'Month of Equations': Meaning of Planck's Law of Blackbody Radiation

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Meaning of the Equation:

Planck's law represents an expression for energy radiated per unit volume by a black body at temperature T at a given frequency.

Proposed by Max Planck in 1900, the Planck's law marked the beginning of the era of Quantum Physics. This equation states that the intensity of radiation (energy density per unit volume at a given frequency) emitted by a black body is a function of the temperature of the body. The pictorial representation of this expression is depicted in the following figure:

Planck's Law

Let us try to understand the physical meaning of this equation:

The question that underlie the finding of this phenomenon was- How does radiation interact with matter? Well, it is seen that when a solid object is heated, firstly it glows and emits thermal radiation. As the temperature is further increased, the object becomes red, then yellow and then white. If the object is a blackbody (an object which a perfect absorber of radiation and also a perfect emitter), the radiation emitted is called black body radiation.

Now, the spectra (graph between the energy density of radiation and frequency) of emitted blackbody radiation is continuous and the peak of this radiation spectrum occurs at a frequency that is proportional to its temperature and hence, responsible for the change in color of the object with increase in temperature of the object. Being very dissimilar to the spectra of heated gases which are found to be of discrete nature, a number of attempts were made to explain the continuous nature of blackbody spectrum but all in vain until Planck postulated that the energy of radiation emitted from the walls of the cavity must be discrete, i.e., the energy given to a black body in the form of heat is absorbed and hence emitted by it in the form of discrete packets of energy such that: E=n h v, where E is the energy absorbed or emitted, n is an integer, h is the Planck's constant having value 6.626 *10^(-34) J-s and v is the frequency of the oscillating electron that absorbs or emits this energy.

 On summing up the discrete energies of all the oscillating electrons present in the walls of this black body, an expression for the energy density emitted by a blackbody is obtained which represents an energy continuum and hence the continuous spectra of black body radiation.

This law removed all the lacuna present in the previous theories that failed at high frequencies and bagged the Nobel prize in Physics for Max Planck in 1918.

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