JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech I Year ENGINEERING PHYSICS - II Previous Question Paper (September - 2023 - R16)

Heisenberg's uncertainty principle states that it is fundamentally impossible to simultaneously measure both the exact position and the exact momentum of a particle with absolute precision. The product of the uncertainties in these two measurements is always greater than or equal to a constant value.

In this expression, Δx represents the uncertainty in position, Δp represents the uncertainty in momentum, and ℏ is the reduced Planck constant (h / 2π).

The E-K curve, or dispersion relation, represents the relationship between the energy (E) of an electron and its wave vector (k) in a crystal lattice. Its importance lies in understanding the electronic properties of materials:

• Band Gap Determination: The curve reveals the existence of allowed energy bands separated by forbidden energy gaps, which distinguish conductors, semiconductors, and insulators.
• Effective Mass: The curvature of the E-K plot is inversely proportional to the effective mass of the electron, defined by the formula:
  m* = ħ² / (d²E / dk²)
  This explains how electrons respond to external electric fields within the periodic potential of the crystal.
• Charge Carrier Dynamics: It helps identify the velocity of electrons and holes, where the group velocity is given by v = (1/ħ) (dE/dk).

The plot typically shows parabolic energy bands for free or nearly-free electrons, with discontinuities at the Brillouin zone boundaries due to Bragg reflection of electron waves by the periodic crystal potential.