SUMMARY OF CLASSICAL PHYSICS

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SUMMARY OF CLASSICAL PHYSICS
MECHANICS
ELECTRICITY
OPTICS
HEAT
SEEMS TO WORK FOR THE VERY BIG (GALAXIES) AND
HUMAN SCALE, BUT WHAT ABOUT AT ATOMIC SCALE?
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LINE SPECTRA
IN 1817, FRAUNHOFER OBSERVED THAT THE SUNS
SPECTRUM HAD DARK LINES
THESE FREQUECIES WERE THE SAME AS THOSE ABSORBED
BY HOT GASES
GASES ABSORB AND EMIT LIGHT AT CERTAIN
FREQUENCIES (SPECTRAL LINES)
THESE LINES CAME IN SEVERAL SERIES
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PHOTO-ELECTRIC EFFECT
IN 1887 HERTZ OBSERVED THAT ELECTRONS WERE
EMITTED FROM A METAL WHEN LIGHT WAS SHONE ON IT
THE ENERGY OF THE ELECTRONS DID NOT DEPEND 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
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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 COULOMBS EASY TO CALCULATE THE MASS
9.1x10-31 kg
IT WAS ASSUMED THE ELECTRONS WERE IMBEDDED IN A
POSITIVE MATRIX
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RADIOACTIVITY
1896 BECQUEREL STUDIED THE RADIATION EMITTED 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
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DISCOVERY OF THE NUCLEUS
RUTHERFORD (AT McGILL) STUDIED HOW ALPHA
PARTICLES INTERACT WITH MATTER
scintillator
Lead sheet
Small scatter expected
Source of alpha particles
Gold foil
High angle scattering
LIKE BOUNCING A CANNONBALL OF A KLEENEX!!
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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!!!
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BLACK BODY RADIATION
ALL HOT BODIES EMIT RADIATION THE EMISSION
SPECTRUM IS THE SAME
Peak wavelength B/T B 2.9 x 10-3 mK
Total energy H sT4 , s 5.67 x 10-8 Wm-2 K-4
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BLACKBODY RADIATION
WHAT IS THE TEMPERATURE OF THE SURFACE OF THE
SUN IF THE PEAK WAVELENGTH 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
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PLANCKS RADIATION LAW
E 1/2 mv2 the average velocity of atoms
SUPPOSE LIGHT IS A STREAM OF PARTICLES CALLED
PHOTONS
FREQ. X WAVELENGTH SPEED OF LIGHT ENERGY h x
FREQ. (h is a constant 6.6 x 10-34 Joules
4.1 x 10-15 eV
E (at room temp) 1/30 Ev hf
hc/wavelength wavelength 50 x 10-6 m, 50
micrometres IR
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PHOTO-ELECTRIC EFFECT
WHY EINSTEIN WON A NOBEL PRIZE
LIGHT IS ABSORBED IN QUANTA (PHOTONS) PHOTONS
HAVE DISCRETE ENERGIES
Sodium
Magnesium
Energy of released electrons
E/f h
Frequency of light
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PHOTO-ELECTRIC EFFECT
ELECTRONS ARE EMITTED IMMEDIATELY WHEN STRUCK BY
THE LIGHT NOT AFTER A CERTAIN AMOUNT OF ENERGY
ID ACCUMULATED
THEREFORE THE ENERGY NEEDED TO CAUSE THE
EMISSION OF AN ELECTRON IS IN ONE PHOTON.
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ENERGY LEVELS IN ATOMS
E0 E1 E2 E3 E4 etc
When electrons jump between allow energy states,
there is a characteristic photon emitted, with
corresponding energy. These emissions are
different for different atoms
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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)

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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?
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20th CENTURY QUESTIONS
PLANCK-EINSTEIN HOW CAN PHOTONS BE WAVES AND
PARTICLES?
X-RAYS WHY DO DIFFERENT METALS EMIT DIFFERENT
WAVELENGTHS?
NUCLEUS WHY DONT ELECTRONS FALL INTO THE
NUCLEUS?
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WAVE OR PARTICLE?
Light behaves like a wave in interference experime
nts, but like a particle in the
photo-electric effect
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WAVE-PARTICLE DUALITY
LIGHT TRAVELS AS A WAVE --- BUT
WHEN IT INTERACTS WITH MATTER IT ACTS LIKE A
STREAM OF PARTICLES
WAVELENGTH FREQ. ENERGY Gamma 10-13
m 3x1021 12 MeV UV 10-7 m 3x1015 12eV Visible
6 x 10-7 m 5x1014 2eV Radio 300
m 106 4x10-9 eV
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TWO-SLIT EXPERIMENT
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TWO-SLIT EXPERIMENT
Interference even when one photon at a time!!!!
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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!
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WHAT IS THE WAVELENGTH OF AN ELECTRON? OR A
PHOTON?
But a photon has no mass! How can it have
momentum?
Photon Momentum is pph mv mc
E hf hc/wavelength, so wavelength hc/E
but mass is related to Energy by E mc2
So mE/c2 and therefore pph Ec/c2 E/c
and photon wavelength hc/E h/ pph
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WAVELENGTH OF ELECTRONS

• Electron momentum pe mev
• wavelength h/pe h/mev
• if v10,000 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)

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ELECTRONS CAN BE SHOWN TO HAVE DIFFRACTION
PATTERNS, JUST LIKE LIGHT.
electrons
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electrons
Two slit - typical interference diffraction
pattern
These patterns exist even if only one electron is
emitted at a time
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SCHOEDINGERS EQUATION
SUPPOSE ELECTRONS ARE LIKE STANDING WAVES IN A
CLOSED BOX
L
E1/2 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
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HEISENBERGSUNCERTAINTY 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
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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 gt h Plancks constant!!!
If we try to squeeze the walls of the box to
more accurately determine x, we
increase uncertainty in momentum.
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UNCERTAINTY
WE CANNOT KNOW PRECISELY WHERE AN ELECTRON IS
AND KNOW, AT THE SAME TIME WHAT ITS MOMENTUM
(SPEED) IS. xp gt h
WE CANNOT KNOW THE ENERGY OF A PARTICLE IN A
SHORT PERIOD OF TIME Et gt h
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HOW CAN THIS BE?
IF AN ELECTRON IS A WAVE .. IT MUST EXHIBIT THE
PROPERTIES OF A WAVE
Reflected electron
Transmitted electron
Can an electron be subdivided???
Incident electron
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PROBABILITY FUNCTION
THE 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
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SCHROEDINGERS CAT
THE PROBABILITY FUNCTION STATES THAT THE ACTUAL
STATE OF MATTER IS AMBIGUOUS UNTIL IT IS
OBSERVED!!!
PUT A CAT IN A BOX WITH A RADIOACTIVE ATOM THERE
IS A PROBABILITY THAT THE ATOM WILL DECAY,
EMITTING AN ALPHA PARTICLE. THE ALPHA WILL
TRIGGER THE RELEASE OF A DEADLY GAS THAT WILL
KILL THE CAT.
SO IS SCHOEDINGERS CAT ALIVE OR DEAD RIGHT NOW?
YOU CANNOT KNOW UNTIL YOU CHECK.
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UNCERTAINTY
ALL THIS ONLY APPLIES WHEN THERE ARE ISOLATED
PARTICLES