JNTU B.Tech I ENGINEERING PHYSICS - II Previous Question Paper (November/December - 2020 - R16)

The Davisson-Germer experiment provided the first experimental proof of the de Broglie hypothesis, which states that particles of matter exhibit wave-like properties. The experiment involved firing a beam of electrons at a nickel crystal and observing the diffraction pattern of the reflected electrons.

The experimental setup consists of an electron gun that produces a beam of electrons accelerated by a potential difference. This beam is directed at a target of nickel crystal. A movable detector is used to measure the intensity of the scattered electrons at various angles relative to the incident beam.

The key observation was that the intensity of the scattered electrons varied significantly with the angle of scattering. A distinct peak in intensity was observed at an angle of 50 degrees when the accelerating voltage was 54 volts. This behavior is characteristic of wave diffraction, similar to X-ray diffraction from crystal planes as described by Bragg's Law:

In this equation, d is the lattice spacing of the nickel crystal, θ is the glancing angle, and λ is the wavelength of the electron. By substituting the known lattice spacing of nickel (0.091 nm) and the experimental angle, the calculated wavelength was found to be approximately 0.167 nm.

This result was compared with the theoretical wavelength predicted by the de Broglie relation:

Using the values for Planck's constant (h), electron mass (m), charge (e), and the accelerating voltage (V = 54 V), the calculated de Broglie wavelength was also approximately 0.167 nm. The close agreement between the experimental result and the theoretical prediction confirmed that electrons behave as waves with a wavelength inversely proportional to their momentum, thereby verifying the wave nature of matter.