Download Chapter 38: Quantization

Chapter 38: Quantization
•Photoelectric Effect
•DeBroglie Matter Waves
•Bohr Model of Atom (next test)
The Photoelectric Effect
• In 1886 Hertz noticed, in the
course of his investigations, that a
negatively charged electroscope
could be discharged by shining
ultraviolet light on it.
• In 1899, Thomson showed that the
emitted charges were electrons.
• Around 1900, Phillip Lenard built
an apparatus which produced an
electric current when ultraviolet
light was shining on the cathode.
• This phenomenon is called the
photoelectric effect.
Phillip Lenard 1900
What does Classical Physics
Predict about how the number and
KE of photoelectrons depends on
frequency and intensity of light if
it is a WAVE?
1.
2.
3.
4.
Electrons should be ejected at
any frequency as long as the
light intensity is high enough
At low light intensities, a
measurable time interval
should pass between the
instant the light is turned on
and the time an electron is
ejected from the metal to allow
time for the electrons to absorb
enough energy to escape.
As the light intensity incident
on the metal is increased, the
electrons should be ejected
with more kinetic energy
The kinetic energy should be
related to the intensity of the
light and independent of
frequency of the light.
What does experiment show about
how the number and KE of
photoelectrons depends on
frequency and intensity of light?
1.
2.
No electrons are emitted if the
incident light falls below some
cutoff frequency, ƒc
Electrons are emitted almost
instantaneously, even at very
low light intensities
3.
The maximum kinetic energy
is independent of light
intensity
4.
The maximum kinetic energy
of the photoelectrons increases
with increasing light
frequency. The maximum
kinetic energy is proportional
to the stopping potential (DVs)
Photoelectric Effect
1. The current I is directly proportional to the light
intensity.
2. Photoelectrons are emitted only if the light
frequency f exceeds a threshold frequency f0.
3. The value of the threshold frequency f0 depends on
the type of metal from which the cathode is made.
4. If the potential difference ΔV is positive, the
current does not change as ΔV is increased. If ΔV
is made negative, the current decreases until, at ΔV
= −Vstop the current reaches zero. The value of Vstop
is called the stopping potential.
5. The value of Vstop is the same for both weak light
and intense light. A more intense light causes a
larger current, but in both cases the current ceases
when ΔV = −Vstop.
The Stopping Potential
An electron with energy Eelec inside a metal loses a
minimum amount of energy E0 as it escapes, so it
emerges with maximum kinetic energy Kmax = Eelec – E0.
Slide 38-26
The Stopping Potential
 A positive anode attracts the photoelectrons.
 Once all electrons reach the anode, a further increase in
DV does not cause any further increase in the current I.
Slide 38-27
The Stopping Potential
The current decreases as the anode voltage becomes
increasingly negative until, at the stopping potential, all
electrons are turned back and the current ceases.
Slide 38-28
The Stopping Potential
 Let the cathode be the
point of zero potential
energy.
 Conserving energy as
the photoelectron
moves to the anode:
 When the potential difference causes the very fastest
electrons to have Kf = 0, this is the stopping potential:
Slide 38-29
https://www.youtube.com/watch?v=v-1zjdUTu0o
The Photoelectric Effect
Proof that Light is a Particle
The Problem with Waves:
Increasing the intensity of a low frequency
light beam doesn’t eject electrons. This
didn’t agree with wave picture of light
which predicts that the energy of waves
add so that if you increase the intensity of
low frequency light (bright red light)
eventually electrons would be ejected –
but they don’t! There is a cut off
frequency, below which no electrons will
be ejected no matter how bright the beam!
Also there is no time delay in the ejection
of electrons as the waves build up!
E  hf
Light is quantized in chunks of planck’s constant.
Electrons will not be ejected in the Photoelectric Effect unless each
photon enough energy. One photon is completely absorbed by each
electron ejected from the metal. As you increase the intensity of the
beam, more electrons are ejected, but their energy stays the same. KE
increases as the frequency increases.
Photons
The Nobel Prize in Physics 1921
was awarded to Albert
Einstein "for his services to
Theoretical Physics, and especially
for his discovery of the law of the
photoelectric effect".
E  hf  KEmax  E0
Photon
Energy
Max KE of
ejected electron
Work to ionize
(Work Function)
The Work Function
 A minimum energy is
needed to free an
electron from a metal.
 This minimum energy
is called the work
function E0 of the
metal.
 Some deeper
electrons may require
more energy than E0
to escape, but all will
require at least E0.
Slide 38-25
Einstein’s Explanation of the
Photoelectric Effect
An electron that has just absorbed a quantum of light
energy has Eelec = hf. (The electron’s thermal energy at
room temperature is so much less than that we can neglect
it.) This electron can escape from the metal, becoming a
photoelectron, if
In other words, there is a threshold frequency
for the ejection of photoelectrons because each light
quantum delivers all of its energy to one electron.
Einstein’s Explanation of the
Photoelectric Effect
• A more intense light delivers a larger number of light
quanta to the surface. These quanta eject a larger number
of photoelectrons and cause a larger current.
• There is a distribution of kinetic energies, because
different photoelectrons require different amounts of
energy to escape, but the maximum kinetic energy is
The stopping potential Vstop is directly proportional to Kmax.
Einstein’s theory predicts that the stopping potential is
related to the light frequency by
Einstein’s Postulates
Einstein framed three postulates about light quanta and
their interaction with matter:
1. Light of frequency f consists of discrete quanta, each
of energy E = hf, where h is Planck’s constant h =
6.63 × 10−34 J s. Each photon travels at the speed of
light c = 3.00 × 108 m/s.
2. Light quanta are emitted or absorbed on an all-ornothing basis. A substance can emit 1 or 2 or 3
quanta, but not 1.5. Similarly, an electron in a metal
can absorb only an integer number of quanta.
3. A light quantum, when absorbed by a metal, delivers
its entire energy to one electron.
Example 38.3 The Photoelectric Threshold
Frequency
Slide 38-48
Lithium has a work function of 2.30 eV. Light with a
wavelength of 400 nm is incident on each this metal.
Determine (a) if the metal exhibits the photoelectric
effect and if so, what is the (b) the maximum kinetic
energy for the photoelectrons.
Photon Energy in eV
QuickCheck 38.3
What happens to this graph of the
photoelectric current if the intensity of
the light is reduced to 50%?
A.
B.
C.
D. None of these.
Slide 38-44
QuickCheck 38.3
What happens to this graph of the
photoelectric current if the intensity of
the light is reduced to 50%?
A.
B.
C.
D. None of these.
Stopping potential
doesn’t change.
Slide 38-45
QuickCheck 38.4
What happens to this graph of
the photoelectric current if the
cathode’s work function is
slightly increased?
A.
B.
C.
D. None of these.
Slide 38-46
QuickCheck 38.4
What happens to this graph of
the photoelectric current if the
cathode’s work function is
slightly increased?
Number of photoelectrons unchanged
A.
D. None of these.
B.
Electrons emerge
slower, so stopping
potential reduced.
C.
Slide 38-47
QuickCheck 38.5
What happens to this graph of the
photoelectric current if the cathode’s
work function is slightly increased?
A.
B.
C.
D. None of these.
Slide 38-50
QuickCheck 38.5
What happens to this graph of the
photoelectric current if the cathode’s
work function is slightly increased?
A.
D. None of these.
B.
C.
Threshold shifts to
shorter wavelength.
Slide 38-51
QuickCheck 38.6
What happens to this graph of the
photoelectric current if the cathode’s
work function is larger than the
photon energy?
A.
B.
C.
D. None of these.
Slide 38-52
QuickCheck 38.6
What happens to this graph of the
photoelectric current if the cathode’s
work function is larger than the
photon energy?
A.
D. None of these.
B.
C.
Below threshold if Ephoton < E0
Slide 38-53
Testing Einstein’s Theory
 Millikan measured
the stopping
potential as the
light frequency
was varied.
 A graph of his
data and a fit to
Einstein’s prediction
is shown.
 Millikan determined h from this experiment, and found it
to agree with Planck’s value determined in 1900:
Slide 38-43
Testing Einstein’s Theory: HW Problem
 Millikan measured
the stopping
potential as the
light frequency
was varied.
 A graph of his
data and a fit to
Einstein’s prediction
is shown.
 Millikan determined h from this experiment, and found it
to agree with Planck’s value determined in 1900:
Slide 38-43
More evidence that Light is a particle.
The photon transfers momentum, like a particle.
pincident  pscattered  pelectron
E  pc  hf 
p 
h
hc

 mc
2

The Compton wavelength of a particle is
equivalent to the wavelength of a photon whose
energy is the same as the rest mass of the particle.
It defines the quantum limit of measurement
where QED dominates. For an EXCELLENT
description of quantum scales, see
http://math.ucr.edu/home/baez/lengths.html
h

mc
Photons
Special Relativity: E  pc
Photoelectric: E  hf
h
Compton:  
p
Particle-Wave: Light
A gamma ray photon has a momentum of 8.00x10-21 kg m/s.
What is its wavelength? What is its energy in Mev?
h
Compton:  
p
E  pc
h  6.626 x1034 J  s
h
6.63  1034 J  s
14
 

8
.
29

10
m
21
p 8.00  10
kg  m s
E  pc  8.00 1021 kg  m s  3.00 108 m s 
 2.40 10
12
 1 MeV
J
13
1.60

10


  15.0 MeV
J
If photons can be particles, then
why can’t electrons be waves?
hf h
p  E/c 

c 
deBroglie Wavelength:
h
e 
p
Electrons are
STANDING
WAVES in
atomic orbitals.
1924: de Broglie Waves
Electrons are STANDING WAVES in atomic orbitals.
h

p
2 rn  n
De Broglie Wavelength
h

mv
34
h  6.626 x10
J s
Electron De Broglie Wavelength
for electron v = 0.1c
  h / mv
34
6.626 x10 J  s

31
7
(9.1x10 kg )(3x10 m / s )
  2.4 x10 m
11
Lynda’s De Broglie Wavelength
34
6.626 x10 J  s

(75kg )2m / s
  4.4 x10 m
36
Too small to notice or to interact with anything!
Electron Diffraction
•If the detector collects
electrons for a long enough
time, a typical wave
interference pattern is
produced.
•This is distinct evidence that
electrons are interfering, a
wave-like behavior.
•The interference pattern
becomes clearer as the
number of electrons reaching
the screen increases. Section 40.7
Interference pattern builds one
electron at a time.
Electrons act like
waves going through
the slits but arrive at
the detector like a
particle.
Double Slit for Electrons
shows Wave Interference
If electron were hard
bullets, there would be
no interference pattern.
In reality, electrons do
show an interference
pattern, like light waves.
Electrons act like
waves going through
the slits but arrive at
the detector like a
particle.
Light Particle Wave Duality
https://www.youtube.com/watch?v=Xmq_FJd1oUQ&t=3s
Which Hole Did the Electron
Go Through?
If you make a very dim beam of
electrons you can essentially send
one electron at a time. If you try
to set up a way to detect which
hole it goes through you destroy
the wave interference pattern.
Conclusions:
• Trying to detect the electron, destroys the interference pattern.
• The electron and apparatus are in a quantum superposition of states.
• There is no objective reality.
Feynman version of the
Uncertainty Principle
It is impossible to design an apparatus
to determine which hole the electron
passes through, that will not at the
same time disturb the electrons enough
to destroy the interference pattern.
-Richard Feynman
Electron Diffraction
Electron Microscope
•The electron microscope relies on the
wave characteristics of electrons.
•Shown is a transmission electron
microscope
– Used for viewing flat, thin
samples
•The electron microscope has a high
resolving power because it has a very
short wavelength.
•Typically, the wavelengths of the
electrons are about 100 times shorter
than that of visible light.
Section 40.5
Limits of Vision
Electron
Waves
e  2.4 x1011 m
Electron Microscope
Electron microscope picture of a fly.
The resolving power of an optical lens depends on the wavelength of
the light used. An electron-microscope exploits the wave-like
properties of particles to reveal details that would be impossible to see
with visible light.
Electron Microscope
Salmonella
Bacteria
Stem Cells
The fossilized shell of
a microscopic ocean
animal is magnified
392 times its actual
size.
Atomic & Molecular Interferometry
Wave Packet:
Making Particles
out of Waves
p
h

cf
p  hf / c
Superposition of waves to make a defined wave packet. The more
waves used of different frequencies, the more localized.
However, the more frequencies used, the less the momentum is known.
This is the basis of the Uncertainty Principle.
Electron Waves leads to
Quantum Atomic Theory
Waves:
De Broglie:
2L
n 
,
n
2
1 2 p
E  mv 
2
2m
h

p
2
n  1, 2,3.....
2
hn
Combine: En 
2
8mL
Energy is Quantized!
History of the Atomic Theory
According to Physics
https://www.youtube.com/watch?v=xazQRcSCRaY