Define Dual Nature of Matter.

The dual nature of matter is a fundamental concept in quantum mechanics that asserts that particles, such as electrons and photons, exhibit both particle-like and wave-like properties under different circumstances. This duality challenges classical notions of distinct particle or wave behavior and is encapsulated in the wave-particle duality principle.

In the wave aspect, particles exhibit characteristics similar to waves, with properties like interference and diffraction. This wave nature is described by a mathematical function known as the wave function, which represents the probability amplitude of finding a particle at a particular location.

On the other hand, particles also display particle-like behavior, such as localized position and discrete energy levels. This is evident in phenomena like the photoelectric effect, where light behaves as discrete particles (photons), and in the double-slit experiment, where electrons exhibit an interference pattern characteristic of waves.

The dual nature of matter is exemplified by Louis de Broglie's wave-particle duality hypothesis and later confirmed by experiments and observations in quantum mechanics. This concept revolutionized our understanding of the microscopic world and laid the groundwork for the development of quantum theory, profoundly influencing modern physics.