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Modern Physics

1.1

CLASSICAL PHYSICS

Newtons laws of motion are the basis of the most elementary principles of classical physics. Equations based on these laws are the simplest and they are suitable for solution of simple dynamical problems, such as the motion of macroscopic bodies, Lagranges equations, Hamiltons equations and Hamiltons principle are also fundamental principles of classical mechanics, because they are consistent with each other and with Newtons laws of motion. Lagranges and Hamiltons equations are useful for solving many complicated dynamical problems. In principle, the properties of bulk matter must be deducible from the properties of electrons and atomic nuclei of which it is composed. However, it is found that many the observed properties of matter cannot be explained on the assumption that the particles obey the laws of classical mechanics. At the end of 19th century and in the beginning of 20th century, many new phenomena such as photoelectric effect, x-rays, line spectra, nuclear radiation were discovered which wanted explanation on the basis of classical physics. Laws of classical mechanics failed to explain the above said newly observed properties of matter.

Therefore the need of new concepts was felt in many areas of physical sciences. The concepts developed led to a new mechanics called quantum mechanics. Another form of quantum mechanics is called wave mechanics. The mathematical theory of this mechanics was developed by Erwin Schroedinger in 1926. Numerous problems of atomic physics have been solved by the application of quantum mechanics. To understand the development of wave mechanics, we begin with brief account of black body radiation, which could not be explained by classical mechanics. This is followed by description of some phenomena like the photoelectric effect, the Compton effect, etc. Explanations of these phenomena are based on Plancks quantum hypothesis.

1.1.1

Black Body Radiation

A body which completely absorbs radiations of all wavelengths incident on it is called a black body, and the radiation emitted by such a body is called black body radiation or full radiation. The nearest approach to a black body is shown in Fig 1.1(a). It consists of a porcelain sphere, having a small opening.

Engineering Physics

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Fig. 1.1 (a) A black body, (b) Spectral energy distribution

The inner surface is coated with lamp black. Any radiation which enters the sphere through the opening suffers a few reflections. At each reflection about 98% of the incident radiation is absorbed. Thus after a few reflections at the inner surface, the radiation is completely absorbed. If the area of the opening is very small, the radiation cannot be reflected out of the sphere again. The sphere also emits radiant energy through the opening. To study the distribution of radiant energy over different wavelengths, the black body is maintained at a constant temperature. By means of an infrared spectrometer and a bolometer the emissive powers of the black body for different wavelengths (or frequency) are measured. The results of the experiment conducted are illustrated in Fig. 1.1(b). The inference is that at a given temperature the radiation energy density initially increases with frequency, then peaks at around a particular frequency and after that decreases finally to zero at very high frequencies.

Black body radiation is an important phenomenon because its properties have a universal character, being independent of the properties of any particular material substance. The other conclusions are:

(i) The area under a curve which measures the total energy of radiation at that temperature, increases according to the fourth power of the absolute temperature. Thus, Stefans law is verified.

(ii) The maximum energy peak shifts towards the shorter wavelength side with the...