# Dual Nature of Light

♦ Learn about : Dual Nature of Light , De Broglie Hypothesis , Characteristics of Matter Waves , Effective Mass of Photon , De -Broglie Wavelength Associated with Moving Particles ♦

Dual Nature of Light :
There are some experimental phenomena of light like reflection, refraction, interference, diffraction etc., which can be explained only on the basis of wave theory of light, i.e. these phenomena verify the wave nature of light. There are some experimental phenomena of light itself like photoelectric effect, compton effect raman effect etc….

Which can be explained only on the basis of the particle nature of light (i.e. quantum theory) i.e. these phenomenon verify the particle nature of light on the basis of the above experimental phenomena it was inferred that light does not have any definite nature, rather its nature depends on its experimental phenomenon.

In some experimental phenomena it behaves like particles (i.e. photons). This is known as the dual theory of light. The wave nature and particles nature both can be possible simultaneously.

### De Broglie Hypothesis

de Broglie imagined that as light (i.e. energy in general) possesses both nature (i.e. wave and particle) similarly matter must also posses both nature particle as well as wave. As matter consists of minute particles, hence its nature is particles nature. de Broglie imagined that despite particle nature of matter waves must also be associated with material particles. These imaginary waves presumed to be associated with material particles, are defined as matter waves.

Matter Waves:

The waves presumed to be associated with moving material particles on the imagination of de Broglie are defined as matter waves.

Characteristics of Matter Waves:

• The wavelength of matter waves is inversely proportional to the momentum of the particle.
• Matter waves travels even in vacuum, hence these are not mechanical waves.
• Matter waves are produced due to the motion of material particle. These waves are associated with every moving particles.
• Actually matter waves are probabilistic waves because these waves represent the probability of fining a particle in space.
• Practical observation of matter waves is possible only when the wave length of matter wave is greater than the size of the particle (i.e. λ >> a).
• These waves are also associated with electrically natural particle hence these cannot be the electromagnetic waves even.
• Matter waves propagate in the form of wave packet with group velocity.
• The phase velocity of matter waves can be greater than the light.
• The wavelength of matter waves does not depend on the nature and charge of the particle.

### Data Related to Photon:

According to Plank’s quantum theory the energy of photon is given by

E = hν    ,  where    h = Plank’s constant

since , c = νλ

E = hc/λ

λ = wavelength of photon

ν = frequency of photon

#### Effective Mass of Photon:

According to Einstein’s theory, if the energy (hn) of photon is converted into matter then the mass of matter created or the mass of photon in moving state is defined as the effective mass of photon. If the effective mass of the photon is m then according to Einstein’s mass – energy relation its energy is

E = mc2  = hν  = hc/λ

Effective mass of photon ,  m = E /c2 = hν/c2

The momentum of photon , P = mc = E/c = hν /c = h/λ

The wavelength associated with photon , λ = h/P = h/mc

Photon is an uncharged particle, its rest mass is zero, spin is h and its velocity is equal to that of light.

###### de Broglie Wavelength Associated with Moving Particles :

Energy of a particle of mass m and moving with velocity v . where, P = momentum of particle

momentum of particle P = mv = √(2mE)

According to de Broglie theory the wavelength associated with the particles. The order of magnitude of wave lengths associated with microscope particles is 10–24Å. Whereas the smallest wavelength whose measurement is possible is that of g-rays (g ~ 10–5 Å – 1Å). This is the reason why the wave nature of microscopic particles is not observable.

The wavelength of matter waves associated with the particles like electron, photon, neutron a-particle, atom molecule etc. is of the order of 10–10 m, the wavelength of X-rays, which is within the limit of measurement. Hence the wave nature of such particles is observable.