What is Planck's law: Definition and 49 Discussions

Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T, when there is no net flow of matter or energy between the body and its environment.At the end of the 19th century, physicists were unable to explain why the observed spectrum of black-body radiation, which by then had been accurately measured, diverged significantly at higher frequencies from that predicted by existing theories. In 1900, Max Planck heuristically derived a formula for the observed spectrum by assuming that a hypothetical electrically charged oscillator in a cavity that contained black-body radiation could only change its energy in a minimal increment, E, that was proportional to the frequency of its associated electromagnetic wave. This resolved the problem of the ultraviolet catastrophe predicted by classical physics. This discovery was a pioneering insight of modern physics and is of fundamental importance to quantum theory.

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  1. Philip Koeck

    I Radiation from solid black bodies

    I understand that Planck's law is derived for a cavity with a hole in it. I haven't found a clear argument that the same result and all results that follow from it also apply to solid surfaces that are black. Can anybody point me to a text that shows this?
  2. H

    I Is Planck's Law of Black-Body Accurate?

    First of all, Is ##\beta## given by the Planck's law of black-body is the amount of power contained in radiation emitted by a black body? I'm not sure to fully understand the law above. Does it means that if amount of power over all the frequencies is greater than the energy needed to remove an...
  3. L

    At what frequency can Planck's law be used to determine the temperature?

    Hi, I am not quite sure if I have calculated the homework correctly :-) I proceeded in such a way that I first calculated from which frequency the two terms are equal, and thus the equation results in zero. Then I figured a relative accuracy of 10% equals a relative error of 90%. So I...
  4. D

    I Planck's law in wavenumber vs. wavelength

    I have asked this question elsewhere. I have gotten no clear answer. What I already know: The interval (differential) sizes (areas) are different in terms of wavelength and wavenumber. The total energy is the same when the curves are integrated over all wavelengths or wavenumbers So please...
  5. T

    B Where is the quantization term in Planck's Law?

    This is a very remedial question, so thanks in advance for you gentle indulgence :smile: Where do I find the quantization term (the "n") in Planck's Law?
  6. Max Loo Pin Mok

    Black body radiation, Planck's law, derivation

    The following are 3 equations of Planck's law or Planck's distribution function. Are they all correct? How do they derive from each other? Equation One: From page 512 of http://metronu.ulb.ac.be/npauly/art_2014_2015/shockley_1961.pdf We denote by Qs the number of quanta of frequency greater...
  7. prodo123

    I Trying to understand my prof's derivation of Planck's Law

    Not many people understood his proof in class, and the textbook's proof wasn't very clear so we went by with other derivations online. Then he filled half the midterm with his method, so I'm trying to understand how he did things. Looking back it seems very similar to the proofs we found online...
  8. V

    B Planck's Law, Color & Sun: Can We See It Greener?

    I was thinking about the color of the sun. I would like to talk about an ideal case, no atmosphere etc. I looking for the peak in Planck's law in wavelengths (wl), i.e., the most radiated wl (or from Wien's law). But if I'm thinking about how we see that photons hitting our eyes and what wl is...
  9. F

    Was the Ultraviolet Catastrophe a Real Problem or Just a Fake?

    Max Planck formulated the quantum hypothesis, that electromagnetic radiation was emitted from heated bodies only in quanta of energy E = hf, where f was the frequency of the radiation and h was a constant now called “Planck's Constant”, in order to solve the Ultraviolet Catastrophe...
  10. heavystray

    B Temperature based on colour index using Planck's law

    Hi, I'm trying to find temperature of stars using the stars' B-V magnitude by using the Planck law. However i do not know how to solve for T (assume other quantities are all given and determined first). Any idea how to do so? I already tried to do it but reach a dead end. Here I attached the...
  11. T

    I Breakdown of Planck's Law under certain Conditions

    The difference between Planck's Law and the Rayleigh-Jeans' Law is, in Rayleigh Jeans, the average energy per mode is ##kT##, whereas in Planck, it is ##\frac{hc}{λ(e^\frac{hc}{λkT}-1)}##. These average energy formulas are multiplied by another formula to give either Planck's Law or the...
  12. K

    Why does Planck's BB emissive power increase with n?

    This question is regarding the dependence of Planck's law for black-body (BB) radiation intensity (or integrating over a hemisphere, the emissive power, E = pi * I). Physically speaking, why is it that a BB emitting in a medium with n>1 (n being index of refraction) emits a higher power/area...
  13. T

    I Inverse of Maxwell-Boltzmann Distribution and Planck's Law?

    I'm looking for the inverse functions of the Maxwell-Boltzmann distribution and Planck's Law. Planck's Law in terms of the wavelength. Any of you know of any literature on this topic?
  14. Destroxia

    Planck's Law: Low, and High Frequency Limit

    Homework Statement a) Derive the Rayleigh-Jeans distribution by taking the low-frequency limit of Planck's distribution. b) Derive the Wien distribution by taking the high-frequency limit of Planck's Distribution. Homework Equations ## u(f) = \frac {8 \pi f^2} {c^3} \frac {hf} {e^{\frac...
  15. P

    I Could Planck have used different energy-frequency relation?

    Hello, as a non-physicist enthusiast, but with decent math background, I tried to learn a bit about origins of quantum theory and very soon raised some questions, which I hope this community will answer. So, Planck tried to model the blackbody radiation on where Raighley and Jeans have failed...
  16. T

    I Planck's 1st Derivation of Planck's Law?

    My information comes from: http://www.cems.uvm.edu/~tlakoba/AppliedUGMath/notes/lecture_13.pdf Quote A: Quote B: Quote C: Quote B and Quote C concern Planck's Law, not Wien's Law. I know how Planck derived it as mentioned in Quote C.However, what are the "phenomenological Thermodynamics"...
  17. Z

    Derivation of Wien's+Reyleigh-Jean's Laws from Planck's Law

    Homework Statement After reading the forum stickies I'm not entirely sure where to put this question since it involves using math to solve a question, but is informally stated and isn't a book problem, either-I just started reading Fong's Elementary Quantum Mechanics, and in the first few...
  18. Alettix

    What is the explanation for the differential form of Planck's law?

    Hello! I have a little trouble with understanding Planck's law of radiation, and wondered if you could help me with it. :) The equation is: ## \frac{dI}{d\lambda} = \frac{2\pi hc^2}{\lambda^5(e^{hc/\lambda kT}-1)} ## (1) where T is the temperature, k Boltzmann's constant, h Planck's constant...
  19. W

    Planck's Law vs Rayleigh-Jeans Law (Blackbody radiation)

    First time here, and looking for help on this. The 2nd part of this problem, I have seen some posts on and am still reviewing, but haven't found much on the 1st part. Homework Statement 1) Use l'Hopital's Rule to show that $${\lim_{\lambda\rightarrow 0^{+}}=0}\text{ and...
  20. A

    Designing an experiment to demonstrate Planck's Law

    For my undergraduate physics lab, we are asked to spend 3 weeks (3 3-hour sessions + any time during the week if I need extra time) doing an experiment of our own choosing. The physics department will provide any experimental tools needed within reason. I have been considering using this...
  21. K

    Getting Planck's Law in terms of frequency from wavelength

    Show that Planck's law expressed in terms of the frequency f is: u(f) = (8πf2/c3)(hf/(ehf/kT - 1)) from the equation: u(λ) = (8πhcλ-5)/(ehc/λkT - 1) When I do this algebraically by simply plugging in λ = c/f, I get: u(f) = (8πhc-4)/(f-5(ehf/kT - 1) which clearly doesn't involve the correct...
  22. Lamdbaenergy

    Planck's law (wavelength, frequency, angle?)

    So I was just looking around today and stumbled upon something called Planck's law. I saw an equation and quite few more of them that looked like this, I'm familiar with all of the other variables and constants already, but don't get the E (hv/kT) part, yet. Is E the energy of the photons you...
  23. Luck0

    Is Planck's Law Based on Incorrect Assumptions About Boltzmann's Distribution?

    So, my instructor said to us that Planck's law of radiation assumes that Boltzmann's distribution is incorrect. But it seems to me that Planck used Boltzmann's law, he just didn't replaced the summation by an integral, because now the energy is discrete. Can someone explain to me if my...
  24. C

    Derivation of Planck's law and the shape of the cavity

    When Planck's law is derive a cubical cavity is often used (for example in: http://disciplinas.stoa.usp.br/pluginfile.php/48089/course/section/16461/qsp_chapter10-plank.pdf) However, the result is applied generally. But in general, it seems like the wave lengths of the standing waves will...
  25. K

    Planck's law for longer wavelengths

    I was just working on a problem that asked me to show that Plank's Law for black body radiation is approximately equal to Rayleigh-Jeans Law, which expresses the energy density of black body radiation as a function of wavelength. I was to show that this relation is only true at high wavelengths...
  26. D

    Why Does Planck's Law Assume Oscillator Energy Applies to Electromagnetic Modes?

    The derivation of Planck's law in my textbook begins with the assumption that the energy of an oscillator with frequency ##\nu## is quantised in units of ##h\nu##. It follows that the average energy of such an oscillator (in equilibrium with a reservoir at temperature ##T##) will be...
  27. O

    From Planck's law to derive the stefan Boltzman constant.

    The following is the Planck's derivation for black body radiation $${\rho}({\lambda}) d{\lambda}=E({\lambda})*f({E(\lambda}))*D({\lambda})d{\lambda}------equation 1$$ $$\int_0^\infty{\rho}({\lambda})d{\lambda}$$ is the density of radiative energy. From...
  28. L

    Why does Planck's Law have different peaks?

    Suppose we have a blackbody at temperature T. Then if we write Planck's law for wavelength, and find the wavelength corresponding to the peak, we get a certain value lambda_max. If, on the other hand, you wrote Planck's law for frequency, and we found the frequency corresponding to peak of...
  29. U

    Archived Planck's law and doppler effect

    Hello, We proved something during the course but I totally forgot how to do it.. Homework Statement Prove that Planck's Law E=h*u is deduced from the equation of Doppler effect u'=u*√((1-β)/(1+β)) Homework Equations Lorentz transformationThe Attempt at a Solution If we take a beam of light of...
  30. A

    Maximizing Planck's law using Taylor polynomial for e^x

    Homework Statement The energy density of electromagnetic radiation at wavelength λ from a black body at temperature T (degrees Kelvin) is given by Planck's law of black body radiation: f(λ) = \frac{8πhc}{λ^{5}(e^{hc/λkT} - 1)} where h is Planck's constant, c is the speed of light, and...
  31. T

    Wavelengths of sunlight, blackbody radiators, Planck's law, CCT

    A blackbody radiator emits radiation across the entire radiation spectrum. The "temperature" of the blackbody radiator (measured in kelvin) can be directly calculated from the peak wavelength of its radiation using http://en.wikipedia.org/wiki/Wien's_displacement_law"]Wien's[/PLAIN]...
  32. S

    Can real bodies deviate from Planck's law?

    Can Planck's law be derived from QED and statistical mechanics? Any references appreciated. Skippy
  33. H

    Planck's Law, Quantum mechanics help

    Homework Statement (2) The orbiting space shuttle moves around the Earth well above 99% of the atmosphere, yet it still accumulates an electric charge on its skin due (in part) to the loss of electrons caused by the photoelectric effect from sunlight. Suppose the skin of the shuttle is coated...
  34. L

    Question about Planck's Law and temperature/light emission

    I have a question about Planck's Law. When I first read about it, I misunderstood it to mean that an object at a certain temperature would only emit a very narrow wavelength of light. But as I've looked into it further it appears as though everything in the universe emits a range of light that...
  35. C

    Planck's Law/ number of photons

    Homework Statement Produce plots of I(λ, T) vs. λ for a blackbody at temperature T = 500 K. Compute the number of photons emitted with 400nm < λ < 450 nm for each temperature, assuming the total surface area is 1.0000 m2, to 5 significant figures. Homework Equations Planck's Law...
  36. P

    Finding maximum in Planck's law

    Homework Statement At what wavelength is u(lambda) a maximum for a star with a surface temperature of 50,000 K? Homework Equations Planck's law u(lambda)=8(pi)hc/(lambda^5*(e^(hc/kTlambda)-1) The Attempt at a Solution I think the maximum is where the derivative of the function...
  37. Math Jeans

    Wavelength limits of Planck's Law

    As is well known, Planck's radiation law for the distribution function of blackbody radiation used a then new concept of energy quanta in order to describe experimental data. The distribution functions formulated by Wilhelm Wien and Lord Rayleigh, describing the same phenomena, were...
  38. Y

    Integration of Planck's law to find photon density in space

    Homework Statement The universe is filled with EM radiation emanating from the Big Bang. This radiation was initially unimaginably hot but, as the universe has expanded, it has cooled to 3K. The distribution of the energy density of these photons in frequency (or wavelength) is given by the...
  39. J

    Deriving Planck's law with Taylor series

    Expanding exp(hc / lambda*k_b * T) by Taylor series = 1 + hc /lambda*k_B * T +... But don't you take the derivative with respect to lambda? So I don't get how it would be this.
  40. R

    Deriving Planck's Law: Solving for the Integral Formula

    Homework Statement I need to find the Planck's law: R(\lambda)=\frac{2hc^2}{\lambda^5}\frac{1}{e^{\frac{hc}{\lambda kT}}-1} Homework Equations The Attempt at a Solution I've done most of the derivation, but I got stuck with an integral: R(\lambda)=\frac{1}{4\pi^3 \hbar^3 c^2}...
  41. K

    Planck's law and ultraviolet catastrophe

    Hi. I know this is a pretty basic principle, however I'm fairly new to the subject and was wondering if anyone is able to give a brief 'layman' explanation of why, as Planck's law states, at lower wavelengths the blackbody radiation falls to zero rather than continuing to climb as stated in the...
  42. C

    What is the paradox in Planck's Law?

    Hi all, Physical law: I understand the derivation of the Planck law for the blackbody spectrum and why it takes slightly different forms whether you are doing the analysis in the frequency domain or the wavelength domain. That is to say, you cannot simply invoke the Planck relation...
  43. C

    Applications of Taylor polynomials to Planck's Law

    Due to too much wrong information being posted on my behalf, I am resubmitting a cleaned up version of my last post. I have 2 hours to get this problem done :(. Essentially, I don't know at all how to find the Taylor Polynomial for g(x) = \frac{1}{x^5 ( e^{b/x} -1)} [/URL]
  44. N

    Planck's Law Problem: Solve for Vmax 3 Sig Digits

    Homework Statement Given Planck's Radiation Formula Find the frequency (Vmax) at which energy density is at a maximum. This requires simple calculus and numerical solution of a simple transcendental equation. You only need to find the answer to 3 significant digits. Homework Equations...
  45. N

    Are I(nu, T) and I(lamda, T) Equivalent in Planck's Law?

    On the wikipeida page http://en.wikipedia.org/wiki/Planck's_law_of_black_body_radiation two formula's are given for spectral radiance, I(nu, T) and I(lamda,T). However, I(nu, T) seems to have units of J/m^2 and I(lamda, T) seems to have units of J/s/m^3. My homework question is to show that...
  46. C

    Calculating Spectral Exitance for Planck's Law & Blackbody

    Hello, My question is in regards to Planck's Law and a blackbody: For the single lambda case I can readily find the spectral exitance. Alternately, if I substitute to create an integral in the form of x^3 / (e^x - 1) and integrate over all lambda, I reach Stefan-Boltzmann. No problems...
  47. M

    Question about Planck's Law of Radiation

    Basically I have to discuss what the high temperature limit/low temperature limits of Planck's Law are, what they mean mathematically, and why the first is "classical" and the second can't be obtained from "classic" physics. If anyone could clarify what these points mean i'd be grateful. I think...
  48. C

    Planck's law of radiation?

    Planck's law of radiation?? Hi, can anybody help me with this problem? Planck's law of radiation for a blackbody radiator quantifies the relation between it's radiative flux and wavelength at a particular temperature. given by: F(w)=C1/[w^5(exp(C2/wT)-1] where...
  49. G

    Deriving Wien's Displacement Law from Planck's Law

    Basically this problem is to derive Wien's displacement law from Planck's law. Specifically: a) Show that there is a general relationship between temperature and &lambda;max stating that T&lambda;max = constant and b) Obtain a numerical value for this constant [Hint: Start with Planck's...
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