Question

Discuss Blackbody radiation. What was done before Planck? What was wrong with it? What did Planck do differently? Be explicit about his assumptions. Draw a rough sketch of the spectrum of light emitted from a blackbody radiator at 200 K. You should be able to locate the maximum frequency. Now redo that sketch for double the temperature, that is 400 K.

Answer 1

A blackbody refers to an opaque object that emits thermal radiation. A perfect blackbody is one that absorbs all incoming light and does not reflect any. At room temperature, such an object would appear to be perfectly black (hence the term blackbody). However, if heated to a high temperature, a blackbody will begin to glow with thermal radiation.

Any ray of radiation entering the hole will be reflected by the cavity's walls and eventually absorbed by them. On the other hand, due to thermal chaotic motion, the molecules of the walls emit some radiation, in addition to also absorbing it. After a sufficiently long time", equilibrium between the walls and the radiation inside the cavity is reached. In the equilibrium, a detailed balance takes place: at any given time, the amount of the emitted radiation of a given wavelength, polarization, and direction equals, on average , the amount of absorbed radiation with the same properties. In other words, importantly for a later discussion,there is a thermodynamic equilibrium between the walls and the radiation.Thus, in practice, radiation from any cavity with a tiny hole very closely approximates the radiation of a black body.

This material of the inner walls of the cavity. That is, it implies that no matter what this material may be, a tiny hole in a cavity will radiate approximately as an ideal black body. You may want to know that while this statement is widely accepted in modern physics, its is still not entirely undisputed. For example, the paper by P.-M. Robitaille posted alongside this Lecture defends an alternative point of view, namely that the radiation of an actual cavity depends both on the material of the cavity's inner walls and also on the angle at which this radiation is measured.

A system evolves in thermal and mechanical isolation from the ambient environment, then its entropy increases." (Entropy is a measure of disorder of the system. Originally, the Second Law was formulated in differerent forms by the mathematical physicists Rudolph Clau-sius, of Germany, and William Thompson (Lord Kelvin), of Ireland, in the 1850's). A corollaryof Planck's formulation of the Second Law is this: Since a system in thermal and mechanical isolation is known to evolve toward thermodynamic equilibrium, then in this equilibrium, the system's entropy must be a maximum. It is this connection between a thermodynamic equilib-rium and the entropy that motivated Planck's interest in the black-body radiation theory.

Assumptions are:

1. A black body in thermal equilibrium emits electromagnetic radiation called black body radiation.

2. The radiation has a specific spectrum and intensity that depends only on the temperature of the body.

3 .Max Planck, in 1901, accurately described the radiation by assuming that electromagnetic radiation was emitted in discrete packets (or quanta). Planck's quantum hypothesis is a pioneering work, heralding advent of a new era of modern physics and quantum theory.