Transcript Quantum Theory

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 THAT
THE SUN’S 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
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
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
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
DISCOVERY OF THE
NUCLEUS
RUTHERFORD (AT McGILL) STUDIED HOW
ALPHA PARTICLES INTERACT WITH MATTER
Lead sheet
Source of
alpha particles
scintillator
Small scatter
expected
Gold foil
High angle scattering
LIKE BOUNCING A CANNONBALL OF A KLEENEX!!
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 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
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
PLANCK’S 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
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
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.
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
LASERS
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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 interference
experiments,
but
like a particle in the photo-electric effect
WAVE-PARTICLE DUALITY
LIGHT TRAVELS AS A WAVE --- BUT
WHEN IT INTERACTS WITH MATTER
IT ACTS LIKE A STREAM OF PARTICLES
WAVELENGTH
Gamma
10-13 m
UV
10-7 m
Visible
6 x 10-7 m
Radio
300 m
FREQ.
3x1021
3x1015
5x1014
106
ENERGY
12 MeV
12eV
2eV
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?
Photon Momentum
is pph = mv = mc
But a photon has no mass!
How can it have momentum?
E= hf = hc/wavelength, so wavelength= hc/E
but mass is related to Energy by E = mc2
So m=E/c2 and therefore pph =Ec/c2 = E/c
and photon wavelength = hc/E = h/ pph
WAVELENGTH OF ELECTRONS
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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
electrons
Two slit - typical interference diffraction pattern
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
L
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
HEISENBERG’S
UNCERTAINTY 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 increase
uncertainty 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
Reflected electron
Transmitted electron
Incident electron
Can an electron be
subdivided???
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
SCHROEDINGER’S 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 SCHOEDINGER’S CAT ALIVE OR DEAD
RIGHT NOW? YOU CANNOT KNOW UNTIL YOU CHECK.
UNCERTAINTY
ALL THIS ONLY APPLIES WHEN THERE
ARE ISOLATED PARTICLES