The dual nature of light l wave theory of light explains most phenomena involving light: propagation in straight line reflection refraction superposition, interference, diffraction polarization Doppler effect l wave theory does not explain: frequency dependence of thermal radiation photoelectric effect l IS LIGHT A WAVE OR A PARTICLE? answer: it is both, depending on what question you ask: it has a “wave'’ aspect and a “particle” aspect Note: according to quantum theory, “particles” (e.g. electrons, protons,..) have also a “wave” aspect! (depends on what question you ask)

Thermal radiation experimental observations:  atoms of a hot solid emit radiation;  increase in temperature  more radiation, and component of maximum intensity shifted towards higher frequency (shorter wavelength) “classical” explanation: the hotter the solid, the more vibrational energy  higher frequency of vibration of atoms/electrons  higher frequency of radiation but frequency spectrum of this radiation (“black body radiation” calculated within framework of electromagnetism and thermodynamics did not agree with measured spectrum; predicted “ultraviolet catastrophe” I  f 4 l Max Planck's hypothesis (1900): energy is quantized; “oscillators” (oscillating atoms) can only have certain amounts of energy relation between energy and frequency of oscillator: E = h f, where h = “Planck’s constant” = 6.63x Js calculation of black body spectrum using Planck's hypothesis gives formula (“Planck formula”) which describes measured spectra. = first evidence that energy is quantized

Photoelectric effect l (first observed by Heinrich Hertz in 1887) l electrons are emitted when certain metallic materials exposed to light (now used in photocells in cameras, and solar energy cells) l some aspects of photoelectric effect could not be explained by classical theory: classical theory: if light continuos flow of e.m. energy takes some (calculable) time for wave to supply sufficient energy for electron to be emitted; find experimentally: current flows almost immediately upon exposure to light; classical theory: light of any frequency could cause photoelectric effect - need only sufficient intensity find experimentally: only light with frequency above certain minimum frequency causes electrons to be emitted classical theory: energy of electrons depends on light intensity find experimentally: energy of electrons depends on frequency l Albert Einstein's explanation : assume that not only energy in atoms is quantized, but also energy carried by light light comes in “packets of energy” called light quanta or photons energy of one photon = h f, where f = frequency of the light. with this assumption, all aspects of photoelectric effect could be explained photon energy vs color of light: E = hf = hc/  blue light has more energy than red light