JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech I Year APPLIED PHYSICS Previous Question Paper (January - 2021 - R18)

de-Broglie's Hypothesis states that matter, like radiation, exhibits a dual nature, behaving as both particles and waves. Louis de Broglie proposed that any moving particle with momentum p is associated with a wave, known as a matter wave or de-Broglie wave, whose wavelength λ is inversely proportional to its momentum.

where h is Planck's constant, m is the mass of the particle, and v is its velocity. This hypothesis suggests that the wave nature is inherent to all matter, though it is only significant for particles with extremely small mass, such as electrons.

Davisson and Germer Experiment provided the first experimental verification of de-Broglie's hypothesis by demonstrating electron diffraction.

• Experimental Setup: The apparatus consists of an electron gun that emits a beam of electrons, accelerated by a potential difference V. This beam is directed at a nickel crystal. A movable detector is used to measure the intensity of the scattered electrons at various angles θ relative to the incident beam.
• Observation: Davisson and Germer observed that the intensity of scattered electrons was not uniform but showed a distinct peak at an accelerating voltage of 54V and a scattering angle of 50°. This pattern is characteristic of wave interference, similar to X-ray diffraction from crystal planes.
• Verification: According to Bragg's Law for diffraction, nλ = 2d sin θ, where d is the interplanar spacing of the nickel crystal. For n=1 and d=0.091 nm, the experimental wavelength was calculated to be approximately 0.165 nm.
• Theoretical Calculation: Using de-Broglie's relation for an electron accelerated through 54V:

The close agreement between the experimental value (0.165 nm) and the theoretical value (0.167 nm) confirms the wave nature of electrons, thereby validating de-Broglie's hypothesis.