Explain the concept of wave-particle duality and provide an example.

Wave-particle duality is a fundamental concept in quantum mechanics that describes the dual nature of particles, such as electrons and photons. It suggests that these particles can exhibit both wave-like and particle-like properties depending on the experimental conditions.

In the classical view of physics, particles were thought to behave solely as discrete, localized entities with distinct positions and trajectories. On the other hand, waves were described as continuous, spread-out phenomena characterized by properties like frequency, wavelength, and interference patterns.

However, in the early 20th century, scientists like Albert Einstein and Max Planck proposed that light, previously considered a wave, could also exhibit particle-like behavior. This idea was further developed by Louis de Broglie, who proposed that if light could have particle-like properties, then particles like electrons, which were traditionally thought of as particles, could also exhibit wave-like properties.

One of the key experiments illustrating wave-particle duality is the double-slit experiment. In this experiment, a beam of particles, such as electrons or photons, is directed at a barrier with two slits. When the particles pass through the slits and hit a screen on the other side, they create an interference pattern, similar to what is observed with light waves. This interference pattern demonstrates the wave-like nature of the particles.

However, when the experiment is conducted with detectors placed at the slits to determine which slit each particle passes through, the interference pattern disappears, and particles behave as distinct, localized entities. This behavior reflects their particle-like nature.

Wave-particle duality challenges our classical intuition because it suggests that particles can exhibit contradictory properties depending on how they are observed or measured. It has profound implications for our understanding of the quantum world, where particles can exist in superposition states, meaning they can simultaneously behave as both particles and waves until observed or measured. This concept is a cornerstone of quantum mechanics and has led to numerous groundbreaking discoveries and technological advancements in fields like quantum computing and quantum cryptography.