JNTU B.Tech I Year 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 setup. This fundamental concept in quantum mechanics reconciles classical wave theory with quantum observations.

• Wave Nature: Light behaves as an electromagnetic wave, characterized by phenomena such as interference, diffraction, and polarization. These properties are explained by Maxwell's equations, where light propagates as oscillating electric and magnetic fields.
• Particle Nature: Light interacts with matter as discrete packets of energy called photons. This is evidenced by the photoelectric effect and Compton scattering, where light energy is quantized as E = hν (where h is Planck's constant and ν is frequency).
• Synthesis: The dual nature is unified by the relationship between momentum (p) and wavelength (λ), given by de Broglie's relation: λ = h/p. In macroscopic scenarios, wave characteristics dominate, while in microscopic interactions with atoms or electrons, particle characteristics become prominent.

The Davisson-Germer experiment provided the first experimental proof of de Broglie's hypothesis that particles, such as electrons, exhibit wave-like behavior. The experimental setup involves:

• Electron Gun: A tungsten filament heated to emit electrons, which are accelerated by a potential difference (V) toward a nickel crystal.
• Target: A single crystal of nickel acts as a diffraction grating.
• Detector: A movable collector (Faraday cylinder) measures the intensity of scattered electrons at various angles (θ).

Observations:

• When a beam of electrons is directed at the nickel crystal, it is scattered in different directions. A distinct peak in the intensity of scattered electrons is observed at an angle of 50° when the accelerating voltage is 54V.
• This peak corresponds to constructive interference, analogous to X-ray diffraction from crystal planes, confirming that electrons undergo diffraction as waves.
• Using Bragg's Law (2d sin θ = nλ) for the nickel crystal spacing (d = 0.91 Å), the experimental wavelength is calculated to be approximately 1.65 Å.
• This matches the theoretical value derived from de Broglie's equation: λ = h / √(2meV) ≈ 1.67 Å.

The close agreement between the experimental and theoretical values confirms the wave nature of matter.