wien's distribution law derivation pdf

As an energy distribution, it is one of a family of thermal equilibrium distributions which include The constant = 5.670 10-8 W m2 K4 = 5.670 10-5 erg cm2 s K4 = Stefan-Boltzmann constant. The book has a large number of solved examples and problems in each chapter, as well as a carefully selected guide to further reading. Weins distribution law , Rayleigh-Jeans law and Plancks Radiation Law According to Wiens distribution law the energy emitted by the blackbody per unit volume in the range of wavelength from to + d is given by where C 1 and C 2 are constants and T is absolute temperature. Fundamental constants were later introduced by Max Planck. 21 Full PDFs related to this paper. The decision to undertake this volume was made in 1971 at Lake Como during the Varenna summer school ofthe Italian Physical Society, where Professor Leon Rosenfeld was lecturing on the history of quantum theory. This relationship is important in astrophysics for determining the temperature of stars. The text has been developed to meet the scope and sequence of most university physics courses and provides a foundation for a career in mathematics, science, or engineering. The total radiation emitted by a b lackbody can be subdivided. Advanced Physics questions and answers. Maxwell-Boltzmann Distribution Scottish physicist James Clerk Maxwell developed his kinetic theory of gases in 1859. It is of interest to look at the limits of the Planck distribution. portant thing about Wien's distribution in the late 1890's was not Wien' s derivation, but rather the fact that it gave an adequate account of all the experi-mental results on the energy distribution in black-body radiation which were then available. This is called Wiens displacement law. The shift of that peak is a direct consequence of the Planck radiation law, which describes the spectral brightness of black-body radiation as a function of wavelength at any given temperature. Wiens Displacement Law m = b/T m = m b = 2898 m K m(Sun) = 2898/6000 = 0.48 m m(Earth) = 2898/300 = 9.66 m 24. [7.14(b)] Prior to Plancks derivation of the distribution law for black-body radiation, Wien found empirically a closely related distribution function that is very nearly but not exactly in agreement with the experimental results, namely = (a/5)eb/kT. Find how many minimum distinct slips one has to make up for all the five digit numbers. Proceed as follows:From equation (1) evaluate the derivative dI/d and set it equal to zero. Wiens displacement law states that the wavelength at which the radiated power is a maximum for a blackbody varies inversely with the temperature. Derivation of Rayleigh jeans law from planks law. The LibreTexts libraries arePowered by MindTouchand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Answer (1 of 2): All three equations describe the temperature versus frequency of a heated gas in a black box. Density, Derivation of Planck's law, Deduction of Wiens distribution law, Rayleigh- Jeans Law, Stefan Boltzmann Law and Wiens displacement law from Plancks law. Fermi-Dirac statistics Applications to liquid helium, free electrons gas (Fermi level and Fermi Energy), Comparison of M-B, B-E, F-D statistics. 11, No. Wiens law: T f u f T Af e b ( ,) = 3 A, constants, to be determined by experiments no theoretical justification Confirmed in near to mid infrared (1- 4 m) by Paschen, at medium ? May 31, 2015. Much of this prerequisite material is provided by brief reviews, making the book a self-contained reference for workers in the field as well as the ideal text for senior or first-year graduate students of astronomy, astrophysics, and Here I calculated the general n dimensional mathematical form of Planck energy density radiation, Stefan's constant. 5. What is a blackbody? Full PDF Package Download Full PDF Package. 0000001356 00000 n The energy distribution law is according to this theory determined as soon as the entropy S of a linear resonator which interacts with the radiation 1000-Solved-Problems-in-Classical-Physics-An-Exercise-Book.pdf. This relationship is important in astrophysics for determining the temperature of stars. Quote A: In 1899, a German physicist Max Planck rederived Wiens formula (i.e., (13.4) with = 5) from phenomenological thermodynamical considerations. To derive Wiens displacement law, we use differential calculus to find the maximum of the radiation intensity curve \(I(\lambda, T)\). The brightness (or luminosity) of a star depends upon its temperature, which in turn determines the star's colour. Assuming this, we may write B = c15 exp(c2/T) = c1 5 exp(c2/T) Then, taking logarithms, logB = logc1 5log c2 T 5 T 4 Radiation Law may be written as: Wien's Displacement Law: Wien's displacement law relates the absolute temperature of the black body and the wavelength corresponding to the maximum radiance of the black body. %%EOF Classic text combines thermodynamics, statistical mechanics, and kinetic theory in one unified presentation. 0000001819 00000 n 0000001539 00000 n Planck's law describes the spectral density of electromagnetic radiation. However, it had been discovered by Wilhelm a black body at the longest wavelengths yet available, fit a new law suggested by Lord Rayleigh (1900) better than the empirical distribution law proposed by Wien (1897), for which Planck had worked out a derivation. The energy distribution law is according to this theory determined as soon as the entropy S of a linear resonator which interacts with the radiation 2, 1998 ON A NONQUANTUM DERIVATION OF PLANCK'S DISTRIBUTION LAW Carlo Cercignani Dipartimento di M atematica Politecnico di Milano 1-20199 Milano, Italy Received 25 July 1997; It has a specific spectrum of wavelengths inversely related to intensity that depend only on the bodys temperature which is assumed for the sake of calculations and theory to be. The consequence is that the shape of the blackbody radiation function would shift proportionally in frequency with temperature. This is the usual form of the Stefan-Boltzmann law. Found inside Page 23In his derivation, Einstein also invokes the requirement of thermal equilibrium with a Wien radiation field [8], which of course radiation law before and after Planck. http://www. mzwtg.mwn.de/arbeitspapiere/Schirrmacher_2001_1.pdf. A particle is an idealized It has a specific spectrum of wavelengths inversely related to intensity that depend only on the bodys temperature which is assumed for the sake of calculations and theory to be. zoning regulations for the town of griswold, connecticut effective date: july, 1973 revised to: april 01, 2019 #109 $15.00 In the first [111 of a series of five paperS which PLANCK presented to the Prussian Academy of Sciences in the years 1897 to t 899, he set forth his program for a theory of radiation. 0000004595 00000 n Black body radiation derivation pdf. (g). [7.12] Derive Wiens law, that max T is a constant, where max is the wavelength corresponding to maximum in the Planck distribution at the temperature T, and deduce an expression for the constant as a multiple of the second radiation constant, c 2 = hc/k. Again applying equation (2), the mean energy squared in this regime then can be written as h E2 i= h hE i: (4) And as before, what was expected from classical calculations { in this case, of energy uctuations in systems of non-interacting particles (e.g. A VITAL step in the proof of Wiens Law, E(T) = T5(T), for complete radiation, is the adiabatic change in volume of a cavity filled with radiation. opinion that Wiens law must be necessarily true, I may perhaps be permit-ted to explain briey the relationship between the electromagnetic theory developed by me and the experimental data. b) Calculate the first four moments about the mean of the given distribution. November 25, 2011. by Mini Physics. Wiens law or Wiens displacement law, named after Wilhelm Wien was derived in the year 1893 which states that black body radiation has different peaks of temperature at wavelengths that are inversely proportional to temperatures. Derivation of the StefanBoltzmann and Wien Radiation Laws The Planck blackbody radiation law (1901) describes the electromagnetic power emitted per unit area per unit wavelength from the surface of a black body (a surface that absorbs all radiation incident upon it) at a temperature T . 0000002711 00000 n Wien took the wavelength of black body radiation and combined it with the MaxwellBoltzmann distribution for atoms. In this topic we will discuss the Wien's law that is the displacement Wien's law which states that the black-body radiation curve for the temperature which are different and will peak at different wavelengths is also that is they are inversely proportional to the temperature. Blackbody radiation, Spectral distribution, Concept of Energy Density, Derivation of Planck's law, Deduction of Wiens distribution law, Rayleigh-Jeans Law, Stefan Boltzmann Law and Wiens displacement law from Plancks law. VA 22202-4302. Quote B: His first derivation of this formula, done in October 1900, was based solely on phenomenological Thermodynamics and required no assumptions about microscopic properties of radiation. Understanding Stellar Evolution is based on a series of graduate level courses taught at the University of Washington since 2004. DISTRIBUTION LAW675 The value of distribution coefficient is 2 4 O 4.412 85.5 0.0516 == CCl H C C (b) Calculation of solubility Applying Distribution law, Solubility of iodine in CCl4 85.5 Solubility of iodine in water = 4 Solubility of iodine in CCl 85.5 0.34 = or Solubility of Radiation : Black body radiation and distribution of energy in its spectrum Stefans law - Stefan Boltzmann law and Wiens distribution law. The objective of this note is to show that in teaching introductory (calculus-based) or intermediate physics, instead of simply stating Wiens mnemonic scheme for back-of-the-env elope calculations. It was found that Weins distribution law explains energy distribution only in the shorter wavelength region. Wiens displacement law states that the wavelength at which the radiated power is a maximum for a blackbody varies inversely with the temperature. 0000000630 00000 n Wiens displacement law Rayleigh-Jeans law Derivation of Plancks law-deduction of Rayleigh-Jeans law and Wiens law. (a) Derive Wien's displacement law from Planck's law. Solar Constant. Unless otherwise noted, LibreTexts content is licensed byCC BY-NC-SA 3.0. About The Book: A revision of a successful junior/senior level text, this introduction to elementary quantum mechanics clearly explains the properties of the most important quantum systems. Derivation of Planck's law, Deduction of Wiens distribution law, Rayleigh-Jeans Law, Stefan Boltzmann Law and Wiens displacement law from Plancks law. We need to evaluate the derivative of Equation \ref{Planck2} with respect to \(\nu\) and set it equal to zero to find the peak wavelength. This is the usual form of the Stefan-Boltzmann law. This can be inferred by using photometry to calculate a colour index. Its effective temperature is about 5777 K.. A black-body is an idealised object which absorbs and emits all radiation frequencies. Wiens approximation (also sometimes called Wiens law or the Wien distribution law) is a law of physics used to describe the spectrum of thermal radiation (frequently called the blackbody function). This law was first derived by Wilhelm Wien in 1896. Derivation of Planck's law, Deduction of Wiens distribution law, Rayleigh- Jeans Law, Stefan Boltzmann Law and Wiens displacement law from Plancks law. The ideal one-semester astrophysics introduction for science undergraduatesnow expanded and fully updated Winner of the American Astronomical Society's Chambliss Award, Astrophysics in a Nutshell has become the text of choice in This means that the majority of the radiation from the wood fire is beyond the human eyes visibility. Also find 1 and 2 . The thermal radiation is emitted over a broad spectrum of wavelengths. An example photocell is the Advanced Photonix PDV-P5002, shown in Figure 21.2.In the dark, this photocell has a resistance of approximately 500 k, and in bright light the resistance drops to approximately 10 k.The PDV-P5002 is sensitive to light in the wavelengths 400-700 nm, approximately the same wavelengths the human eye is responsive to. Wien's law was derived 4 years BEFORE Planck's radiation formula, and all of the derivations of Wien's law that I can find on the internet are based off of Planck's law. Divided into five parts, with most chapters corresponding to a two-hour lecture, the book begins with a unique account of the historical development from Kirchhoff's law for the black-body radiation to Planck's quantum hypothesis and <> The Stefan-Boltzmann law We integrate Planck's distribution law over all wavelengths: These radiations are emitted by blackbody when they remain in thermal equilibrium at a given temperature. This law was first derived by Wilhelm Wien in 1896. equation being interpreted as a probability distribution of discrete particles. This book provides a comprehensive exposition of the theory of equilibrium thermodynamics and statistical mechanics at a level suitable for well-prepared undergraduate students. 0000003016 00000 n Combining these two formulas, we obtain The results show that Planck's law accurately can be derived numerically. 0000000016 00000 n 2 0 obj Another way to obtain the temperature of a black body is by taking the area under the Planck curve, i.e. This is because stars produce the majority of their light as perfect thermal radiators (known as black-bodies). Black body radiation derivation pdf. The book provides a step by step construction of the framework of relativistic quantum field theory, starting from a minimal set of basic foundational postulates. T = b. The crucial step is the conversion of the wavelength derivative to the frequency derivative, d = d(c/) = d(c 1) = c d( 1) = (c/ 2)d. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. The Sun approximates a black body radiator. Solution: Plancks function is B = c15 exp(c2/T)1 For values of interest in atmospheric and solar science, the exponential term is much larger than unity. This book traces the evolution of the ideas that eventually resulted in the elementary quantum theory in 1925/26. "Field Guide to Infrared Optics, Materials, and Radiometry covers all aspects of IR optics, including monochromatic and chromatic optical aberrations as well as important concepts such as depth of focus, depth of field, hyperfocal distance, Within two \[\dfrac{d}{d\nu} \left \{ \rho (\nu, T) \right \} = \dfrac{d}{d\nu} \left \{ \dfrac {2 h \nu^3 }{c^3\left(e^{\frac {h\nu}{k_B T}}-1\right)} \right \} =0 \label{eq2}\]. startxref We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. We can easily deduce that a wood fire which is approximately 1500K hot, gives out peak radiation at 2000 nm. (high f) Lummer and Pringsheim up to 18 m, Rubens and Kurlbaum up to 60 m, Wiens law does not hold in the far infrared [7.14(b)] Prior to Plancks derivation of the distribution law for black-body radiation, Wien found empirically a closely related distribution function that is very nearly but not exactly in agreement with the experimental results, namely = (a/5)eb/kT. Proceed as follows: (1) ( , T) = 2 h 3 c 3 ( e h k B T 1) We need to evaluate the derivative of Equation 1 with respect to and set it equal to zero to find the peak wavelength. Wiens displacement law, 1893: the wavelength marking the maximum power emission of a blackbody, max, shifts towards 5 81 (, ) hc k TB 1 hc uT e = emission of a blackbody, , shifts towards shorter wavelengths with increasing temperature 1 max 3 ~ 2.898 10 m K T T = Stefan-Boltzmann law, 1879: The constant = 5.670 10-8 W m2 K4 = 5.670 10-5 erg cm2 s K4 = Stefan-Boltzmann constant. Derivation of StefanBoltzmann Law from Wien's Law . From the reviews: "Haus book provides numerous insights on topics of wide importance, and contains much material not available elsewhere in book form. [] an indispensable resource for those working in quantum optics or electronics. A. Wiens displacement law states that the black body radiation curve for different temperatures peaks at a wavelength inversely proportional to the temperature. Unit - IV Statistical Mechanics: Phase space, Macrostate and Microstate, Entropy and Thermodynamic probability, Maxwell-Boltzmann law - distribution of velocity. a. The shift of that peak is a direct consequence of the Planck radiation law which describes the spectral brightness of black body radiation as a function of wavelength at any given temperature. Max Karl Ernst Ludwig Planck, ForMemRS (German: [maks plak] (); English: / p l k /; 23 April 1858 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918.. Planck made many Reference Books: Thermal Physics, S. Garg, R. Bansal and C. Ghosh, 1993, Tata McGraw-Hill. 4 0 obj Legal. by integrating Plancks law over all wave-lengths. Wiens law or Wiens displacement law, named after Wilhelm Wien was derived in the year 1893 which states that black body radiation has different peaks of temperature at wavelengths that are inversely proportional to temperatures. Derivation of Rayleigh jeans law from planks law. law: I( ;T) = 2h 3 c2 1 e h kT 1 (8) The power radiated by a surface of area Athrough a solid angle d in the di erential frequency range ( ; + d ) is: I( ;T)Ad d (9) where: d = sin d d (10) where is the angle from the North Pole and is the longitude. Rather, Planck's constant h was created and introduced into his new formula. this is forgotten Wien's law, which is derived from Plancks law, efficiently shows how the peaks of the correct and the transformed curves are at different positions. trailer Laws governing black body radiation, like Stefan's law and Wien's law. xref 481 0 obj<>stream The Boltzmann equation still forms the basis of the kinetic theory of gases and has proved fruitful not only for the classical gases Boltzmann had in mind, but als- if properly generalized - for the electron gas in a solid and the Solar Constant. xb```b``qe`a` Bl@qBK0060r:z%W[OU&sy\ l]}lRk 9. This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Another way to obtain the temperature of a black body is by taking the area under the Planck curve, i.e. The students can use the book as a readily available mentor for providing hints or complete solutions as per their needs. Key features of the book are: - Concept building by problem solving. Planck's Black Body Radiation Law is proved starting from the kinetic theory of gases. Check out our new LibreCommons search portal. an adequate grounding for the Wien distribution law, if the theory were to be in accord with experiment. This can be solved via the quotient rule or product rule for differentiation. Wien's Law and Black-body Radiation. REPORT DATE 30 SEP 1984 2. Setting this derivative equal to zero to determine the maximum gives the equation Wien's Displacement Law An interesting feature of the blackbody spectrum at a given temperature is the wavelength for which the energy density is the greatest. The objective of this note is to show that in teaching introductory (calculus-based) or intermediate physics, instead of simply stating Wiens In both limiting frequency ranges it transforms into Poisson distributions; in the Wien limit, it is the distribution of the number of photons, whose most probable value is given by Boltzmann's expression, while in the Rayleigh-Jeans limit, it is the distribution of the number of Planck oscillators. . The book not only deals with a topic of importance and interest to all scientists, but is also a polished literary work, described (accurately) by one of its original reviewers as a scientific detective story."John Gribbin, New x[[o~EM,l=m>txa{V33$%R$m-3\/_}]y&Tvg9GF#W./XvOJW?7l@6{,xgM2}Kf}-VuKE0E2GF&Hsc2#Y>"r(ksJTq{y&cr (ATr /oBRRa&/TtGeDBG 2.MId E4Xy{LFW:5.Vd|Ys^szv|x*k.W[4Z[:-qc.Vz]Wz{~]sRkv $wt^9kPulW0!tRtLvea(Tzm;RSKz6OUya& "d4v$. Stefan-Boltzmann law MT = T4 MT = W m-2 = 5.669 x 10-8 W m-2 K-4 m(Sun) = 5.669e-8 X 60004 MT = 7.3 x 107 W m-2 endobj This formula shows small deviations from Plancks at long wavelengths. 2. Quote A: In 1899, a German physicist Max Planck rederived Wiens formula (i.e., (13.4) with = 5) from phenomenological thermodynamical considerations. 19. 466 16 A good description is in r. A simple derivation of plancks law used to describe black body radiation. This revised edition of Feynman's legendary lectures includes extensive corrections Feynman and his colleagues received and Caltech approved. opinion that Wiens law must be necessarily true, I may perhaps be permit-ted to explain briey the relationship between the electromagnetic theory developed by me and the experimental data. Have questions or comments? Quote B: His first derivation of this formula, done in October 1900, was based solely on phenomenological Thermodynamics and required no assumptions about microscopic properties of radiation. The Stefan-Boltzmann law says that the power emitted per unit area of the emitting body is: P A = Z 1 0 I( ;T)d Z cos d Derive Wien's displacement law from Planck's law. 466 0 obj <> endobj % Peak of Blackbody Radiation To find the peak of the radiation curve as indicated in Wien's displacement law, it is necessary to take the derivative of the Planck radiation formula with respect to wavelength. = 2 is the angular frequency of the wave. 0000002939 00000 n Max Planck developed the law in 1900, originally with only empirically determined constants, and later showed that, expressed as an energy distribution; it is the unique stable distribution for radiation in thermodynamic equilibrium. Selecting the latter for convenience requires rewriting Equation \ref{eq2} as a product: \[ \dfrac{d}{d\nu} \left \{ \rho (\nu, T) \right \} = \dfrac{2h}{c^3} \dfrac{d}{d\nu} \left \{ ( \nu^3) \left( e^{\frac {h\nu}{k_B T}}-1 \right)^{-1} \right \} = 0\], applying the product rule (and power rule and chain rule), \[ = \dfrac{2h}{c^3} \left [ (3 \nu^2) \left( e^{\frac {h\nu}{k_B T}}-1 \right)^{-1} - ( \nu^3) \left( e^{\frac {h\nu}{k_B T}}-1 \right)^{-2} \left(\dfrac{h}{k_BT}\right) e^{\frac {h\nu}{k_B T}} \right] = 0\], \[ (3 {\nu^2}) {\left( e^{\frac {h\nu}{k_B T}}-1 \right)^{-1}} = ( \nu^{3}) \left( e^{\frac {h\nu}{k_B T}}-1 \right)^{-2} \left(\dfrac{h}{k_BT}\right) e^{\frac {h\nu}{k_B T}} \], \[ 3 \left( e^{\frac {h\nu}{k_B T}}-1 \right) - \left(\dfrac{hv}{k_BT}\right) e^{\frac {h\nu}{k_B T}} =0 \label{eq10}\], We can do a substitution \(u=\frac {h\nu}{k_B T} \) and Equation \ref{eq10} becomes, Finding the solutions to this equation requires using Lambert's W-functions and results numerically in, \[ u = \dfrac {h\nu}{k_B T} \approx 2.8214 \label{eq20}\], \[ \begin{align} \nu &\approx \dfrac{2.8214\, k_B}{h} T \\[4pt] &\approx \dfrac{(2.8214 )(1.38 \times 10^{-23} J/K) }{6.63 \times 10^{-34} J\,s} T \\[4pt] &\approx (5.8 \times 10^{10} Hz/K)\, T \end{align}\]. This paper will present brief biographies of the four pillars of the T4 radiation law, Stefan, Boltzmann, Wien and Planck, and outline the methodologies used to obtain their results. Setting this derivative equal to zero to determine the maximum gives the equation 0000002664 00000 n For more information contact us at[emailprotected]or check out our status page at https://status.libretexts.org. 0000007487 00000 n endobj DATES COVERED 30-09-1984 to 30-09-1984 4. 0000003971 00000 n Derivation of Planck's law, Deduction of Wien s distribution law, Rayleigh-Jeans Law, Stefan Boltzmann Law and Wien s displacement law from Planck s law. From Planck's constant h and the Boltzmann constant k, Wien's constant (Equation \ref{eq20}) can be obtained. 0000004817 00000 n %PDF-1.5 Throughout this volume, the authors provide detailed reconstructions of the central arguments and derivations of the physicists involved, allowing for a full and thorough understanding of the key principles. b. The book reviews fundamental concepts in conduction, forced convection, free convection, boiling, condensation, heat exchangers and mass transfer succinctly and without unnecessary exposition. Plancks law equal to zero, dB() d = 0 In the exercises you will show that the result gives Tmax = 2.9 103mK. 1. shn l] (statistical mechanics) A formula for the spectral distribution of radiation from a blackbody, which is a good approximation to the Planck radiation formula at sufficiently low temperatures or wavelengths, for example, in Plancks law equal to zero, dB() d = 0 In the exercises you will show that the result gives Tmax = 2.9 103mK. by integrating Plancks law over all wave-lengths. <]>> 1. Derivation of Planck's law, Deduction of Wiens distribution law, Rayleigh-Jeans Law, Stefan Boltzmann Law and Wiens displacement law from Plancks law. Read Paper. 0000002122 00000 n <>>> Proceed as follows: \[\rho (\nu, T) = \dfrac {2 h \nu^3 }{c^3\left(e^{\frac {h\nu}{k_B T}}-1\right)} \label{Planck2}\]. Maxwell's finding was later generalized in 1871 by a German physicist, Ludwig Boltzmann, to express the distribution of energies among the molecules. Gerhard Kramm and Nicole Mlders, Plancks blackbody radiation law 3 Since Planck3 considered beside the velocity of light in vacuum Stefans constant for estimating the ratiok4 h3 =const and Wiens displacement relationship4 ()T const. Planck's law of radiation - law. Derivation of Rayleigh jeans law from planks law. Weins distribution law, Rayleigh-Jeans law and Plancks Radiation Law According to Wiens distribution law the energy emitted by the blackbody per unit volume in the range of wavelength from to + d is given by where C1and C2 are constants and T is absolute temperature. On a Nonquantum Derivation of Plancks Distribution Law On a Nonquantum Derivation of Plancks Distribution Law Cercignani, Carlo 2013-12-30 00:00:00 Foundations of Physics Letters, Vol. Wien's displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. The exponential curve was created by the use of Eulers number e raised to the power of the temperature multiplied by a constant. As an energy distribution, it is one of a family of thermal equilibrium distributions which include
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