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Heisenberg's Uncertainty Principle states that it's impossible to simultaneously know the exact position and momentum of a particle. It implies that particle behavior can only be probabilistically determined, reflecting wave-like properties.

The wave-particle duality suggests that electrons exhibit wave-like behavior. This leads to the concept of atomic orbitals, which represent the probability distribution of an electron's position, rather than defined orbits.

Phenomena such as electron diffraction and neutron scattering experiments demonstrate the wave nature of particles like electrons and neutrons, supporting the wave-particle duality of all matter.

The double-slit experiment, performed by Thomas Young in 1801, was key in establishing wave-particle duality, showing that light can display characteristics of both waves and particles.

In the context of wave-particle duality, 'quantum' refers to the smallest discrete quantity of some physical property that a particle can possess, highlighting the duality where these quantized properties sometimes behave like waves and sometimes like particles.

The de Broglie wavelength equation is $\lambda = \frac{h}{p}$, where $\lambda$ is the wavelength, $h$ is Planck's constant, and $p$ is the momentum of the particle.

Electron microscopes use the wave-like nature of electrons to achieve very high-resolution imaging by focusing electron waves using electromagnetic lenses, analogous to how light microscopes use the wave nature of light.

Louis de Broglie proposed the wave-particle duality theory in his 1924 PhD thesis, suggesting that all matter has both wave-like and particle-like properties.

The Compton effect demonstrates wave-particle duality by scattering photons off electrons and showing that light (photons) exhibits particle-like behavior, experiencing changes in wavelength upon interaction with electrons.