Introduction to Classical Mechanics:

• Classical Mechanics is a branch of physics, which deals with the motion of the objects, which are directly observable or with the help of the instruments like microscope. These objects are known as macroscopic particles.
• Quantum Mechanics is a branch of physics, which deals with the motion of the objects, which are not observable or even with the help of the instruments like microscope. These objects are known as Microscopic particles.

Classical Mechanics failed to explain the following

1. Stability of Atom
2. Black body of Radiation
3. Spectrum of Hydrogen
4. Photo Electric Effect
5. Compton Effect
6. Specific Heat of Solids…..etc

• In 1904 to explain all these, the Quantum Mechanics was introduced.
• According to Classical theory, the energy of radiation takes place continuously. But according to Planck’s idea the energy take s place only discontinuously and discretely i.e, energy releases in the form of Energy Packets. Each Packet is called “Quanta”.

Waves and Particles :

• A particle 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 (1) Mass m (2) Velocity v (3) Momentum p and (4) Energy E
• 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 a rather spread out disturbance. A wave is specified by its (1) Frequency (2) Wavelength (3) Phase of wave velocity (4) Amplitude and (5) Intensity

(1) Frequency :

 Frequency describes the number of waves that pass a fixed place in a given amount of time.  $$\nu =\frac{c}{\lambda}$$

(2) Wavelength :

The distance, measured in the direction of propagation of a wave, between two successive crests or troughs in the wave that are characterized by the same phase of oscillation is called as Wavelength.

(3) Phase of wave velocity :

The velocity with which a simple harmonic wave is propagated, equal to the wavelength divided by the period of vibration.

(4) Amplitude :

The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position. It is equal to one-half the length of the vibration path.

(5) Intensity :

• Intensity is the power transferred per unit area.
• 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 localized 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.
• 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.
• Planck’s quantum theory was successful in explaining black body radiation, the photo electric 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 photon or quanta. Thus, we conclude that radiations behave like particles.