JNTU B.Tech I APPLIED PHYSICS Previous Question Paper (June - 2022 - R18)

According to the Planck-Einstein relation, the energy of a photon is given by E = hν = hc/λ. From Einstein's mass-energy equivalence, E = mc². Equating these two expressions for a photon, we have mc² = hc/λ, which simplifies to λ = h/mc = h/p, where p is the momentum. De Broglie extended this concept to all material particles, proposing that a particle of mass m moving with velocity v has an associated wavelength λ given by the de Broglie relation:

where h is Planck's constant and p is the linear momentum of the particle.

The existence of matter waves was experimentally verified by Davisson and Germer in 1927 by observing the electron diffraction pattern from a nickel crystal.

The experimental setup consists of an electron gun that produces a beam of electrons, accelerated by a potential V towards a nickel 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 (θ) relative to the incident beam.

The key observations were:

• At a specific accelerating voltage of 54 V and a scattering angle of 50°, a sharp maximum in the intensity of scattered electrons was observed.
• This diffraction pattern is analogous to X-ray diffraction from crystal planes, confirming the wave nature of electrons.
• The wavelength λ of the electrons can be calculated using Bragg's Law, 2d sin θ = nλ, where d is the interplanar spacing of the nickel crystal. For the observed peak, the calculated wavelength was approximately 1.65 Å.
• This value matches the theoretical de Broglie wavelength calculated using λ = h / sqrt(2meV), confirming that electrons exhibit wave-like behavior.