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.
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?
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...
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...
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...
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?
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...
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...
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...
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...
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...
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...
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...
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?
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...
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...
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"...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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]...
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...
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...
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...
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...
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...
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...
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.
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}...
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...
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...
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]
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...
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...
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...
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...
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...
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 λmax stating that Tλmax = constant
and
b) Obtain a numerical value for this constant
[Hint: Start with Planck's...