Jawaharlal Nehru Technological University Hyderabad B.Tech I ENGINEERING PHYSICS II Previous Question Paper (November/December - 2020 - R16)

The Davisson-Germer experiment provided the first experimental proof of the wave nature of matter, as proposed by de Broglie. The apparatus consists of an electron gun that emits a beam of electrons, which are accelerated by a potential difference towards a nickel crystal target. The electrons strike the crystal and are scattered in various directions. A movable detector measures the intensity of the scattered electrons at different angles.

Key observations and findings:

• When the accelerating potential was set to 54 V, a sharp peak in the intensity of scattered electrons was observed at a scattering angle of 50 degrees relative to the incident beam.
• This peak corresponds to constructive interference, similar to Bragg diffraction of X-rays by crystal planes.
• According to Bragg's law, the condition for constructive interference is given by:

where d is the interplanar spacing of the nickel crystal (0.091 nm), θ is the glancing angle (which is 65 degrees for a 50-degree scattering angle), and λ is the wavelength of the electron wave. Substituting these values, the experimental wavelength is calculated to be approximately 0.165 nm.

Verification of the de Broglie hypothesis:

• The de Broglie wavelength for an electron accelerated through a potential V is given by:

Substituting V = 54 V, the theoretical wavelength is calculated to be approximately 0.167 nm. The close agreement between the experimental value (0.165 nm) and the theoretical value (0.167 nm) confirms that electrons exhibit wave-like behavior and undergo diffraction, thereby validating the de Broglie hypothesis.