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Black body radiation and planck’s radiation law


Black body radiation basics

When a body is heated,it emits radiation.The nature of the radiation depends upon the temperature.At low temperature,a body emits radiation which is principally of long wavelengths in the invisible infrared region.At high temperature ,the proportion of shorter wavelength radiation increases. Furthermore,the amount of emitted radiation is different for different wavelengths.It is of interest to see how the energy is distributed among different wavelengths at various temperatures. For example,when platinum wire is heated,it appears dull red at about 500 C°,changes to cherry red at 900 c°,becomes orange red at 1100 c,yellow at 1300 C° and finally white at about 1600 C°.This shows that as the temperature is increased,the radiation becomes richer in shorter wavelengths.

In order to understand the distribution of radiation emitted from a hot body.We consider a non reflecting object such as a solid that has a hollow cavity within it.It has a small hole and the radiation can enter or escape only through this hole.The inside is blackened with soot to make it as good an absorber and as bad a reflector as possible.The small hole appears black because the radiation that enters is reflected from the inside walls many times and is partly absorbed at each reflection until none remains.Such a body is termed as black body and has the property to absorb all the radiation entering it.A black body is body is both an ideal absorber and ideal radiator.

Intensity Distribution Diagram

Lummer and Pringsheim measured the intensity of emitted energy with wavelength radiated from a black body at different temperatures.The amount of radiation emitted with different wavelengths is shown in the form of energy distribution curves for each temperature in figure below.

graphical representation of black body radiation

These curves reveal the following interesting facts.

  1. At a given temperature,the energy is not uniformly distributed in the radiation spectrum of the body.
  2. At a given temperature T,the emitted energy has maximum value for a certain wavelength λmax and the product λmax ×T remains constant.

λmax ×T=Constant …..(1)

The value of the constant is about 2.9 × 10-3 m K. This equation means that as T increases, λ shifts to shorter wavelength.

For all wavelengths,an increase in temperature causes an increase in energy emission.The radiation intensity increases with increase in wavelengths and at a particular wavelength λmax ,it has a maximum value.With further increase in wavelength,the intensity of radiation decreases.

The area under each curve represents the total energy (E) radiated over all wavelengths at a particular temperature.It is found that area is directly proportional to the fourth power of kelvin temperature T.Thus

E ∝ T4  OR  E=σT………..(2)

Where σ is called Stephen’s constant.Its value is 5.67 ×10-6 Wm2k-4 and the above relation is known as Stephen Boltzmann law.

Planck’s radiation law and Assumption

Electromagnetic wave theory of radiation cannot explain the energy distribution along the intensity wavelengths curves.The successful attempts to explain the shape of energy distribution curves gave rise to a new and non classical view of electromagnetic radiation.In 1900,Max plank founded a mathematical model resulting in an equation that describes the shape of observed curves exactly.He suggested that energy is radiated or absorbed in discrete packets,called quanta rather than as a continuous wave.Each quantum is associated with radiation of a single frequency.The energy E of each quantum is proportional to the frequency f,and:

E = hf …….(3)

Here h is Plank’s constant.Its value is 6.63×10 -34 J s. This fundamental constant is an important in physics as the constant c,the speed of light in vacuum.

Max Planck received the Nobel prize in physics in 1918 for his discovery of energy quanta.

Black body radiation (video)

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