black-body radiation & the quantum hypothesis
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Black-body Radiation & the Quantum Hypothesis. Micro-world Macro-world Lect 13. Max Planck. Thermal atomic motion. Air. solid. Heat energy = KE and PE associated with the random thermal motion of atoms. Temperature avg KE. Temperature scales. Fahrenheit. 212 F. - PowerPoint PPT PresentationTRANSCRIPT
Black-body Radiation & the Quantum Hypothesis
Micro-world Macro-world
Lect 13
Max Planck
Thermal atomic motion
Heat energy= KE and PE associated with the random thermal motion of atoms
Air solid
Temperature avg KE
Temperature scales
Fahrenheit 212 F
32 F
- 459 F
room temp 27o C 300oK 80 F
Black-body Radiation
peak = 2.9 x 10-3 m
T(Kelvin)
Lig
ht
inte
nsit
y
UV
IR
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
“Room temperature” radiation
Photo with an IR camera
IR Cat
IR house
5800oK
=5x10
-7m
300oK
=1x10
-5m
Light absorbtion in the atmosphere
Vis
ible
lig
ht T=300o
Infraredlight
Back to Planck, etc…
the UV catastrophe
Pre-1900 theory
Theory & experiment disagree wildly
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”
Other “quantum” systems
The quantum of the US monetary system
We don’t worry about effects of quantizationBecause the penny’s value is so small (~10와 )
Suppose the quantum were a $1000 bill
A quantum this large would have anenormous effect on “normal” transactions
The quantum of the US Income tax system
US Income tax with a $1 quantum
Nu
mb
er
of
taxp
ayers
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
How quanta defeat the UV catastrophe
Low frequency,small quantum,
Negligible effects
high frequency,large quantum,
huge effects
Withoutthe quantum
With the quantum
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
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
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
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
photons
“Quantum Jump”
Photoelectric effect
Vacuumtube
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
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
What does Maxwell’s theory say?
E
E
E
Electrons incathode areaccelerated bythe E-field ofthe light wave
More intense light hasbigger E-fields
EE
E
And, thereforeLarger acceleration
Electron KE should depend on E-field strength light intensity
Electron’s motion
Not what is
observed
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
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
Light quanta “photons”
Einstein’s light quantawere given the name“photons” by Arthur Compton
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)
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
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
For E
Electron KE (electron Volts)
red
0 0.5 1.0 1.5
yellow
blue
violet
KEKE
Photons are weird particles
v=c (always)
11 – v2/c2
(always)
11 – c2/c2
11 – 1
What is the photon’s rest mass?
E=mc2 m= Ec2
m = m0 m0 = m =
m
= 0
m0 = 0 Rest mass = 0
Photon’s momentum
For any particle: p=mv
for a photon: m=Ec2 & v = c
p = cEc2
= Ec
Photon energy & momentum
E = hf
p = Ec =
hfc
Wavelength: = cf
= h
= fc
1
“particles” of light
E=hf
hp =
Two body collisions
conservationof momentum
Compton scattering
Scatter X-rays from electrons
Recoil electron &scattered photonconserve momentum
p=h/i
p=h/f
-
Compton’s expt proved the existence of photons
& won him the 1927 Nobel Prize (Physics)
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
Wave? Particles??
Maxwell
Light is a wave of oscillating E- and B-fields
James Clerk Maxwell
E
B
Einstein
Light is comprised of particle-like quanta
called photons
E=hf
hp =
Who’s right??
Waves explain diffraction & interference
Photons explain photoelectric effect & Compton scattering
Impossible to explain interference with particles
With 2 slits openno light goes here
Block off one slit
Now lightcan go here
Impossible to explain PE-effectand Compton scattering with waves
Electron KE (electron Volts)
red
0.5 1.0 1.5
yellow
blue
violet
Make an interferencepattern with low intensity light
One photon at a time goes through the two-slit apparatus
-Light behaves like a wave when it propagates through space-And as a particle when it interacts with matter
Photon photography