Radiation Laws

Radiation Laws:

 The electromagnetic energy follows certain physical laws as it moves away from the source. Isaac Newton in his theory analysed the dual nature of light energy exhibiting both discrete and continuous phenomena associated with the stream of minuscule particles travelling in a straight line. This notion is consistent with modern theories of Max Plank (1858 – 1947) and Albert Einstein (1879 – 1955). Plank ascertained that electromagnetic energy is absorbed and emitted in discrete units called ‘photons’. The size of each unit is directly proportional to the frequency of the energy’s radiation. Therefore, Plank’s theory proposed that electromagnetic energy can be quantified by its wavelength and frequency and its intensity is expressed by ‘Q’ and is measured in Joules. The energy released by a radiating body in the form of a vibrating photon travelling at a speed of light can be quantified by relating the energy’s wavelength with its frequency. Plank defined a constant ‘h’ to relate frequency (n) to radiant energy ‘Q’ and is expressed as follows:

                                                             Q = hn ............................................. (2)

Since c = ln (see equation 1), therefore equation 2 can be rewritten as l hc Q = (3) where, Q=energy of photon in Joules (J) h=Plank’s constant (6.6 × 10-34) Js c=speed of light (3 × 108 m/s) F F l=wavelength in metres n=frequency (cycles/second, Hz) The above equation reveals that longer wavelengths have low energy of photons while for short wavelengths the energy will be high. For instance, blue light is on the short wavelength end of the visible spectrum (0.446 to 0.500 µm) thus has higher energy radiation in contrast to red light (0.620 to 0.700 µm) on the far end of the visible spectrum has low energy radiation.

Black Body Radiation:

All objects with temperature above absolute zero emit electromagnetic energy whereas the amount of energy and the associated wavelengths depend upon the temperature of the object. As the temperature of an object increases, the quantum of energy emitted also increases, and the corresponding wavelength of the maximum emission becomes shorter. The above hypothesis can be expressed by using the concept of blackbody. A blackbody is a hypothetical source of energy that behaves in an idealised manner such that it absorbs all or 100% of the radiation incident upon it and emits back (or radiates) the energy as a function of temperature. The Kirchhoff’s, Stefan-Boltzmann and Wien’s displacement laws explain the relationship between temperature, wavelength, frequency and intensity of energy.

1.Kirchhoff’s Law:

Kirchhoff’s law states that the ratio of emitted radiation to the absorbed radiation flux is same for all black bodies at the same temperature and forms the basis of the term emissivity (e), which is defined as the ratio between the emittance of a given object (M) and that of a blackbody at the same temperature (Mb):

                                                        e = M/Mb .................................................(4)

 The emissivity of a true blackbody is 1, and that of perfect radiator (a white body) would be zero. This implies that all objects have emissivities between these two extremes. Objects that absorb high proportions of incident radiation and re-radiate this energy have high emissivities, where as those which absorb less radiation have low emissivities, i.e. they reflect more energy that reaches them.

(ii) Stefan-Boltzmann Law:

 The Stefan-Boltzmann law defines the relationship between the total emitted radiation (W) (expressed in watts cm-2 ) and temperature (T) (absolute temperature, K):

                                                               W = sT 4  ........................................... (5)

The total radiation emitted from a black body is proportional to the fourth power of its absolute temperature. The constant (s) is the Stefan-Boltzmann constant (5.6697 × 10-8 ) (watts m-2 K -4 ). In short, Stefan-Boltzmann law states that hot blackbodies emit more energy than cool blackbodies.

(iii) Wien’s Displacement Law:

This law specifies the relationship between the wavelength of emitted radiation and the temperature of the object:

                                                        l = 2898/T ................................................ (6)

 Where, l is the wavelength hat which the radiance is at a maximum and (T) is the absolute temperature in Kelvin (K). as objects become hotter, the wavelength of maximum emittance shifts to shorter wavelengths. This law is useful for determining the optimum wavelength of object having temperature (T) Kelvin. Together, the Wien and Stefan-Boltzmann law are powerful tools. With the help of these laws, temperature and radiant energy can be determined from an object’s emitted radiation. For example, temperature distribution of large water bodies can be mapped by measuring the emitted radiation, similarly, discrete temperatures over a forest canopy can be detected to plan and manage forest fires.