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Black-body Radiation & the Quantum Hypothesis
Micro-world Macro-world
Lect 13
Max Planck
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Thermal atomic motion
Heat energy= KE and PE associated with the random thermal motion of atoms
Air solid
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Temperature avg KE
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Temperature scales
Fahrenheit 212 F
32 F
- 459 F
room temp 27o C 300oK 80 F
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Black-body Radiation
peak = 2.9 x 10-3 m
T(Kelvin)
Lig
ht
inte
nsit
y
UV
IR
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peak vs Temperature
peak = 2.9 x 10-3 m
T(Kelvin)T
3100K(body temp)
2.9 x 10-3 m3100 =9x10-6m
58000K(Sun’s surface)
2.9 x 10-3 m58000 =0.5x10-6m
infrared light
visible light
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“Room temperature” radiation
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Photo with an IR camera
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IR Cat
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IR house
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5800oK
=5x10
-7m
300oK
=1x10
-5m
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Light absorbtion in the atmosphere
Vis
ible
lig
ht T=300o
Infraredlight
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Back to Planck, etc…
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the UV catastrophe
Pre-1900 theory
Theory & experiment disagree wildly
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Planck’s solution
EM energy cannot be radiated or absorbedin any arbitrary amounts, but only in discrete“quantum” amounts.
The energy of a “quantum” depends on frequency as
Equantum = h fh = 6.6 x 10-34 Js
“Planck’s constant”
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Other “quantum” systems
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The quantum of the US monetary system
We don’t worry about effects of quantizationBecause the penny’s value is so small (~10와 )
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Suppose the quantum were a $1000 bill
A quantum this large would have anenormous effect on “normal” transactions
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The quantum of the US Income tax system
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US Income tax with a $1 quantum
Nu
mb
er
of
taxp
ayers
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US Income tax with a $1000 quantum
All these guys don’thave to pay anything
Nu
mb
er
of
taxp
ayers
Quantum effectsare negligible tothese taxpayers
Quantum effects arehuge to these guys
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How quanta defeat the UV catastrophe
Low frequency,small quantum,
Negligible effects
high frequency,large quantum,
huge effects
Withoutthe quantum
With the quantum
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Planck’s quantum is small for “ordinary-sized” objects but large for atoms etc
“ordinary”pendulumf = 1 Hz
Hydrogen atomf 2x1014 Hz
Equant= hf =6.6x10-34Jsx1Hz
=6.6x10-34J
Equant= hf
=(6.6x10-34Js)x(2x1014Hz)
=(6.6 x 2) x 10-34+14J
=1.3 x 10-19Jvery tiny
about the same
as
the electron’s KE
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Typical energies in “ordinary” life
Typical energy ofa tot on a swing:
Etot = mghmax
hma
x
= 20kgx
= 200 kgm2/s2
= 200 Jmuch, much larger than
Equant=6.6x10-34J
= 20kgx10m/s2x= 20kgx10m/s2x1m
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Typical electron KE in an atom
1 “electron Volt”Energy gained by anelectron crossing a 1Vvoltage difference
1V
- - -Energy = q V
1eV = 1.6x10-19C x 1V
= 1.6x10-19 Joules
Equant = 1.3 x 10-19J
similar
for f 2x1014 Hz
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Classical vs Quantum world
In everyday life,
quantum effects
can be safelyignored
At atomic & subatomic
scales,quantum effectsare dominant &
must be considered
This is because Planck’s
constant is so small
Laws of naturedeveloped
withoutconsideration ofquantum effects do not work for
atoms
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photons
“Quantum Jump”
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Photoelectric effect
Vacuumtube
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Experimental results
Electron KE (electron Volts)
f0
For light freq below f0,no electrons leave the cathode
Even if the light Is very intense
0 0.5 1.0 1.5
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Experimental results
Electron KE (electron Volts)
f0
For light freq above f0,the KE of electrons that leave the cathode increases with increasing freq
But does not changeWith light intensity
0 0.5 1.0 1.5
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What does Maxwell’s theory say?
E
E
E
Electrons incathode areaccelerated bythe E-field ofthe light wave
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More intense light hasbigger E-fields
EE
E
And, thereforeLarger acceleration
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Electron KE should depend on E-field strength light intensity
Electron’s motion
Not what is
observed
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But that’s not what is observed
Electron KE (electron Volts)
f0
0 0.5 1.0 1.5
Above f0,the KE onlydepends on freq, & not on the light’s intensity
Below f0, no electrons jump out of the cathode no matter what the light’s intensity is
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Einstein’s explanation
KEelectron = hf -
Light is comprised of particle-like
quanta each with energy Equant = hf
The quanta collide with electrons &Transfer all their energy to them
Each electron needs a minimum energy to escape the cathode. This is called
If Equant is less than , the electron can’t escape
If Equant is greater than , the electron escapes & the quantum energy in excess of becomes electron KE
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Light quanta “photons”
Einstein’s light quantawere given the name“photons” by Arthur Compton
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Photon Energy for red light
Red light: f = 4.0x1014 Hz
Ephoton = hf
= (6.6x10-34 Js) x (4.0x1014 Hz)
= 2.6 x 10-19 J
1eV 1.6 x 10-19 J
x
=
2.6 1.6
eV
=1.6 eV
(Hz = 1/s)
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Photon Energies for visible light
color: freq Equant = hf
Red 4.0x1014 Hz 2.6x10-19J 1.6 eV
Yellow 5.0x1014Hz 3.3x10-19J 2.1 eV Green 6.0x1014
Hz 4.0x10-19J 2.5 eVBlue 6.7x1014Hz 4.4x10-19J 2.8 eVViolet 7.5x1014
Hz 5.0x10-19J 3.1 eV
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Producing photoelectrons with photons
-
--
-2.1eV
-Not enough
energy to getover the barrierRed photon-
Clears the barrier with energy to
spare
KE=0.7eV
Blue photon
Surfac
e
barr
ier
1.6eV
2.8eV
inside the metal
outside ofthe metal
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For E
Electron KE (electron Volts)
red
0 0.5 1.0 1.5
yellow
blue
violet
KEKE
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Photons are weird particles
v=c (always)
11 – v2/c2
(always)
11 – c2/c2
11 – 1
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What is the photon’s rest mass?
E=mc2 m= Ec2
m = m0 m0 = m =
m
= 0
m0 = 0 Rest mass = 0
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Photon’s momentum
For any particle: p=mv
for a photon: m=Ec2 & v = c
p = cEc2
= Ec
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Photon energy & momentum
E = hf
p = Ec =
hfc
Wavelength: = cf
= h
= fc
1
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“particles” of light
E=hf
hp =
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Two body collisions
conservationof momentum
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Compton scattering
Scatter X-rays from electrons
Recoil electron &scattered photonconserve momentum
p=h/i
p=h/f
-
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Compton’s expt proved the existence of photons
& won him the 1927 Nobel Prize (Physics)
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Photon “spectrum”
Ult
ra-
vio
let
Infr
a-
red
X-
rays
- rays
mic
ro
wave
srad
io
wave
sTV
/FM
AM
4x10-3eV 4x10-11eV 4eV 4x103eV 4x106eV 4x10-7eV
visible light
1.6 – 3.1eV
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Wave? Particles??
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Maxwell
Light is a wave of oscillating E- and B-fields
James Clerk Maxwell
E
B
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Einstein
Light is comprised of particle-like quanta
called photons
E=hf
hp =
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Who’s right??
Waves explain diffraction & interference
Photons explain photoelectric effect & Compton scattering
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Impossible to explain interference with particles
With 2 slits openno light goes here
Block off one slit
Now lightcan go here
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Impossible to explain PE-effectand Compton scattering with waves
Electron KE (electron Volts)
red
0.5 1.0 1.5
yellow
blue
violet
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Make an interferencepattern with low intensity light
One photon at a time goes through the two-slit apparatus
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-Light behaves like a wave when it propagates through space-And as a particle when it interacts with matter
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Photon photography
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