for the large-scale phenomena which we encounter in everyday life, and it emerges only in the study of the processes occurring on the atomic scale.

  LIGHT QUANTA AND THE PHOTOELECTRIC EFFECT

  Having let the spirit of quantum out of the bottle, Max Planck was himself scared to death of it and preferred to believe the packages of energy arise not from the properties of the light waves themselves but rather from the internal properties of atoms which can emit and absorb radiation only in certain discrete quantities. Radiation is like butter, which can be bought or returned to the grocery store only in quarter-pound packages, although the butter as such can exist in any desired amount (not less, though, than one molecule!). Only five years after the original Planck proposal, the light quantum was established as a physical entity existing independently of the mechanism of its emission or absorption by atoms. This step was taken by Albert Einstein in an article published in 1905, the year of his first article on the Theory of Relativity. Einstein indicated that the existence of light quanta rushing freely through space represents a necessary condition for explaining empirical laws of the photoelectric effect; that is, the emission of electrons from the metallic surfaces irradiated by violet or ultraviolet rays.

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  Statistical and Thermal Physics

  An Introduction

  • Michael J.R. Hoch(Author)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  285 C H A P T E R 15 Photons and Phonons— The “Planck Gas” 15.1 INTRODUCTION In 1900, Max Planck introduced the concept of the quantum of elec-tromagneticradiation,latercalledthephoton,intophysics.Hedidthis to explain the spectral properties of electromagnetic radiation emitted throughasmallaperturebyaconstant-temperature“blackbody”enclos-ure. This marked the start of quantum physics, which led to the devel-opmentofquantummechanicsinthe1920s.Theenergy e ofaphotonof frequency v isgivenbyPlanck’sfamousexpression, ε = h v ,oralternatively ε = ħω ,where ω istheangularfrequency. Inside a constant-temperature enclosure, photons are continually absorbedandemittedbythewalls.Thenumberofphotonsintheenclo-sureisnotfixedbutfluctuatesaroundsomeaveragenumberforanycho-sen frequency. This fluctuation in the number of photons represents an important difference from the situation in the fermion and boson sys-temsconsideredinChapters13and14,wherethenumberofparticles N isfixed.Thechemicalpotentialforphotonsisnotdefinedbecausethere isnoconstrainton N .Itfollowsthat μ shouldbeomittedinthephoton distribution,andthisisshowninSection15.3.Photonshavespin1and are bosons. Because they travel at the speed of light, there are two and notthreeallowedspinorientations.Classically,electromagneticradiation is considered to be a transverse wave with two polarization directions. 286 ◾ Statistical and Thermal Physics: An Introduction Putting μ = 0 in the Bose–Einstein distribution given in Equation 14.1 leadstothePlanckdistributionforphotons, uni3008 uni3009 n e e r r r = -= -1 1 1 1 be b w planckover2pi , (15.1) where ε r istheenergyofphotonsinstate r .For βε r ≪ 1,theaveragenumber ofphotonsfoundinstate r becomesverylargebecausethedenominatorin Equation15.1becomesverysmall.

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  Physics : Imagination And Reality

  • P R Wallace(Author)
  • 1991(Publication Date)
  • World Scientific

    (Publisher)

  Chapter 13 F U N D A M E N T A L P R I N C I P L E S OF Q U A N T U M T H E O R Y The accumulation of spectroscopic evidence that atomic radia-tion showed frequency peaks, along with Einstein's introduction of the light quantum (which was first called a photon only in 1926), was strong evidence that atoms existed in discrete energy states. The hydrogen atom, for example, had strong peaks in the emission and absorption of light at frequencies proportional to where n x and n 2 were integers. This could be interpreted thus: hy-drogen atoms existed in energy states —R/n 2 , and when a hydrogen atom in a state n 2 made a transition to a state rii , it would emit a light quantum of energy and hence of frequency equal to this quantity divided by h, the Planck constant. But how could this be? The hydrogen atom might be likened to a sort of solar system held together by electric rather than grav-itational forces, the negatively charged electron playing the role of a planet orbiting around a positively charged proton sun. But planets in solar systems can have arbitrary energy. Furthermore, it 336 1 «r i „ / « ( ' i v? i 'n) Fundamental Principle! of Quantum Theory 337 was known from Maxwell's electromagnetic theory that accelerating charges emitted a continuous spectrum of electromagnetic radiation. Worse than that, radiation was predicted to be so strong that the electron lost energy very rapidly, and would in fact spiral in to the nucleus in a minute fraction of a second. Nothing in a world built in this way would be stable! Even if one could think of a mechanism for transitions between atomic states in which the atom suddenly lost a discrete quantity of energy, other questions remained. What determined when the atom would make such transitions, or in what direction the atom would emit its quantum of radiation? The new quantum ideas seemed to pose a myriad of new and seemingly unfathomable puzzles.

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  Electromagnetic Processes

  • Robert J. Gould(Author)
  • 2020(Publication Date)
  • Princeton University Press

    (Publisher)

  Loosely put, this constant might be designated as a quantization parameter, but this is probably not a good description. Another try at description might be to call it the fundamental indeterminacy parameter, but it is questionable whether the uncertainty relations deserve the title of principle, since they follow from the superposition principle (which really is a principle). Given that discrete particle motion is to be described in terms of an associated wave or propagation vector k and frequency co, Planck's constant is then the proportionality factor between k and the particle momentum: p = hk. (1.1) The uncertainty relations for an individual particle follow from this relation and the superposition principle. If momentum is to be regarded as a particle dynamical property and the wave propagation vector a kinematical variable, we might designate h more descriptively as a parameter of particle dynamics. However, we shall, as usual, refer to h simply as Planck's constant like everyone else. 2 CHAPTER 1 The third most fundamental physical constant may be the electronic charge (e), since it seems to be a fundamental unit common to the various charged elementary particles. That is, although there is a spectrum of masses for the particles, except for the fractionally charged quarks, the particle charges are multiples of e. From the three physical constants c, ft, and e, it is not possible to construct a fundamental length by various combinations of products. From e and h it is possible to form a characteristic velocity v 0 = e 2 /h, (1.2) and this velocity is of significance for particle processes. Combining the fundamen-tal physical constants, a dimensionless number a = e 2 /hc « 1/137 (1.3) can be formed that is of great importance, especially for electromagnetic processes.

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  Fly by Night Physics

  How Physicists Use the Backs of Envelopes

  • Anthony Zee, A. Zee(Authors)
  • 2020(Publication Date)
  • Princeton University Press

    (Publisher)

  . . which occur in the equation for radiative entropy offer the possibility of establishing a system of units for length, mass, time and temperature which are independent of specific bod-ies or materials and which necessarily maintain their meaning for all time and for all civilizations, even those which are extraterrestrial and non-human. [Max Planck] Surely you guessed! Max Planck 4 is properly revered for his introduction of the fundamental constant into physics. With this far-reaching and magnanimous gesture, he gave us a natural system of units, sometimes known as God-given units. In a tremendously insightful paper, Planck pointed out that with the three fundamental constants 5 G , c , and , in order of their entrance into the grand drama of physics, we finally have a universal set of units for mass M , length L , and time T , the three basic concepts we need to do physics with. Planck gave us God-given units 133 Three big names, three basic principles, three natural units To see how these units are defined, note that Heisenberg’s uncertainty principle tells us that over the momentum Mc is a length. Equating the two lengths GM / c 2 and / Mc , we see that the combination c / G has dimension of mass squared. In other words, the three fundamental constants G , c , and allow us to define a mass, 6 known rightfully as the Planck mass: M P = c G (1) We can then immediately define, with Heisenberg’s help, a Planck length: l P = M P c = G c 3 (2) and, with Einstein’s help, a Planck time: t P = l P c = G c 5 (3) Newton, Einstein, Heisenberg, three big ∗ names, three basic principles, three natural units to measure space, time, and energy. We have reduced the MLT system to “nothing”! We no longer have to invent or find some unit, such as the transition frequency of some agreed-on atom, 7 to measure the universe with. We measure mass in units of M P , length in units of l P , and time in units of t P .

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