5. Wave-Particle Duality and the Development of Quantum Mechanics

Concept Explanation:

Wave-particle duality is the concept that all particles exhibit both wave-like and particle-like properties. This idea was first introduced by Louis de Broglie, who proposed that particles such as electrons have a wavelength associated with their momentum, given by:

λ = h / p

where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle.

This dual nature of particles was experimentally confirmed by the double-slit experiment, where electrons created an interference pattern characteristic of waves when passed through two slits, despite being particles.

The development of quantum mechanics, spearheaded by scientists like Schrödinger and Heisenberg, provided a mathematical framework for understanding the behavior of particles at the atomic and subatomic levels, where classical mechanics fails to accurately describe phenomena.

Example Problem:

Calculate the wavelength of an electron moving with a velocity of 2 × 10⁶ m/s. The mass of the electron is 9.11 × 10⁻³¹ kg.

Solution:

Using de Broglie’s equation:

λ = h / p = h / mv

Substitute the known values:

λ = 6.626 × 10⁻³⁴ J·s / (9.11 × 10⁻³¹ kg × 2 × 10⁶ m/s) = 3.63 × 10⁻¹⁰ m