De-Broglie’s Hypothesis
According to De-Broglie as there is symmetry in nature, particles must behave as waves.
For light radiation of wavelength λ, according to the Planck equation,
E = hc/λ, where E is energy, c is the speed of light, λ is wavelength and h is Planck’s constant, 6.63×10-34 Js.
By Einstein’s mass energy relation
E = mc2, where E is energy, m is mass and c is the speed of light.
From equations (1) and (2), we have
=> mc2 = (hc/λ)
=> mc = (h/λ)
=> λ = h/mc
According to De-Broglie
If a particle of mass ‘m’ is moving with velocity ‘v’, then the wavelength associated with it is given by,
λ = h/mv (as p = mv)
λ = h/p
where, p is the momentum
The Kinetic Energy of the particle is given by
Ek = p2/(2m) [p =√(2mEk )]
then, λ in terms of kinetic energy Ek is given by,
λ = h/√(2mEk )
If the charged particle q is accelerated by potential difference V, then the wavelength is given by,
Ek = qV
λ = h/√(2mqV)
If the electron e is accelerated by potential difference V, then the wavelength is given by,
λ = h/√(2meV )
Substituting m = 9.1 × 10-31 kg , h = 6.63 × 10-34 J-s , e = 1.6 × 10-19 C
λ = √(150/V) 10-10
λ = √(150/V) A°
λ = 12.27/√V A°
Dual Nature of Light
Dual nature of light describes that light has dual nature. It behaves as both particle i.e. corpuscles nature (Energy particle of Planck) and waves nature i.e. electromagnetic waves. In phenomena like the Compton effect, the Photoelectric effect light behaves as the particle, and in the phenomenon of light diffraction, interference, and polarization light behaves as the wave because they are explained based on wave theory. In the microscopic description, if the light is propagating in the medium then the wave nature of light is considered and if light mutually interacts with the matter then the particle nature of the light is considered.
Basic Terminology
- Photon: According to Planck’s quantum theory of radiation, an electromagnetic wave travels in the form of discrete packets called quanta. This one quantum of light radiation is called a photon.
- Photoelectric Effect: The phenomenon of emission of electrons from a metal surface, when electromagnetic radiations of sufficiently high frequency are incident on it, is called the photoelectric effect.
- Compton Effect: The scattering of a photon by an electron is called the Compton effect.
- De-Broglie Waves: The wave associated with the moving particles are called matter waves or De-Broglie waves.