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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
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 electronhttp://www.colorado.edu/physics/2000
Modern PhysicsLarge objects
small speeds
“Newtonian Physics”
F = ma
Large objects
large speeds
“relativistic mechanics”
F = dp/dt
Atomic scalessmall speedsQuantum Mechanics“Schrödinger Equation”
Atomic particlesLarge speedsrelativistic quantum mechanics“Dirac Equation”
speed
size
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)
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
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
10000K
12500K
14500K Classical predictionfor 14500 K
As T decreases, of peak increases
Cannot explain the peak
Watts m-2s-1
Partially explained by Planck 19002
5 /
2 1( , )
1c Th k
hcR T
e
R(,T)
4
2( , )
ckTR T
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 constanth=6.63x10-34 J.s
Frequency 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