Radiation (part-2)

Black body and black body radiation

By Prevost’s theory of exchanges, bodies in temperature equilibrium with their surroundings emit radiation of the same character and intensity as that which they absorb. Lampblack, for examples, possesses the power of absorbing nearly all the radiation which is incident upon it and retains this power as its temperature is raised. Such a body having the power to absorb radiation of all wave-lengths completely is termed a black body. No material surface absorbs all the radiant energy incident on it. Lampblack reflects about 2% and so it approximates very closely to a black body. A black body is realized experimentally by having a uniform temperature enclosure with an aperture, small in comparison with the internal dimensions of the enclosure, through which the radiation may emerge. The emission of thermal radiation from and the absorption of radiation from and the absorption of radiation of all wave-lengths passing into, such an enclosure is complete. This radiation from such an enclosure is known as black body radiation or more appropriately full radiation. The smaller the aperture, the more completely is the radiation black. So a correction is to be applied for the lack of blackness due to the finite size of the aperture. This is due to the fact that some of the radiation coming from the wall is able to escape out and the state of thermodynamic equilibrium does not hold. This is avoided by Fery in his particular type of black body.

Application of Kirchhoff’s law to astrophysics

Kirchhoff’s law was responsible for the birth of two entirely new branches of science, astrophysics (physics of the suns and stars) and spectroscopy.

In 1680 Newton had shown that the sunlight can be decomposed by means of a prism into seven colors of the rainbow, but Fraunhofer, who repeated the experiment in 1801 with better instruments, found to hiss surprise that the spectrum was not continuous but crossed by dark lines. He could not account for the origin of these dark lines, neither did any of his contemporaries. But he realized their great importance, measured them and catalogued their wave-lengths. He also investigated the light from stars and found similar dark lines in their spectra. Other physicists, notably, Fizeau observed that if the solar spectrum is examined side by side with the spectrum from a sodium flame, the two yellow lines of the sodium spectrum occupy the same place as the Fraunhofer D-lines in the solar spectrum. Similar is the case with the hydrogen spectrum. Although these facts paved the way for a possible solution, the dark lines of Fraunhofer remain unexplained, until Kirchhoff completely solved the problem on the basis of his law. 

 

Kirchhoff arrived at the same law from thermodynamic reasoning and apply it to explain the dark lines as follows:

Sodium can emit the D-lines when it is excited; hence it can also absorb the same light when white light falls upon it and allows other light to pass through it unaffected. The gases in the outer cooler mantle round the sun, therefore, deprive the continuous spectrum from the central mass of the lines they themselves can emit and give rise to the dark lines. The D-lines (absorption spectrum of sodium) in the Fraunhofer spectrum prove that there is sodium in the sun’s atmosphere. Similarly, the other dark lines testify to the presence of their respective elements in the sun’s atmosphere. The presence of dark lines in the spectra of stars is accounted for in similar manner. It is by the analysis of such dark lines, one is able to tell of what elements the analysis of such dark lines, one is able to tell of what elements the cooler atmosphere surrounding the sun and stars are composed.

Kirchhoff’s discovery is of much greater importance than the mere success in explaining the fraunhofer bands. It clearly asserts that every different type of atom, when it is properly excited emits light of definite wavelength which is characteristic of the atom. 

Radiation pyrometers

Pyrometers are instruments for measuring high temperatures by means of radiation. In most thermometers the elements must be brought into contact with the body and if the temperature is too high the element is likely to melt. The radiation method does not depend upon contact with the body and so has not this limitation, but does assume that the body is a perfect black body. Frequently this will not be so and as a result the measured temperature will be lower than the actual.