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Wave-Particle Duality • e/m radiation exhibits diffraction and interference => wave-like • particles behave quite differently - follow well defined paths and do not produce interference patterns • when << size of opening, wave behaves like a particle • light exchanges energy in “lumps” or ‘quanta’ just like particles Water waves flare out when passing through opening of width a a Wave-Particle Duality • • • • • • • • 1900: sound, light, e/m radiation were waves electrons, protons, atoms were particles 1930: quantum mechanics provided a new interpretation light behaves as a particle: photoelectric & Compton effect E=hf = hc/ p=h/ particles behave as waves: electron diffraction => localized packets of energy => particle-like f, “wave-particle duality” E,p light http://www.colorado.edu/physics/2000 electron Double Slit Experiment with electrons (1989) Modern Physics Large objects Large objects small speeds large speeds “Newtonian Physics” “relativistic mechanics” F = ma F = dp/dt size Atomic scales small speeds Quantum Mechanics “Schrödinger Equation” speed Atomic particles Large speeds relativistic quantum mechanics “Dirac Equation” Electromagnetic Waves • Maxwell(1860) showed that light is a travelling wave of electric and magnetic fields • E = Em sin (kx-t) • B = Bm sin (kx-t) • v= /k = c ~ 3 x 10 8 m/s • the speed is the same in all reference frames • v= c/n in material media ( n=1 for vacuum) Transverse Wave E and B are both to v and E B Light • Light is a wave c=f • => exhibits interference and diffraction • => oscillating electric and magnetic fields are solutions of Maxwell’s equations • => Maxwell’s equations predict a continuous range of ’s from -rays to long radio waves • electromagnetic spectrum Electromagnetic Spectrum Power 2 Sensitivity of eye to various Radiation • heated objects “glow” if the temperature is high enough • =>embers in a fire, stove element • => bar of steel heated to 12000 K glows in deep red colour • thermal radiation • charges in material vibrate in SHM(accelerate) and produce e/m radiation • also occurs at lower T but is longer => infra-red and not visible R(,T) 14500K Classical prediction for 14500 K Cannot explain the peak R ( , T ) 2 ckT Watts m-2s-1 4 12500K 10000K As T decreases, of peak increases Partially explained by Planck 1900 R ( , T ) 2 c 2 h 1 5 ehc / kT 1 Modern Physics • 1905 Einstein proposed: • when an atom emits or absorbs light, energy • is not transferred in a smooth continuous fashion but rather in discrete “packets” or “lumps” of energy • “photons” have energy E=hf Frequency Planck’s constant h=6.63x10-34 J.s c=f Modern Physics • h plays a similar role to c in relativity • if c then no relativity! v/c <<1 always => signals transmitted instantaneously • if h 0 then no quantum mechanics => no stable atoms! Example • Consider a 100W sodium vapour lamp with = 590 nm • what is the energy of a single photon? • E=hf = hc/ =(6.63x10-34 J.s)(3x108 m/s)/590x10-9 m) = 3.37x10-19 J • Power = dE/dt =[number of photons/sec] x 3.37x10-19 J = 100 W • number of photons/sec = 3 x 1020 Example • The amount of sunlight hitting the earth is about 1000 W/m2 and ~ 500 nm • photons/sec/m2 ~ 2.5x 1021 • we do not see the grainy character of the energy distribution => appears continuous • photoelectric effect (lab 4) • if we shine a beam of light of short enough onto a clean metal surface, the light will knock electrons out of the metal surface