Final answer:
The concept of wave-particle duality is central to understanding quantum phenomena, with electron microscopes and the photoelectric effect serving as classic examples of wave and particle models, respectively. Quantum mechanics emerges as a necessity to explain observations beyond the realm of classical theories.
Step-by-step explanation:
The question deals with the wave-particle duality of light and matter, a fundamental concept in quantum physics. Electron microscopes use the wave nature of electrons to resolve microscopic details far beyond what conventional light microscopes can achieve, capitalizing on the short wavelengths associated with electron beams compared to visible light. The particle model of light is exemplified in the photoelectric effect, where light is shown to consist of particles (photons) with quantized energy that can eject electrons from a metal surface if their frequency is above a certain threshold. This dichotomy in behavior illustrates the wave-particle duality which shows that matter can display both wave-like and particle-like properties, challenging classical theories and necessitating quantum mechanics for a fuller understanding.
Observations at the atomic level that classical mechanics could not explain were pivotal in developing quantum theory. Wave-particle duality is a critical concept, highlighting that neither classical waves nor particles can wholly describe quantum phenomena. The quantum mechanics framework, interpreting matter waves as fundamental and statistical, allows for predictions about probable positions and properties of particles, leading to the formulation of Heisenberg's uncertainty principle and the foundation of modern quantum physics.