What are photons? What role did Einstein's explanation of the photoelectric effect play in the development of the particle-wave interpretation of the nature of electromagnetic radiation?

A photon is a type of elementary particle that represents a quantum of light or other electromagnetic radiation. It carries energy proportional to the radiation frequency but has zero rest mass. The energy of a photon is given by the Planck-Einstein relation: \[E=hf\] where \(E\) is the energy of the photon, \(h\) is the Planck constant, and \(f\) is the frequency of the light.

Einstein proposed that light is composed of individual packets of energy called photons. This concept explained the photoelectric effect: the emission of electrons or other free carriers when light shines on a material. Electrons emitted in this manner are called photoelectrons. This happens because photons in the light beam transfer their energy to the electrons, giving the electrons enough energy to be 'knocked' out of their atoms. The energy required to knock an electron out is known as the work function, symbolized by \(ϕ\). If the energy of the photon, \(hf\), is more than the work function, \(ϕ\), the electron will be emitted with a maximum kinetic energy, \(K.E.\) given by: \[K.E.=hf-ϕ\) This explanation, which contrasted with the wave theory of light prevailing at that time, won Einstein the Nobel Prize in Physics in 1921.

What Einstein's interpretation provided was a particle description of light, which reasoned that light can behave as both a wave and a particle. This dual nature is known as the wave-particle duality and is a fundamental concept in quantum theory. This new understanding marked an important development in physics as it integrated two previously incompatible views - the wave theory and particle theory of light. In particular, it enabled the development of quantum mechanics, where particles may exhibit both types of behavior.