Black body radiation

BLACK BODY RADIATION

Perfect black body:

A perfect black body is the one which absorbs and emits all the radiations, (corresponding to all wavelengths) that fall on it. The radiation, given out by a perfect black body is called black body radiation.

Kirchoff's Law:

Ratio of emissive power to the coefficient of absorption, of any given wavelength is the same for all bodies at a given temperature and is equal to the emissive power of the black body at that temperature.

 e_λ / a_λ = E

Experiment

In practice, a perfect black body is not available. Therefore let us consider a hollow copper sphere coated with lamp black on its inner surface.

A fine hole is made for radiations to enter into the sphere as shown in Fig. 7.1.

Now, when the radiations are made to pass through the hole, it undergoes multiple reflections and are completely absorbed. Thus, the black body act as a perfect absorber.

Now, when this black body is placed in a temperature bath of fixed temperature, the heat radiations will come out only through the hole in the sphere and not through the walls of the sphere.

Therefore, we can conclude that the radiations are emitted only from the inner surface of the sphere and not from the outer surface of the sphere. Thus a perfect black body is a perfect absorber and also a perfect radiator of all wavelengths.

Energy Spectrum

When a perfect black body is allowed to emit radiations at different temperatures, then the distribution of energy for different wavelengths at various temperatures is obtained as shown in Fig. 7.2.

From Fig. 7.2 the following results are formulated.

(i) The energy distribution is not uniform for any given temperature.

(ii) The intensity of radiation (E) increases with respect to the increase in wavelength and at a particular wavelength, it becomes maximum (λ_m) and after this, it starts decreasing with respect to the increase in wavelength.

(iii) When the temperature is increased (shown as dotted line), the maximum wavelength (λ_m) decreases.

(iv) For all the wavelengths, an increase in temperature causes increase in energy.

(v) The total energy emitted at any particular temperature can be calculated from the area under that particular curve.