INTRODUCTION Wave and particle duality To understand the wave and particle duality, it is necessary to know what is a particle and what is a wave. The concept of a particle is easy to grasp. It has mass, it is located at some definite point, it can move from one place to another, it gives energy when slowed down or stopped. Thus, the particle is specified by i mass m, ii velocity v, iii momentum p, and iv energy E. The concept of a wave is a bit more difficult than that of a particle. A wave is spread out over a relatively large region of space, it cannot be said to be located just here and there, it is hard to think of mass being associated with a wave. Actually a wave is nothing but rather a spread out disturbance. A wave is specified by its i frequency, ii wavelength, iii phase of wave velocity, iv amplitude, and v intensity. Considering the above facts, it appears difficult to accept the conflicting ideas that radiation has a dual nature, i.e., radiation is a wave which is spread out over space and also a particle which is localised at a point in space. However, this acceptance is essential because radiation sometimes behaves as a wave and at other times as a particle as explained below i Radiations including visible light, infra-red, ultraviolet, X-rays, etc. behave as waves in experiments based on interference, diffraction, etc. This is due to the fact that these phenomena require the presence of two waves at the same position at the same time. Obviously, it is difficult for the two particles to occupy the same position at the same time. Thus, we conclude that radiations behave like wave. ii Planck s quantum theory was successful in explaining black body radiation, the photoelectric effect, the Compton effect, etc. and had clearly established that the radiant energy, in its interaction with matter, behaves as though it consists of corpuscles. Here radiation interacts with matter in the form of photons or quanta. Thus, we conclude that radiations behave like particle. Radiations, thus, sometimes behave as a wave and at some other time as a particle, i.e., it has a wave particle dualism. Here it should be remembered that radiation cannot exhibit its particle and wave properties simultaneously. 1.1
Matter Waves According to de-Broglie s hypothesis, a moving particle is associated with a wave which is known as de-Broglie wave. The wavelength of the matter wave is given by l
h h , mv p
where m is the mass of the material particle, v its velocity and p is its momentum.
1.1 WAVE VELOCITY AND GROUP VELOCITY