Download Presentation Lesson 27 Quantum Physics

Lesson 27
Quantum Physics
Eleanor Roosevelt High School
Chin-Sung Lin
The Model of Atom
The Planetary Model of Atom
• Niels Bohr’s model
• Positive charge is in the center of
the atom (nucleus )
• Atom has zero net charge
• Electrons orbit the nucleus like
planets orbit the sun
• Attractive Coulomb force plays
role of gravity
The Planetary Model of Atom
• Circular motion of orbiting electrons causes them to emit
electromagnetic radiation with frequency equal to orbital
frequency, and carries away energy from the electron
– Electron predicted to continually lose energy
– The electron would eventually spiral into the nucleus
However most atoms are stable!
The Planetary Model of Atom
• Experimentally, atoms do emit electromagnetic radiation,
but not just any radiation!
• Each atom has its own ‘fingerprint’ of different light
frequencies that it emits
400 nm
500 nm
600 nm
700 nm
Hydrogen
Mercury
Wavelength (nm)
The Planetary Model of Atom
• The Balmer Series of emission
lines empirically given by
n=4
Rydberg constant :
RH = 1.097 ´ 10 7 m -1
n = 4,  = 486.1 nm
n = 3,  = 656.3 nm
Hydrogen
n=3
The Planetary Model of Atom
• One electron orbits around
one proton and only certain
orbits are stable
• Radiation emitted only when
electron jumps from one
stable orbit to another
• Here, the emitted photon has
an energy of E initial – E final
Einitial
Photon
Efinal
The Planetary Model of Atom
• Hydrogen emits only photons of a particular
wavelength, frequency
• Photon energy = hf, so this means a particular energy
The Planetary Model of Atom
• Energy is quantized
n=4
n=3
E3 = -
13.6
eV
32
n=2
E2 = -
13.6
eV
22
n=1
E1 = -
13.6
eV
12
Energy axis
Zero energy
The Planetary Model of Atom
Zero energy
n=4
n=3
13.6
E 3 = - 2 eV
3
n=2
E2 = -
13.6
eV
22
Photon
emitted
hf=E2-E1
n=4
n=3
E3 = -
13.6
eV
32
n=2
E2 = -
13.6
eV
22
E1 = -
13.6
eV
12
Photon
absorbed
hf=E2-E1
n=1
E1 = -
13.6
eV
12
Photon is emitted when electron
drops from one quantum state
to another
n=1
Absorbing a photon of correct energy
makes electron jump to higher
quantum state.
The Planetary Model of Atom
• A useful model of the atom must be consistent with a
model for light, for most of what we know about atoms
we learn from the light and other radiations they emit
• Most light has its source in the motion of electrons
within the atom
Models of Light
The Model of Light
• Two primary models of light: the particle model and the
wave model
The Model of Light
• Isaac Newton believed in a particle model of light
• Christian Huygens believed that light was a wave
• Thomas Young demonstrated the wave property of light –
Interference
• James Clerk Maxwell proposed that light is a part of broader
electromagnetic wave spectrum
• Heinrich Hertz produced radio wave as Maxwell’s prediction
• Albert Einstein resurrected the particle theory of light
Light Quanta
• Max Planck believed that light existed as continuous waves.
However, he proposed that atoms emit and absorb light in
little chunks – quanta (pl. of quantum)
• Einstein further proposed that light itself is composed of
quanta (now called photons)
• A quantum is an elementary unit (smallest amount) of
something
• Mass, electric charge, light, energy, and angular momentum
are all quantized
• Only a whole number of quanta can exist
Light Quanta
• Photons have no rest energy
• Photons move at speed of light
• The energy of a photon is its kinetic energy (E)
• The photon’s energy is directly proportional to its frequency
• E = hf (h is Planck’s constant) is the smallest amount of
energy that can be converted to light of frequency f
• Light is a stream of photons, each with an energy hf
Photoelectric Effect
Photoelectric Effect
• The photoelectric effect refers to the emission of
electrons from the surface of a metal in response to
incident light
• Energy is absorbed by electrons within the metal, giving
the electrons sufficient energy to be 'knocked' out of the
surface of the metal
Photoelectric Effect
• Maxwell wave theory of light predicts that the more
intense the incident light the greater the average energy
carried by an ejected (photoelectric) electron
• Experiment shows that the energies of the emitted
electrons to be independent of the intensity of the
incident radiation
• Einstein (1905) resolved this paradox by proposing that
the incident light consisted of individual quanta, called
photons, that interacted with the electrons in the metal
like discrete particles, rather than as continuous waves
Photoelectric Effect
• For a given frequency of the incident radiation, each
photon carried the energy E = hf, where h is Planck's
constant and f is the frequency
Photoelectric Effect
• Light travels as a wave
• Light interacts with matter as a stream of particles
Waves vs. Particles
Waves vs. Particles
• Images made by a digital camera. In each successive image,
the dim spot of light has been made even dimmer by
inserting semitransparent absorbers like the tinted plastic
used in sunglasses
Waves vs. Particles
• Which model can explain the phenomenon?
Waves vs. Particles
• If light was a wave, then the absorbers would simply cut down
the wave's amplitude across the whole wavefront
• The digital camera's entire chip would be illuminated
uniformly
• But figures show that some pixels take strong hits while
others pick up no energy at all
• Instead of the wave picture, the image that is naturally evoked
by the data is something more like a hail of bullets from a
machine gun
• Each "bullet" of light apparently carries only a tiny amount of
energy – light is consist of a stream of particles
Waves vs. Particles
Electron beam is directed toward a crystal
Waves vs. Particles
Diffraction & interference pattern is observed
Waves vs. Particles
• The behavior of a particle of matter (in this case the
incident electron) can be described by a wave
• Electrons behave like a wave!
Waves vs. Particles
• If waves can have particle properties, cannot particles
have wave property?
• De Broglie answered this question in 1924
• He suggested that all matter (electrons, protons, atoms,
marbles, cars, and even human) have wave properties
• This phenomenon is commonly known as the waveparticle duality
Waves vs. Particles
• If waves can have particle properties, cannot particles
have wave property?
• De Broglie answered this question in 1924
• He suggested that all matter (electrons, protons, atoms,
marbles, cars, and even human) have wave properties
• This phenomenon is commonly known as the waveparticle duality
Material Waves
Material Waves
• All matter have wave properties
• The wavelength of a particle is called the
de Broglie wavelength
• A tiny particle moving at typical speed has
a detectable wavelength
• Objects in our daily life have tiny
wavelengths which are beyond detection
Wavelength of an Electron
• Need less massive object to show wave effects
• Electron is a very light particle
• Mass of electron = 9.1x10-31 kg
• Larger velocity, shorter wavelength
• Wavelength depends on mass and velocity
Wavelength of a Football
Example: A football’s weight is 0.4 kg and the speed is 30 m/s.
Calculate the wavelength of the football
Momentum:
mv = (0.4 kg)( 30 m /s) =12 kg · m /s
Material Waves
• Example: Calculate the de Broglie wavelength of an
electron traveling at 2% the speed of light
Material Waves
• Example: Calculate the de Broglie wavelength of an ball
traveling at 330 m/s
Material Waves
• A beam of electrons behaves like a beam of light,
however, the wavelength is typically thousands of times
shorter than the wavelength of the visible light
Material Waves
• The electron microscope can distinguish detail not
possible with optical microscopes
Electron Waves
• The Bohr’s model explained the spectra of the element. It
explained why elements emitted only certain frequencies of
light since electrons can only transfer among certain energy
levels
• The model failed to explain why electrons only occupied
certain energy levels I the atom
• Bohr showed that in such a model the electrons would spiral
into the nucleus in about 10-10 s, due to electrostatic
attraction
• This can be resolved by viewing electrons as waves instead of
particles
Electron Waves
• In 1923, de Broglie, proposed that a way to explain the
discrete energy levels was that electrons behave like waves
• To ‘fit a wave’ around a nucleus is when the wavelength fits
the circumference a whole-number of times (so called
standing waves ), and these states correspond to the
observed energy levels of the electrons
Electron Waves
• The radius of a ground state, n = 1, electron has a
circumference of one standing wave
• The radius of the first excited state, n = 2, has a circumference
of two standing waves
Electron Waves
• Thus, an electron's orbit cannot decay because it is
constrained by its standing wave forms
• Only those radii whose circumferences equaled a multiple of
the electron's de Broglie wavelength were permitted
Electron Waves
• De Broglie’s predictions for the electron orbits were quickly
confirmed by experiment and were found to perfectly fit the
observed energy levels of electrons in atoms
• De Broglie thus created a new field in physics, the wave
mechanics, uniting the physics of energy (wave) and matter
(particle). For this he won the Nobel Prize in Physics in 1929
Relative Sizes of Atoms
Relative Sizes of Atoms
• The radii of the electron orbits in the Bohr’s atomic model are
determined by the amount of electric charge in the nucleus
• As the positive charge in the nucleus increased, the negative
electrons also increased. The inner orbits shrink in size due to
stronger electric attraction. However, it won’t shrink as much
as expected due to the increasing electrons
• The heavier elements are not much larger in diameter than
the lighter elements
•
Each element has unique arrangement of electron orbits
unique to that element
Relative Sizes of Atoms
Atomic Energy Levels &
Photon Energy
47
Bohr’s Atomic Model
• Electron orbits around the
nucleus and only certain
orbits are stable
• Radiation emitted only when
electron jumps from one
stable orbit to another
Photon
Ephoton
Einitial
Efinal
• The emitted photon has an
energy E photon = E initial – E final
48
Quantized Energy Levels
• Energy level diagrams on page 3 of your reference table
49
Quantized Energy Levels
• Each atom has a set of
discrete energy levels
• Each level has been
assigned a quantum
number (n)
• An electron transits in
hydrogen between
quantized energy levels
50
Quantized Energy Levels
• How many different
transitions to the lower
energy levels can an
electron have when the
electron is at n = 4?
51
Quantized Energy Levels
• How many different
transitions to the lower
energy levels can an
electron have when the
electron is at n = 4?
3 different transitions:
n = 4 —> n = 3
n = 4 —> n = 2
n = 4 —> n = 1
52
Quantized Energy Levels
• How many different
transitions to the lower
energy levels can an
electron have when the
electron is at n = 7 ?
53
Quantized Energy Levels
• How many different
transitions to the lower
energy levels can an
electron have when the
electron is at n = 7 ?
6 different transitions
54
Energy of Photons
• Calculate the energy of
photons for those possible
transitions form n = 4
55
Energy of Photons
• Calculate the energy of
photons for those possible
transitions form n = 4
3 possible transitions:
n = 4 —> n = 3
-0.85 eV – (-1.51 eV) = 0.66 eV
n = 4 —> n = 2
-0.85 eV – (-3.40 eV) = 2.55 eV
n = 4 —> n = 1
-0.85 eV – (-13.6 eV) = 12.75 eV
56
Quantized Energy Levels
• How much energy is
required to ionize the
Hydrogen atom?
57
Quantized Energy Levels
• How much energy is
required to ionize the
Hydrogen atom?
E > 13.6 eV
58
Electronvolts & Joules
• The electronvolt (eV) is a unit of energy
• It is the kinetic energy gained by an electron when it
accelerates through an electric potential difference of 1 volt
• Since V = W/q, or W = qV, for a single electron
1 eV = 1.602×10−19 C x 1 V ( or 1 J/C) = 1.602×10−19 J
1 eV = 1.60 × 10−19 J
59
Energy of Photons
• Calculate the energy of
photons for the transitions
form n = 4 to n = 2 in joules
60
Energy of Photons
• Calculate the energy of
photons for the transitions
form n = 4 to n = 2 in joules
n = 4 —> n = 2
-0.85 eV – (-3.40 eV)
= 2.55 eV
= 2.55 eV x 1.6 x 10 -19 J/eV
= 4.08 x 10 -19 J
61
Quantized Energy Levels
• How much energy (in joules)
is required to ionize the
Hydrogen atom?
62
Quantized Energy Levels
• How much energy (in joules)
is required to ionize the
Hydrogen atom?
E > 13.6 eV
E > 13.6 eV x 1.6 x 10 -19 J/eV
E > 2.18 x 10 -18 J
63
Electron Transition
• Hydrogen emits only
photons of particular
energies
• The emitted photon has
an energy
E photon = E initial – E final
64
Atomic Spectrum
• Hydrogen emits only photons of a set of particular energy
• Photon energy E = hf = hc/λ
(h = 6.63 × 10–34 J•s)
• It emits a set of particular wavelengths, and frequencies
65
Atomic Spectrum
Zero energy
n=4
n=3
13.6
E 3 = - 2 eV
3
n=2
E2 = -
13.6
eV
22
Photon
emitted
hf=E2-E1
n=4
n=3
E3 = -
13.6
eV
32
n=2
E2 = -
13.6
eV
22
E1 = -
13.6
eV
12
Photon
absorbed
hf=E2-E1
n=1
E1 = -
13.6
eV
12
Photon is emitted when electron
drops from one quantum state
to another
n=1
Absorbing a photon of correct energy
makes electron jump to higher
quantum state.
66
Electron Transition
• E photon = E initial – E final
• E photon = h f = h c / λ
• The emitted photon has a
frequency and wavelength:
f = E photon / h
λ = h c / E photon
h = 6.63 × 10–34 J•s
(Plank’s constant)
67
Frequency of Photons
• Calculate the frequency of photons for the transitions form
n = 4 to n = 2 in a hydrogen atom
68
Frequency of Photons
• Calculate the frequency of photons for the transitions form
n = 4 to n = 2 in a hydrogen atom
E photon = E initial – E final
= -0.85 eV – (-3.40 eV)
= 2.55 eV
= 2.55 eV x 1.6 x 10 -19 J/eV
= 4.08 x 10 -19 J
f=E/h
= 4.08 x 10 -19 J / 6.63 × 10–34 J•s
= 6.15 x 10 14 Hz
69
Wavelength of Photons
• Calculate the wavelength of photons for the transitions form
n = 4 to n = 2 in a hydrogen atom
70
Wavelength of Photons
• Calculate the wavelength of photons for the transitions form
n = 4 to n = 2 in a hydrogen atom
E photon = E initial – E final
= 4.08 x 10 -19 J
λ = h c / E photon
= (6.63 × 10 –34 J•s) (3.00 x 10 8 m/s) / 4.08 x 10 -19 J
= 4.88 x 10 –7 m
71
Type of Photons
• Identify the type of photons for the transitions form n = 4 to
n = 2 in a hydrogen atom
72
Type of Photons
• Identify the type of photons for the transitions form n = 4 to
n = 2 in a hydrogen atom
E photon = E initial – E final = 4.08 x 10 -19 J
f = E / h = 6.15 x 10 14 Hz
73
Electromagnetic Spectrum
• Electromagnetic spectrum diagram on page 2 of your reference table
74
Type of Photons
• Identify the type of photons for the transitions form n = 4 to
n = 2 in a hydrogen atom
E photon = E initial – E final = 4.08 x 10 -19 J
f = E / h = 6.15 x 10-14 Hz
According to the electromagnetic spectrum, it’s visible light
(blue)
75
Atomic Energy Levels & Photon Energy
• What are the resources available in the reference table?
• How to calculate the energy of photon emitted by an electron
changing its energy level?
• How to convert eV to Joule?
• How to calculate the frequency of an emitted photon?
• How to calculate the wavelength of an emitted photon?
• How to identify the type of a photon?
76
Steps of Solving Energy Level Problems
• Extract the information of Energy Level Diagrams on your
reference table
• Calculate the energy of photon by E photon = E initial – E final
• Convert the photon energy from eV to Joule by 1 eV = 1.60 ×
10−19 J
• Calculate the photon frequency by f = E photon / h
• Calculate the photon wavelength by λ = h c / E photon
• Identify the type of a photon according to the electromagnetic
spectrum on your reference table
77
Quantum Physics
Quantum Physics
• Newtonian laws that work so well for the macroworld of our
daily life do not apply to events in the microworld of atom
• Classic mechanics is for macroworld as quantum mechanics is
for the microworld
• Measurements in the macroworld is based on certainty while
the measurements in the microworld is governed by
probability
Heisenberg Uncertainty Principle
• Using
– x = position uncertainty
– p = momentum uncertainty
• Heisenberg showed that the product
Planck’s
constant
( x )  ( p ) is always greater than ( h / 4 )
Q&A
The End