The dual nature of light

1. The dual nature of light • wave theory of light explains most phenomena involving light: • propagation in straight line • reflection • refraction • superposition, interference, diffraction • polarization • Doppler effect • wave theory does not explain: • frequency dependence of thermal radiation • photoelectric effect • 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)

2. 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  f4 • 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” = 6.63x10-34 Js • calculation of black body spectrum using Planck's hypothesis gives formula (“Planck formula”) which describes measured spectra. • = first evidence that energy is quantized

3. Photoelectric effect • (first observed by Heinrich Hertz in 1887) • electrons are emitted when certain metallic materials exposed to light (now used in photocells in cameras, and solar energy cells) • 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 • 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