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 electronhttp://www.colorado.edu/physics/2000

Double Slit Experiment with electrons (1989)

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)

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

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