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)

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

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