1. 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

2. Water waves flare out when passing through opening of width a a

3. 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 lightelectron http://www.colorado.edu/physics/2000

4. Double Slit Experiment with electrons (1989)

5. Modern Physics Large objects small speeds “Newtonian Physics” F = ma Large objects large speeds “relativistic mechanics” F = dp/dt Atomic scales small speeds Quantum Mechanics “Schrödinger Equation” Atomic particles Large speeds relativistic quantum mechanics “Dirac Equation” speed size

6. Electromagnetic Waves Maxwell(1860) showed that light is a travelling wave of electric and magnetic fields E = E m sin (kx-  t) B = B m 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)

7. Transverse Wave E and B are both  to v and E  B

8. 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

9. Electromagnetic Spectrum Power   2

10. Sensitivity of eye to various

11. Radiation heated objects “glow” if the temperature is high enough =>embers in a fire, stove element => bar of steel heated to 1200 0 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

12. 1000 0 K 1250 0 K 1450 0 K Classical prediction for 1450 0 K As T decreases, of peak increases Cannot explain the peak Watts m -2 s -1 Partially explained by Planck 1900 R(,T)

13. 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 Planck’s constant h=6.63x10 -34 J.s Frequency c= f

14. Modern Physics h plays a similar role to c in relativity if c   then no relativity! v/c signals transmitted instantaneously if h  0 then no quantum mechanics => no stable atoms!

15. 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)(3x10 8 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 10 20

16. Example The amount of sunlight hitting the earth is about 1000 W/m 2 and ~ 500 nm photons/sec/m 2 ~ 2.5x 10 21 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