Physics
Plancks Quantum Theory
Planck's quantum theory revolutionized physics by proposing that energy is emitted or absorbed in discrete units called quanta. This theory laid the foundation for quantum mechanics and challenged classical physics, leading to the development of modern physics. Planck's work was instrumental in explaining phenomena such as blackbody radiation and the photoelectric effect, and it ultimately transformed our understanding of the behavior of matter and energy at the atomic and subatomic levels.
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11 Key excerpts on "Plancks Quantum Theory"
eBook - PDF- Richard L. Myers(Author)
- 2005(Publication Date)
- Greenwood(Publisher)
Planck's formula assumed that the energy radiated was in integral multiples of hf, where h was a constant and/was the frequency of radiation in hertz. The constant h is referred to as Planck's constant, and its accepted modern value is 6.6260755 X 10~ 34 J-s. According to Planck's equation, the smallest quantum of energy radiated at a given frequency is equal to hf. The next highest quantum is 2hf and then 3hf and so forth. The idea of quantized energy was a radi- cal departure from classical physical thought and marked the beginning of modern physics. While today modern science accepts a quan- tum viewpoint, it was not readily accepted when Planck introduced the idea in 1900. Energy and matter can be considered contin- uous in the macroscopic everyday world, but they take on a quantum nature on the atomic level. For instance, the quantity of matter can be considered continuous and measured very precisely in fractions of grams. Although when a piece of iron is considered, it really consists of a tremendous number of individ- ual iron quanta called iron atoms. Likewise, energy comes in discrete quantum units. The Photoelectric Effect Planck introduced the idea of quan- tized energy in 1900 to explain blackbody radiation. The next significant evidence that supported quantum theory came from inter- preting the photoelectric effect using the new model. The photoelectric effect refers the emission of electrons from the surface of certain metals when illuminated with light. Some important observations associated with the photoelectric effect were that elec- trons were emitted immediately when the metal was illuminated by light, the bright- ness did not affect the kinetic energy of ejected electrons but the frequency did, and electrons couldn't be emitted with certain wavelengths no matter what the intensity. Albert Einstein used quantum theory in 1905 to explain these observations. Planck assumed that blackbody radiation was emitted in discrete quanta.
eBook - PDFLet 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.
eBook - PDF- Ian Duck, E C George Sudarshan(Authors)
- 2000(Publication Date)
- World Scientific(Publisher)
And never a mention of the word 'quantum'. In the midst of this uncertainty, confusion, competition, and conflict, Planck had the purest insight to introduce the quantum of energy, but not the insight to develop the idea any further. We now explore in depth Planck's great achievement recorded in his three classic papers in Annalen der Physik of 1900 and 1901. §1-2. Blackbody Radiation. The Planck Spectrum of Blackbody Radiation is the primary cornerstone of modern physics and its importance cannot be overstated. Its manifestations range from the phonons of solid state physics, to the photons of the cosmic background radiation, from the Bose-Einstein condensation of supercooled atoms to the elusive phase transition in the quark-gluon plasma, with many fascinating and important variants in between. It was the motivating force in the development of quantum Chapter I. Planck Invents the Quantum 9 statistics which has become the subject matter of every undergraduate text on modern physics. By the introduction of the quantum of energy hf it was directly responsible for Einstein's elucidation of the photon, for the Bohr atom, for de Broglie's postulate of the wave nature of matter, and for the eventual development of quantum mechanics in all its glory. Our purpose here is to take our streamlined and sophisticated understanding of Planck's result and go back from this modern vantage point to understand as best we can, in as deep and intimate a way as possible, the steps that led Planck to the quantum. It is clearly incorrect - but nonetheless tempting - to undervalue Planck's accomplishment as somehow a lucky trick that worked, something that fell to him by chance as one of many fiddling about to parametrize the data. And even with the hindsight of 43 years, reflecting on his discovery at age 85 in wartime Berlin [6], Planck could barely explain his insight more deeply than at the first instant.
eBook - PDF- John Mcgervey(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
He invented the radical idea of quantization, which is now a fundamental part of all atomic theory. 2. He used this idea to explain in detail the shape of the black-body radiation spectrum. 3. He invented the fundamental constant h (now known as Planck's con-stant, of course), and he determined its value. 4. He determined the value of e, another fundamental constant which many physicists were then attempting to measure, and his determination of it was by far the most accurate which had been made up to that time. Planck's work did not create nearly the sensation that one might expect from this impressive list of achievements. Fortunately, however, his work was not unnoticed by Albert Einstein, as we shall now see. 3.2 THE PHOTOELECTRIC EFFECT Planck had assumed that the energy of oscillators in the walls of a cavity is quantized, but he said nothing about the energy in the electromagnetic field in the cavity. However, if the oscillators can possess energy only in multiples of hv, they can only radiate energy in multiples of hv also, and therefore, at least in this case, the field energy must also be quantized. In 1905 (when most people either had not heard of Planck's theory, or, having heard of it, did not believe it), Einstein made a logical generalization. He wrote 5 : 5 A. Einstein, Ann. Phys. (Leipzig) 17, 132-148 (1905). Translated by J. McGervey. 74 THE OLD QUANTUM THEORY According to the assumption considered here, the spreading of a light beam emanating from a point source does not cause the energy to be distributed continuously over larger and larger volumes, but rather the energy consists of a finite number of energy quanta, localized at space points, which move without breaking up and which can be absorbed or emitted only as wholes. The energy of each quantum was of course assumed to be hv, equal to the quanta of energy possessed by Planck's oscillators.
eBook - PDFTheoretical 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.
eBook - PDFQuantum Concepts in Physics
An Alternative Approach to the Understanding of Quantum Mechanics
- Malcolm Longair(Author)
- 2013(Publication Date)
- Cambridge University Press(Publisher)
It is evident that the natural units of time and length are very small indeed, while the mass is much greater than that of any known elementary particle. A century later, these quantities were to play a central role in the physics of the very early Universe. 2.8 Planck and the physical significance of h It was a number of years before the truly revolutionary nature of what Planck had achieved in these crucial last months of 1900 was appreciated. Perhaps surprisingly, he wrote no papers on the subject of quantisation over the next five years. The next publication which casts some light on his understanding was his text Lectures on the Theory of Thermal Radiation of 1906 (Planck, 1906). Thomas Kuhn gives a detailed analysis of Planck’s thoughts on quantisation through the period 1900–1906 (Kuhn, 1978). What is clear from Kuhn’s analysis is that Planck undoubtedly believed that the classical laws of electromagnetism were applicable to the processes of the emission and absorption of radiation, despite the introduction of the finite energy elements in his theory of quantisation. Planck describes two versions of Boltzmann’s procedure in statistical physics, the first being the version described in Sect. 2.6, in which the energies of the oscillators take values 0, ε, 2ε, 3ε, and so on. There is a second version in which the molecules were considered to lie within the energy ranges 0 to ε, ε to 2ε, 2ε to 3ε, and so on. This procedure leads to exactly the same statistical probabilities as the first version. In a subsequent passage, in which the motions of the oscillators are traced in phase space, he again refers to the energies of the trajectories corresponding to certain energy ranges U to U + U , the U eventually being identified with h ν . Thus, Planck regarded quantisation as referring to the average properties of the oscillators. Planck had little to say about the nature of the quantum of action h , but he was well aware of its fundamental importance.
eBook - PDF- Ian D. Lawrie(Author)
- 2012(Publication Date)
- CRC Press(Publisher)
The remaining sections develop the mathematical theory in somewhat more general terms, and this provides a point of departure for the quantum field theories to be studied in later chap- ters. 5.0 Wave Mechanics The observations which led to the quantum theory are often summarized by the notion of particle–wave duality. Phenomena that might normally be re- garded as wave motions turn out to have particle-like aspects, while particles behave in some respects like waves. The phenomena in question are basically of three kinds. First, there is evidence that electromagnetic radiation, which for many purposes is described in terms of waves, behaves for other purposes like a stream of particles, called photons. (It is interesting to recall that Newton believed in a ‘corpuscular’ theory of light, propounded in his Opticks, but for reasons that have turned out to be quite erroneous.) In the photoelectric effect, for example, light incident on the surface of a metal causes electrons to be ejected. Contrary to what might have been expected, the energy of one of these electrons is found to be quite independent of the intensity of the radiation, although the number ejected per unit time does increase with the intensity. On the other hand, the energy of an electron increases with the frequency of the radiation. As Einstein was the first to realize, this can be understood if the radiation is considered to consist of photons, each carrying a definite amount of energy E = hν, (5.1) where ν is the frequency and h = 6.6256 × 10 −34 J s is Planck’s constant. The energy of a single photon is transferred to a single electron, and the observed kinetic energy of the electron is this quantum of energy less a certain amount, the work function, required to release the electron from the metallic surface. Planck himself had been concerned with understanding the spectrum of black- body radiation, namely the way in which the energy radiated by a black object is distributed over frequencies.
eBook - PDF- 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.
eBook - ePubFrom X-rays to Quarks
Modern Physicists and Their Discoveries
- Emilio Segrè(Author)
- 2012(Publication Date)
- Dover Publications(Publisher)
Planck adds a poignant note: “It gave me particular satisfaction, in compensation for the many disappointments I had encountered, to learn from Ludwig Boltzmann of his interest and complete agreement in my new line of reasoning.” However, although Boltzmann agreed, Planck’s reasoning was subject to numerous serious objections. Such fundamental and revolutionary ideas were not easily assimilated. In spite of the various flaws mentioned above, the work was not ignored, but it was not at the center of attention. There were many spectacular discoveries at this time, and Planck himself was so diffident of the methods used that he spent years trying to explain his results in a less revolutionary way.Figure 4.5 Other excerpts from the same paper by Planck. Above, equation (12) contains the formula for the distribution of energy in the blackbody radiation as a function of frequency v and temperature θ . The constant h appears in it as well as the velocity of light c and Boltzmann’s constant k. Below, the numerical values of h and k in 1900 [formulae (15) and (16)]. Using these numbers, one can obtain the numerical values of the charge of the electron, of Avogadro’s number, and of other universal constants in physics. These values stood unsurpassed for many years.In 1931 the American physicist R. W. Wood asked Planck how he had invented something as incredible as the quantum theory. Planck answered, “It was an act of desperation. For six years I had struggled with the blackbody theory. I knew the problem was fundamental and I knew the answer. I had to find a theoretical explanation at any cost, except for the inviolability of the two laws of thermodynamics” [Armin Hermann, The Genesis of Quantum Theory (MIT Press, 1971), p. 23]. At the end of his life he commented further:However, even at the beginning Planck was aware of the importance of his discovery. It is reported that, on a walk, Planck told his son that he had found something worthy of Newton.My vain attempts to somehow reconcile the elementary quantum with classical theory continued for many years, and cost me great effort,. Many of my colleagues saw almost a tragedy in this, but I saw it differently because the profound clarification of my thoughts I derived from this work had great value for me. Now I know for certain that the quantum of action has a much more fundamental significance than I originally suspected.As time passed, Planck became one of the most highly regarded German physicists. He was secretary of the Prussian Academy of Sciences and one of the most influential representatives of German science. Einstein, who did not sympathize with the German establishment, nevertheless had a deep respect for his colleague, even if they differed in political and scientific outlook. Their friendship was further reinforced by their common love for music, which they played together. Besides his scientific eminence, Planck’s character inspired universal respect. A firm conservative, he found himself compelled by the strength of factual evidence and logical rigor to promote one of the greatest revolutions in natural philosophy.
- G.G. Emch(Author)
- 2000(Publication Date)
- North Holland(Publisher)
2UY CHAPTER 7. THE “OLD” QUANTUM THEORY SYNOPSIS While the theory of relativity presented a severe criticism of the classical Newtonian notions on the separate essences of space and time, t h e new theory still won a rather rapid and widespread acceptance, perhaps for the reason t h a t it provided a unification of previously disparate concepts. Not so with quantum theory, where a quarter of a century had to pass before some unify- ing picture would emerge. In view of the contradictions the “old” quantum theory generated in the course of its development, a chapter of mostly histori- cal (if somewhat “whiggish”) character seems to be called for, retracing the experimental motivations for the radical departure from classical paradigms. To pin down the birthdate of a scientific theory is almost always a rather contrived exercise; in the case of quantum theory, however, the date (Dec. 14, 1900) of Planck’s famous communication on the “black body radiation”, made before the German Physical Society, certainly signaled the outbreak of a new era. Still, we know from Planck’s own pen that he “had been wrestling for six years with the problem of equilibrium between radiation and matter”, and that he was, as yet, not satisfied with the result. His contribution was two-fold. Firstly, he produced a formula 81r c3 uy = -hv’[exp(hv/kT) - I]-’ which fitted experimental data and which was significantly different from the predictions of classical theories. Secondly, he proposed a derivation of his formula, for which he resorted, “as an act of desperation”, to the ideas of Boltzmann on “the relationship between entropy and probability” comple- mented by an ad hoe postulate, now understood to be t h a t light is absorbed and emitted by matter in discrete energy quanta.
- Marc J. Madou(Author)
- 2011(Publication Date)
- CRC Press(Publisher)
The photoelectric phenomenon could not be understoodwithouttheconceptofalightparticle, i.e.,aquantumamountoflightenergyforaparticu-larfrequency.Einstein’spaperexplainingthepho-toelectriceffectwasoneoftheearliestapplications ofquantumtheoryandamajorstepinitsestablish-ment.Theremarkablefactthattheejectionenergy wasindependentofthetotalenergyofillumination showedthattheinteractionmustbelikethatofa particlethatgaveallofitsenergytotheelectron! ThisfitinwellwithPlanck’shypothesisthatlightin theblackbodyradiationexperimentcouldexistonly indiscretebundleswithenergy.Inquantumtheory, thefrequency, ν ,ofthelightdeterminestheenergy, E , of the photons and E = h ν , where h is Planck’s constant(h = 6.626069 × 10 − 34 J·s)( Figure 3.26 ). This assumption explains quantitatively all the observations associated with the photoelectric effects.Aphotonhitsanelectronandisabsorbed. Theenergyoftheemittedelectronisgivenbythe energy of the photon minus the energy needed to releasetheelectronfromthesurface.Thisexplains theobservanceofathresholdvaluebelowwhichno electronsareemitted.Thus,itdependsonthefre-quencyoflightfallingonthesurfacebutnotonits intensity.Italsoexplainswhythereisnotimelag;a photonhitsanelectron,isabsorbedbytheelectron, andtheelectronleaves.Higherintensitylightcon-tainsmorephotons,andsoitwillknockoutmore electrons.However,ifthefrequencyofthelightis suchthatasinglephotonisnotenergeticenoughto releaseanelectronfromthesurface,thennonewill beejectednomatterhowintensethelight.Gilbert N.Lewisin1926calledEinstein’slightparticlespho-tons.Justastheword photon highlightstheparticle aspectofanelectron,theword graviton emphasizes Retarding potential Cs Li Ag Slope = h Light frequency eV 0 ν ν 0 Intercept = – φ FIGURE3.25 A plot of retarding or stopping voltage versus frequency of incident light. Slope is the Planck con-stant h . The intercept with the frequency axis (at kinetic energy zero) is the threshold frequency, ν 0 , and the stop voltage axis intercept is the binding energy.
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