Download Chapter 28 - Purdue Physics

Chapter 28
Quantum Theory
Quantum Regime
Draw physics diagram
Quantum Regime
 Macroscopic world explanations fail at the atomic-
scale world
 Newtonian mechanics
 Maxwell’s equations describing electromagnetism
 Atomic-scale = quantum regime
 “Quantum” refers to a very small amount of energy
 development of quantum theory began in early
1900s
Waves vs. Particles
 Classically: energy can
be carried by particles
and waves
 Waves = interference
pattern when passed
through a double slit
 Particles (bullets) = no
interference pattern will
be formed
Section 28.1
Particles and Waves, Classical
 Waves exhibit inference; particles do not
 Particles deliver energy in discrete amounts
 The energy delivered by a wave is not discrete
 Wave energy = described by its intensity
 Energy absorbed depends on:


intensity
absorption time
Section 28.1
Interference with Electrons?
 Quantum regime – extremely strange
 All human intuition is wrong!
 Lets use electrons in a double slit experiment
 Shoot them through ONE AT A TIME!
 What do you think happens?
*long pause till someone answers*
Section 28.1
Interference with Electrons?
 INTERFERENCE PATTERN OBSERVED!
 The blue lines show the probability of the electrons
striking particular locations
Section 28.1
Interference with Electrons, cont.
 The probability curve of the electrons has same form




as light intensity in the double-slit interference
experiment
This shows that electrons undergo constructive and
destructive interference
Also shows particle-like behavior since the electrons
arrive one at a time at the screen
Q: How can this happen?
A: It just does.
Section 28.1
Particles and Waves, Quantum
 All objects, including light and electrons, can exhibit
interference (waves)
 All objects, including light and electrons, carry
energy in discrete amounts (particles)
 These discrete “parcels” are called quanta
 Wave-particle duality
Section 28.1
WPD Formal Definition
 The notion that the properties of both classical
waves and classical particles are present at the
same time is also called wave-particle duality
 To understand QM sometimes we must think of the
objects in question as
 Waves (electron interference)
 Particles (photoelectric effect)
Section 28.3
WPD Formal Definition
 The possibility that all particles have wave-like
properties was first proposed by Louis de Broglie
 He did this in his PhD thesis (70 pages)
 Nobel prize 5 years later
 De Broglie made very simple (and epic) suggestion:
 If a particle has a momentum p, it will have a
wavelength
h
λ
p
Section 28.3
Electron Interference
 An experiment was
designed to observe
interference of classical
particles
 The experiment showed
conclusively that electrons
have wavelike properties
 Later done with many
other particles
 Wavelength was in good
agreement with de
Broglie’s theory
Section 28.3
Wavelengths of Macroscopic
Particles
 From de Broglie’s equation and using the classical
expression for kinetic energy
h
λ

p
h
2m(KE )
 As the mass of the particle (object) increases, its
wavelength decreases
 In principle, you could observe interference with
baseballs
 Has not yet been observed
Section 28.3
Example: Interference with
______ ?
λ
h

p
h
2m(KE )
Section 28.3
The Nature of Quanta
 3 principles that are thought to always hold:
 conservation of energy
 conservation of momentum
 conservation of charge
 The energy and momentum of a photon come in
discrete quantized units
 Electric charge also comes in quantized units
 Electrons and photons are particle-waves
 Example?
Section 28.8
Photoelectric Efffect
 In the 1880s someone
pointed a flashlight at a
metal
 Some weird stuff
happened, and physics
could not explain it yet
 Quantum Mechanics
was needed to explain it
 BTW the person to
explain it was Einstein
Section 28.2
Photoelectric Efffect
 What’s a metal?
 Think of it as a sea of electrons
 Electrons are free to move around within the metal
(this is why metals conduct)
 Electrons are bound to the metal
 Need energy to be removed from the metal (atom)
 This energy is the work function
 Different metals – different work function
 Measure work function with voltmeter
 Wc = eV
Section 28.2
Photoelectric Efffect
 The work function, Wc
is the minimum energy
required to remove a
single electron from a
piece of metal
Wc  eV
Section 28.2
Photoelectric Efffect
Section 28.2
Photoelectric Effect
 To remove electron from a




metal: shine light onto it
Light striking a metal is
absorbed by the electrons
If an electron absorbs an
amount of light energy
greater than Wc, it is
ejected off the metal!
BAM!
This is called the
photoelectric effect
Fun fact: This is what Einstein got his
Nobel prize for. Not E=mc^2.
Section 28.2
Light Review
 Light has
 Frequency
 Wavelength
 Travels at c
 Intensity (how bright it is)
 Energy
 Is a particle or a wave?

Both!
#nofilter #JustLightThings
#wave #particle #lolcats
Photoelectric Effect
What is observed?
1. Critical frequency ƒc =
below which no electrons
get emitted!
2. Above ƒc = kinetic energy
of emitted electrons varies
linearly with the frequency
3. Critical frequency
independent of light
intensity
4. KE of electron independent
of light intensity
Photoelectric Effect
Classical Explanation Fails
 Critical frequency is independent of the light intensity
 Classically, the energy is proportional to the intensity


It should always be possible to eject electrons by increasing the
intensity
Below the critical frequency there, are no ejected electrons no
matter how great the light intensity
 KE of an ejected electron is independent of the light
intensity
 Classically, increasing the intensity will cause ejected
electrons to have a higher KE
 Experiments actually show the electron kinetic energy
depends on the light’s frequency NOT intensity
Section 28.2
Photoelectric Effect
Quantum Explanation
 Einstein proposed that light carries energy in
discrete quanta – particles - photons
 Each photon carries a quantum of energy Ephoton =
hƒ
 h is a constant of nature called Planck’s constant
 h = 6.626 x 10-34 J ∙ s
 A beam of light = collection of photons
 Each photon has energy dependent on its frequency
 Intensity = the number of photons in the beam
 All photons in beam have same energy
Section 28.2
Photoelectric Effect, Explanation 2
 The absorption of light by an
electron = collision between
two particles (photon and
electron)
 The photon energy is absorbed
by the electron



If energy is less the work
function, electron doesn’t
escape
If energy if more than work
function, electron escapes
Rest of photon energy goes
into KE of electron
Section 28.2
Explanation 2, cont.
 KE of ejected electrons depends on frequency (not
intensity)
 Critical Frequency -> photons whose energy is equal to the
work function
h ƒc = Wc
 The electron is just ejected and would have no kinetic
energy
 If the photon has a higher energy, the difference goes into
kinetic energy of the ejected electron
KEelectron = h ƒ - h ƒc = h ƒ - Wc
 This linear relationship is what was found experimentally
Section 28.2
Momentum of a Photon
 A light wave with energy E also carries a certain
momentum:
pphoton 
E hƒ h


c
c
λ
 Photons carry a discrete amount of both energy and
momentum!
 Strange because..
 Photons are different than classical particles
 Photons do not have any mass
 Photons exhibit interference effects
Section 28.2
Photoelectric Example
 We take potassium (W=2.21eV) and shine on it a
light with wavelength 600 nm.
 What happens?
 Make this light 10 times as bright. What happens
now?
 Take a light of 250 nm.
 What happens?
 Make this light 10 times as bright. What happens
now?
Section 28.2