Describe the properties and behavior of an object that exhibits both particle-like and wave-like behavior.

• Quantum theory was developed to explain observations of matter and energy that could not be explained using classical mechanics. These phenomena include, but are not limited to, atomic spectra, blackbody radiation, and the photoelectric effect.
• Quantum theory is necessary to describe the properties of matter at atomic and subatomic scales.
• In quantum theory, fundamental particles can exhibit both particle-like and wave-like behavior.
• Light can be modeled both as a wave and as discrete particles, called photons.
• A photon is a massless, electrically neutral particle with energy proportional to the photon’s frequency. Relevant equations:
• Photons travel in straight lines unless they interact with matter.
• The speed of a photon depends on the medium through which the photon travels.
• The speed of all photons in free space is equal to the speed of light, c = 3.00×10⁸ m/s.
• In general, the speed of photons through a given medium is inversely proportional to the index of refraction of that medium.
• Particles can demonstrate wave properties, as shown by variations of Young’s double-slit experiment.
• A wave model of matter is quantified by the de Broglie wavelength, which increases as the momentum of a particle decreases. Relevant equation:
• Quantum theory is necessary to describe systems where the de Broglie wavelength is comparable to the size of the system.
• Values of energy and momentum have discrete, or quantized, values for bound systemsdescribed by quantum theory.

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