## LESSON 5. Basic concept of Wave and Particle

For the wave and particle duality we must to know,

What is a particle?

What is wave?

The concept of particle is easy to understand because

(i) It has mass

(ii) It is located at definite point

(iii) It moves from one to another place.

(iv) It gives energy when stopped.

The concept of wave is quite difficult compare to particle because

(i) A wave is spread out over a relatively large region of space

(ii) It is can’t be said to be location.

(iii) It is hard to think of mass being associated with it.

For a simplicity,

The wave is specified by its

(i) Frequency

(ii) Wavelength

(iii) Phase or wave velocity

(iv) Amplitude

(v) Intensity

Basic of above concept, It is difficult to accept the conflicting ideas that, the radiation has dual nature; the radiation is a wave, which is spread out over the space. So, the radiation sometimes behaves like a wave and as a particle.

How is it?

(i) Visible light

(ii) Infrared

(iii) Ultra-violet ray and X-Ray are behaved as a wave in the phenomena of interference and diffraction.

Because in these phenomena. Two waves are simultaneously coinciding at the same position at same time. Actually, it is difficult for two particles to occupy the same position at same time. So the radiation behaves like wave.

The Black Body Radiation, Photoelectric Effect and Compton Effect are established that there is a interaction of radiation energy with matter. Here radiation interact with matter in the form of photons so radiation behaves liked a particle. Thus, the wave and particle nature is not exhibits simultaneously.

De-Broglie Concept of matter wave

From phenomena of Diffraction, Interference and Polarization,

It is noted that light is one kind of wave motion. Further, some new phenomena such as Photo-electric Effect and Compton Effect are not explained on the basis of wave-theory. But these are explained on the basis of quantum theory.

In quantum theory, the light or photons are asset with literature on mass, velocity and momentum.

But photon theory was applied to the phenomena of interference and diffraction. It is not able to explain.

So light has dual nature, it posses both particle and wave properties.

• In some cases, the waves are predominant and some other cases the particles are predominant.

• The dual properties are depending upon the condition under which the particular phenomena occur.

• It is note that wave and particle never expected to appear together.

De-Broglie extended the wave-particle parallelism of optics to all fundamental things existing independently from other things.

Fundamental existing things like

• Electron

• Protons

• Neutrons

• Atoms and

• Molecules

He suggested that matter has also dual nature i.e. wave and particle like radiation. There is detail connection between waves and written work in caseof particle also.

A moving particle is always associated with the wave and it is controlled by wave same as photon is controlled by wave.

On the concept of wave-particle duality, he noted that if the radiation (light) can act as wave sometime and act as particle at other time.

Then the material (matter) particle (electron and neutron) should act as wave at some other times. Hence, the De-Broglie hypothesis

A moving particle is associated with wave which is known as De-Broglie wave.

The wavelength of matter wave is

$\lambda$ = ${h \over {mv}}$ = ${h \over P}$

m Mass of material particle

v Velocity of material particle

P Momentum of material particle