JNTU B.Tech I ENGINEERING PHYSICS II Previous Question Paper (July/August - 2021 - R16)

The dual nature of light refers to the phenomenon where light exhibits both wave-like and particle-like properties depending on the experimental conditions. This concept is central to quantum mechanics, bridging classical wave theory and quantum corpuscular theory.

Wave nature is demonstrated by phenomena such as interference, diffraction, and polarization, which are explained by treating light as an electromagnetic wave oscillating in space and time. Conversely, particle nature is evidenced by phenomena like the photoelectric effect, Compton scattering, and blackbody radiation, where light interacts with matter in discrete packets of energy called photons.

The energy of a photon is given by the relation:

where h is Planck's constant, ν is the frequency, and λ is the wavelength. This equation effectively links the wave property (frequency/wavelength) to the particle property (energy), establishing that light is neither purely a wave nor purely a particle, but possesses a dual character.

The Davisson-Germer experiment provided the first experimental proof of the de Broglie hypothesis, which states that moving particles exhibit wave-like properties. The experiment involved firing a beam of electrons at a nickel crystal and measuring the intensity of the scattered electrons at different angles.

1. An electron gun produces a beam of electrons, which are accelerated by a potential difference V toward a nickel crystal target.
2. The electrons scatter off the atomic planes of the crystal. A movable detector measures the intensity of the scattered electrons as a function of the scattering angle θ.
3. It was observed that for a specific accelerating voltage (54 V) and a specific angle (50°), there was a sharp maximum in the intensity of the scattered electrons. This peak is characteristic of constructive interference, similar to Bragg diffraction of X-rays.
4. The de Broglie wavelength of the electrons is calculated using the formula:
   λ = h / √(2meV)
5. Substituting the values (V = 54 V), the calculated wavelength is approximately 0.167 nm.
6. Using Bragg's law for the crystal lattice, nλ = 2d sin(φ), where d is the interplanar spacing, the experimental wavelength was found to be in excellent agreement with the theoretical value.

This diffraction pattern confirmed that electrons behave as waves with a wavelength associated with their momentum, thereby validating the existence of matter waves.