What is blackbody radiation electricity outage houston


• The value of the wavelength λ max at which the radiancy reaches its maximum decreases as the temperature increases. The experiments show that the maximum wavelength is inversely proportional to the temperature. In fact, we have found that if you multiply λ max and the temperature, you obtain a constant, in what is known as Wein’s displacement law:

The above description involved a bit of cheating. Light is reflected off objects, so the experiment described runs into the problem of what is actually being tested. To simplify the situation, scientists looked at a blackbody, which is to say an object that does not reflect any light.

Consider a metal box with a small hole in it. If light hits the hole, it will enter the box, and there’s little chance of it bouncing back out. Therefore, in this case, the hole, not the box itself, is the blackbody. The radiation detected outside the hole will be a sample of the radiation inside the box, so some analysis is required to understand what’s happening inside the box.

• Each individual wave contributes an energy kT to the radiation in the box. From classical thermodynamics, we know that the radiation in the box is in thermal equilibrium with the walls at temperature T. Radiation is absorbed and quickly reemitted by the walls, which creates oscillations in the frequency of the radiation. The mean thermal kinetic energy of an oscillating atom is 0.5 kT. Since these are simple harmonic oscillators, the mean kinetic energy is equal to the mean potential energy, so the total energy is kT.

R( λ) = (8 π / λ 4) kT ( c / 4) (known as the Rayleigh-Jeans formula)Unfortunately, the Rayleigh-Jeans formula fails horribly to predict the actual results of the experiments. Notice that the radiancy in this equation is inversely proportional to the fourth power of the wavelength, which indicates that at short wavelength (i.e. near 0), the radiancy will approach infinity.

This failure is called the ultraviolet catastrophe, and by 1900 it had created serious problems for classical physics because it called into question the basic concepts of thermodynamics and electromagnetics that were involved in reaching that equation. (At longer wavelengths, the Rayleigh-Jeans formula is closer to the observed data.) Planck’s TheoryIn 1900, the German physicist Max Planck proposed a bold and innovative resolution to the ultraviolet catastrophe. He reasoned that the problem was that the formula predicted low-wavelength (and, therefore, high-frequency) radiancy much too high. Planck proposed that if there were a way to limit the high-frequency oscillations in the atoms, the corresponding radiancy of high-frequency (again, low-wavelength) waves would also be reduced, which would match the experimental results.

If the energy of these quanta are proportional to the radiation frequency, then at large frequencies the energy would similarly become large. Since no standing wave could have an energy greater than kT, this put an effective cap on the high-frequency radiancy, thus solving the ultraviolet catastrophe.

Each oscillator could emit or absorb energy only in quantities that are integer multiples of the quanta of energy ( epsilon): E = n ε, where the number of quanta, n = 1, 2, 3, . . .The energy of each quanta is described by the frequency ( ν): ε = h νwhere h is a proportionality constant that came to be known as Planck’s constant. Using this reinterpretation of the nature of energy, Planck found the following (unattractive and scary) equation for the radiancy: ( c / 4)(8 π / λ 4)(( hc / λ)(1 / ( ehc/ λ kT – 1)))The average energy kT is replaced by a relationship involving an inverse proportion of the natural exponential e, and Planck’s constant shows up in a couple of places. This correction to the equation, it turns out, fits the data perfectly, even if it isn’t as pretty as the Rayleigh-Jeans formula. ConsequencesPlanck’s solution to the ultraviolet catastrophe is considered the starting point of quantum physics. Five years later, Einstein would build on this quantum theory to explain the photoelectric effect, by introducing his photon theory. While Planck introduced the idea of quanta to fix problems in one specific experiment, Einstein went further to define it as a fundamental property of the electromagnetic field.