Solved Examples on Dual Nature of Light
Example 1: What is the De-Broglie wavelength associated with an electron, accelerated through a potential difference of 100 Volts?
Answer:
De-Broglie wavelength associated with an electron accelerated through a potential difference of V,
λ = 12.27/√V A°
In the question V = 100 Volts
λ = 12.27/√100 A°
λ = 12.27/10 A°
λ = 1.227 A°
Example 2: Find the De-Broglie wavelength associated with an electron moving with a velocity 0.5c and rest mass = 9.1×10-31 kg.
Answer:
De-Broglie wavelength associated with an electron moving with a velocity v
λ = h /mv
In the given question, v = 0.5c = 0.5 × 3×108 = 1.5×108 m/s
λ = 6.6×10-34/ (9.1×10-31×1.5×108)
λ = 4.8 × 10-12 m
Example 3: What will be the De-Broglie wavelength of an electron of energy 400 eV? Given h = 6.6×10-34 J-s , e = 1.6×10-19C and m = 9.1×10-31 kg.
Answer:
De-Broglie wavelength λ in terms of energy E is given by,
λ = h/√(2mE)
λ = 6.6×10-34/√(2×9.1×10-31×400×1.6×10-19)
λ = 0.611 A°
Example 4. For what kinetic energy of a proton, will the associated De-Broglie wavelength be 16.5 nm? Mass of proton = 1.675×10-27, h = 6.63×10-34 J-s.
Answer:
De-Broglie wavelength in terms of kinetic energy is given by,
λ = h/√(2mEk )
Ek = h2/(λ22m)
Ek = ( 6.63×10-34)2/[(16.5×10-9)2×2×1.675×10-27]
Ek = 4.82×10-25 J
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.