Question

That radiation and matter have properties both of particles and of waves is called what? ​

Answer 1

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We call this twofold nature the particle-wave duality, meaning that EM radiation has both particle and wave properties. This so-called duality is simply a term for properties of the photon analogous to phenomena we can observe directly, on a macroscopic scale.

Answer 2

Wave - Particle Theory states that radiation and matter have properties both of particles and of waves.