SUMMARY OF CLASSICAL PHYSICS

MECHANICS

OPTICS

ELECTRICITY

HEAT

SEEMS TO WORK FOR THE VERY BIG(GALAXIES) AND HUMAN SCALE,BUT WHAT ABOUT AT ATOMIC SCALE?

LINE SPECTRA

IN 1817, FRAUNHOFER OBSERVED THATTHE SUN’S SPECTRUM HAD DARK LINES

THESE FREQUECIES WERE THE SAME AS THOSE ABSORBED BY HOT GASES

THESE LINES CAME IN SEVERAL SERIES

GASES ABSORB AND EMIT LIGHT AT CERTAIN FREQUENCIES (SPECTRAL LINES)

PHOTO-ELECTRIC EFFECT

IN 1887 HERTZ OBSERVED THAT ELECTRONS WERE EMITTED FROM A METAL WHENLIGHT WAS SHONE ON IT

THE ENERGY OF THE ELECTRONS DID NOTDEPEND ON THE INTENSITY OF THE LIGHT

ELECTRON ENERGY WAS DEPENDENT ON THE FREQUENCY OR WAVELENGTH OF THE LIGHT, ABOVE A CRITICAL FREQUENCY.DIFFERENT FOR EACH METAL

DISCOVERY OF THE ELECTRON

1899 THOMSON MEASURED THE CHARGE/MASS RATIO OF AN ELECTRON

1909 MILLIKEN MEASURED THE ELECTRON CHARGE q= -1.6 x 10-19 COULOMBSEASY TO CALCULATE THE MASS 9.1x10-31 kg

IT WAS ASSUMED THE ELECTRONS WERE IMBEDDED IN A POSITIVE MATRIX

RADIOACTIVITY

1896 BECQUEREL STUDIED THE RADIATIONEMITTED FROM URANIUM SALTS

HE FOUND THREE TYPES OF RADIATION

BETA RAYS - ELECTRONS (-VE CHARGE)

GAMMA RAYS - LIKE X-RAYS

ALPHA RAYS - He NUCLEI - +2 CHARGE

DISCOVERY OF THE NUCLEUS

RUTHERFORD (AT McGILL) STUDIED HOWALPHA PARTICLES INTERACT WITH MATTER

Lead sheet

Gold foil

scintillator

Source ofalpha particles

LIKE BOUNCING A CANNONBALL OF A KLEENEX!!

Small scatterexpected

High angle scattering

NUCLEUS

MASS OF ALPHA PARTICLE = 8000 ELECRONS

MATTER MUST HAVE SMALL DENSE NUCLEI

THESE NUCLEI HAVE POSITIVE CHARGE

ELECTRONS ARE IN ORBIT AROUND THE NUCLEI

BUT! ACCELERATING CHARGES LOSE ENERGY!!!

BLACK BODY RADIATION

ALL HOT BODIES EMIT RADIATIONTHE EMISSION SPECTRUM IS THE SAME

Peak wavelength = B/TB = 2.9 x 10-3 mK

Total energy H = sT4 , s = 5.67 x 10-8 Wm-2 K-4

BLACKBODY RADIATION

WHAT IS THE TEMPERATURE OF THE SURFACE OF THE SUN IF THE PEAKWAVELENGTH IS 4 x 10-7 m (GREEN)

PEAK WAVELENGTH = b/T= 2.9 x 10-3

4 x 10-7

= 7 x 104 or 70,000 K

PLANCK’S RADIATION LAW

E = 1/2 mv2 the average velocity of atoms

SUPPOSE LIGHT IS A STREAM OF PARTICLESCALLED PHOTONS

FREQ. X WAVELENGTH = SPEED OF LIGHTENERGY = h x FREQ. (h is a constant = 6.6 x 10-34 Joules

=4.1 x 10-15 eVE (at room temp) = 1/30 Ev = hf = hc/wavelengthwavelength = 50 x 10-6 m, 50 micrometres = IR

PHOTO-ELECTRIC EFFECT

WHY EINSTEIN WON A NOBEL PRIZE

LIGHT IS ABSORBED IN QUANTA (PHOTONS)PHOTONS HAVE DISCRETE ENERGIES

Frequency of light

Energyof releasedelectrons

Sodium Magnesium

E/f = h

PHOTO-ELECTRIC EFFECT

ELECTRONS ARE EMITTED IMMEDIATELYWHEN STRUCK BY THE LIGHTNOT AFTER A CERTAIN AMOUNT OF ENERGY ID ACCUMULATED

THEREFORE THE ENERGY NEEDED TO CAUSE THE EMISSION OF AN ELECTRONIS IN ONE PHOTON.

ENERGY LEVELS IN ATOMS

E0

E1

E2

E3

E4

etc

When electrons jump betweenallow energy states, thereis a characteristic photonemitted, with correspondingenergy.

These emissions are differentfor different atoms

LASERS

• HOW DOES A LASER WORK?• PUMPING ATOMS TO AN EXCITED STATE• ELECTRONS IN HIGHER ENERGY BANDS• LIGHT CAIUSED WHEN SOME ELECTRONS

FALL TO LOWER ENERGY STATE, TRIGGERS OTHERS TO FALL, EMITTING MORE PHOTONS, AND SO ON.

• ALL THESE PHOTONS ARE IN LOCK STEP (COHERENT EMISSION)

20th CENTURY QUESTIONS

SPECTRA: WHY CERTAIN WAVELENGTHS ONLY?

PHOTO-ELECTRIC EFFECT: WHY ENERGY OF ELECTRON?INDEPENDENT OF INTENSITY OF LIGHT?

RADIOACTIVITY: WHERE IS THE POSITIVE CHARGE?WHY ARE SOME ATOMS UNSTABLE?

BLACKBODY CURVE: WHY DOES IT DEPEND ON TEMP?

20th CENTURY QUESTIONS

PLANCK-EINSTEIN: HOW CAN PHOTONS BE WAVES AND PARTICLES?

X-RAYS: WHY DO DIFFERENT METALS EMIT DIFFERENT WAVELENGTHS?

NUCLEUS: WHY DON’T ELECTRONS FALL INTO THE NUCLEUS?

WAVE OR PARTICLE?

Light behaves like a wave in interferenceexperiments,

but

like a particle in the photo-electric effect

WAVE-PARTICLE DUALITY

LIGHT TRAVELS AS A WAVE --- BUT

WHEN IT INTERACTS WITH MATTERIT ACTS LIKE A STREAM OF PARTICLES

WAVELENGTH FREQ. ENERGYGamma 10-13 m 3x1021 12 MeVUV 10-7 m 3x1015 12eVVisible 6 x 10-7 m 5x1014 2eVRadio 300 m 106 4x10-9 eV

TWO-SLIT EXPERIMENT

TWO-SLIT EXPERIMENT

Interference even when one photon at a time!!!!

WAVE PARTICLE DUALITY

ALL SMALL PARTICLES ACT LIKE WAVES

ALL WAVES ACT LIKE PARTICLES

IS LIGHT A WAVE OR A PARTICLE? - YES!

A STREAM OF ELECTRONS IS ALSO A WAVE!

WHAT IS THE WAVELENGTH OF AN ELECTRON? OR A PHOTON?

E= hf = hc/wavelength, so wavelength= hc/E but mass is related to Energy by E = mc2

Photon Momentum is pph = mv = mc

But a photon has no mass! How can it have momentum?

and photon wavelength = hc/E = h/ pph

So m=E/c2 and therefore pph =Ec/c2 = E/c

WAVELENGTH OF ELECTRONS

• Electron momentum pe = mev;

• wavelength = h/pe = h/mev

• if v=10,000 m/s, me = 9x10-31 kg

• and h= 6.6 x 10-34 Joules; • the wavelength of the electron is 7 nanometres; • the higher the velocity, the shorter the wavelength,

so electron microscopes can see things smaller than optical microscopes (wavelength 400-900 nm)

ELECTRONS CAN BE SHOWN TO HAVE DIFFRACTION PATTERNS, JUST LIKE LIGHT.

electrons

Two slit - typical interference diffraction pattern

electrons

These patterns exist even if only one electron is emitted at a time

SCHOEDINGER’S EQUATION

SUPPOSE ELECTRONS ARE LIKE STANDING WAVES IN A CLOSED BOX

E=1/2 mv2 = p2/2m and wavelength = h/p

Standing wavelength = 2L/n; En = h2 n2 so energy is in levels 8mL2 depending on n and L

L

HEISENBERG’SUNCERTAINTY PRINCIPLE

IF THE ELECTRON ACTS LIKE A STANDING WAVE, WHERE IS IT AT ANY GIVEN TIME?

SUPPOSE WE CONFINE THE ELECTRON TO A BOX OF LENGTH “L”

Wavelength = 2L

UNCERTAINTY PRINCIPLE

UNCERTAINTY IN POSITION “x” IS RELATED TO “L”

UNCERTAINTY IN MOMENTUM “p”

WAVELENTH = h/p; uncertainty in p~ h/L

xp = L h/L > h Planck’s constant!!!

If we try to squeeze the walls of the box to more accurately determine x, we increaseuncertainty in momentum.

UNCERTAINTY

WE CANNOT KNOW PRECISELY WHERE AN ELECTRON IS AND KNOW, AT THE SAME TIME WHAT ITS MOMENTUM (SPEED) IS.

xp > h

WE CANNOT KNOW THE ENERGY OF A PARTICLE IN A SHORT PERIOD OF TIME

Et > h

HOW CAN THIS BE?

IF AN ELECTRON IS A WAVE ..IT MUST EXHIBIT THE PROPERTIES OF A WAVE

Incident electron

Reflected electron

Transmitted electron

Can an electron be subdivided???

PROBABILITY FUNCTIONTHE ELECTRON AS A WAVE FUNCTION

THE WAVE FUNCTION REPRESENTS THE PROBABILITY THAT THE ELECTRON WILL BE IN A GIVEN POSITION

UNTIL IT HAS BEEN DETECTED, IT COULD BE ANYWHERE !!!!

WHEN IT HAS BEEN DETECTED, IT IS ONLY ONE PLACE

SCHROEDINGER’S CATTHE PROBABILITY FUNCTION STATES THATTHE ACTUAL STATE OF MATTER IS AMBIGUOUS UNTIL IT IS OBSERVED!!!

PUT A CAT IN A BOX WITH A RADIOACTIVE ATOMTHERE IS A PROBABILITY THAT THE ATOM WILL DECAY, EMITTING AN ALPHA PARTICLE. THE ALPHA WILL TRIGGER THE RELEASE OF A DEADLY GASTHAT WILL KILL THE CAT.

SO IS SCHOEDINGER’S CAT ALIVE OR DEAD RIGHT NOW? YOU CANNOT KNOW UNTIL YOU CHECK.

UNCERTAINTY

ALL THIS ONLY APPLIES WHEN THEREARE ISOLATED PARTICLES