Transcript Black-body Radiation & the Quantum Hypothesis

Black-body Radiation & the
Quantum Hypothesis
Max Planck
Micro-world Macro-world
Lect 13
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
room temp
27o C
300oK
80 F
32 F
- 459 F
Black-body Radiation
Light intensity
l peak
UV
IR
2.9 x 10-3 m
=
T(Kelvin)
lpeak vs Temperature
T
3100K
(body temp)
58000K
(Sun’s surface)
l peak
2.9 x 10-3 m
=
T(Kelvin)
2.9 x 10-3 m
-6m
=9x10
3100
infrared light
10-3
visible light
2.9 x
m
-6m
=0.5x10
58000
“Room temperature” radiation
Photo with an IR camera
IR Cat
IR house
5800oK
300oK
Visible light
Light absorbtion in the atmosphere
T=300o
Infrared
light
Back to Planck, etc…
the UV catastrophe
Theory & experiment disagree wildly
Pre-1900 theory
Planck’s solution
EM energy cannot be radiated or absorbed
in any arbitrary amounts, but only in discrete
“quantum” amounts.
The energy of a “quantum” depends on frequency
as
Equantum = h f
h = 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 quantization
Because the penny’s value is so small (~10와)
Suppose the quantum were a
$1000 bill
A quantum this large would have an
enormous effect on “normal” transactions
The quantum of the US Income tax
system
Number of taxpayers
US Income tax with a $1 quantum
Number of taxpayers
US Income tax with a $1000
quantum
Quantum effects are
huge to these guys
All these guys don’t
have to pay anything
Quantum effects
are negligible to
these taxpayers
How quanta defeat the UV
catastrophe
Without
the quantum
With the quantum
high frequency,
large quantum,
huge effects
Low frequency,
small quantum,
Negligible effects
Planck’s quantum is small for “ordinarysized” objects but large for atoms etc
“ordinary”
pendulum
f = 1 Hz
Hydrogen atom
f  2x1014 Hz
Equant= hf
Equant= hf
=6.6x10-34Jsx1Hz
=6.6x10-34J
=(6.6x10-34Js)x(2x1014Hz)
=(6.6 x 2) x 10-34+14J
=1.3 x 10-19J
Typical energies in “ordinary” life
Typical energy of
a tot on a swing:
Etot = mghmax
22x1m
20kgx
===20kgx10m/s
20kgx10m/s
x
= 200 kgm2/s2
= 200 J
hmax
much, much larger than
Equant=6.6x10-34J
Typical electron KE in an atom
1 “electron Volt”
- - 1V
Energy gained by an
electron crossing a 1V
voltage difference
Energy = q V
1eV = 1.6x10-19C x 1V
= 1.6x10-19 Joules
similar
Equant = 1.3 x 10-19J
for f  2x1014 Hz
Classical vs Quantum world
In everyday life,
quantum effects
can be safely
ignored
This is because
Planck’s constant
is so small
At atomic &
subatomic scales,
quantum effects
are dominant &
must be considered
Laws of nature
developed without
consideration of
quantum effects do
not work for atoms
photons
“Quantum Jump”
Photoelectric effect
Vacuum
tube
Experimental results
Electron KE
(electron Volts)
For light freq below f0,
no electrons leave the
cathode
f0
Even if the light
Is very intense
0
0.5
1.0
1.5
Experimental results
For light freq above f0,
the KE of electrons that
leave the cathode increase
with increasing freq
Electron KE
(electron Volts)
f0
0
0.5
But does not change
With light intensity
1.0
1.5
What does Maxwell’s theory say?
E
E
E
Electrons in
cathode are
accelerated by
the E-field of
the light wave
More intense light has
bigger E-fields
E
E
E
And, therefore
Larger acceleration
Electron KE should depend
on E-field strength light intensity
Electron’s motion
But that’s not what is observed
Above f0,the KE only
depends on freq, & not
on the light’s intensity
Electron KE
(electron Volts)
Below f0, no electrons jump
out of the cathode no
matter what the light’s
intensity is
0
f0
0.5
1.0
1.5
Einstein’s explanation
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 f
If Equant is less than f, the electron can’t escape
If Equant is greater than f, the electron escapes & the
f
quantum energy in excess of f becomes electron KE
KEelectron = hf - f
Light quanta  “photons”
Einstein’s light quanta
were given the name
“photons” by Arthur
Compton
Photon Energy for red light
Red light:
f = 4.0x1014 Hz
(Hz = 1/s)
Ephoton = hf = (6.6x10-34 Js) x (4.0x1014 Hz)
= 2.6 x 10-19 J
=
2.6 eV
1.6
x
1eV
1.6 x 10-19 J
=1.6 eV
Photon Energies for visible light
color:
Red
Yellow
Green
Blue
Violet
freq
4.0x1014 Hz
5.0x1014Hz
6.0x1014 Hz
6.7x1014Hz
7.5x1014 Hz
Equant = hf
2.6x10-19J
3.3x10-19J
4.0x10-19J
4.4x10-19J
5.0x10-19J
1.6 eV
2.1 eV
2.5 eV
2.8 eV
3.1 eV
Producing photoelectrons with
photons
Clears the barrier
with energy to
spare
-
-
1.6eV
KE=0.7eV
outside of
the metal
f=2.1eV
2.8eV
-
-
-
-
inside the metal
Not enough
energy to get
over the barrier
For E
Electron KE
(electron Volts)
violet
blue
yellow
red
KE
0
0.5
KE
1.0
1.5
Photons are weird particles
v=c (always)
g=
1
1 – v2/c2
=
1
1 – 1
1
1 – c2/c2
=
=

(always)
What is the photon’s rest mass?
E=mc2
m = g m0
m0 = 0
 m0 =
E
c2
 m=
m
g
=
m

=0
 Rest mass = 0
Photon’s momentum
For any particle: p=mv
for a photon: m= E2
c
p = E2 c
c
& v=c
E
=
c
Photon energy & momentum
E = hf
p =
E
c
=
Wavelength: l = c
f
hf
c

=
h
l
f
c
=
1
l
“particles” of light
p =
E=hf
h
l
Two body collisions
conservation
of momentum
Compton scattering
Scatter X-rays from electrons
p=h/li
-
Recoil electron &
scattered photon
conserve momentum
Compton’s expt proved the
existence of photons
& won him the
1927 Nobel Prize
(Physics)
4x10-11eV
g-rays
X-rays
Ultraviolet
Infrared
micro
waves
TV/FM
AM
radio
waves
Photon “spectrum”
4x10-7eV
4x10-3eV
4eV
4x103eV
visible light
1.6 – 3.1eV
4x106eV
Wave? Particles??
Maxwell
E
B
James Clerk Maxwell
Light is a wave of oscillating E- and B-fields
Einstein
p =
h
l
E=hf
Light is comprised of particle-like quanta
called photons
Who’s right??
Waves explain diffraction & interference
Photons explain photoelectric effect &
Compton scattering
Impossible to explain interference
with particles
With 2 slits open
no light goes here
Block off one slit
Now light
can go here
Impossible to explain PE-effect
and Compton scattering with waves
Electron KE
(electron Volts)
yell
ow
red
0.5
violet
blue
1.0
1.5
Make an interference
pattern 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