Lecture PowerPoint
Physics: Principles with
Applications, 6th edition
Giancoli
© 2005 Pearson Prentice Hall
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Modern
Physics
26.9 The Ultimate Speed
A basic result of special relativity is that
nothing can equal or exceed the speed of light.
This would require infinite momentum – not
possible for anything with mass.
26.10 E = mc2; Mass and Energy
At relativistic speeds, not only is the
formula for momentum modified; that for
energy is as well.
The total energy can be written:
(26-7b)
Where the particle is at rest,
(26-8)
26.10 E = mc2; Mass and Energy
All the formulas presented here become the
usual Newtonian kinematic formulas when the
speeds are much smaller than the speed of
light.
There is no rule for when the speed is high
enough that relativistic formulas must be
used – it depends on the desired accuracy of
the calculation.
Chapter 27
Early Quantum Theory and
Models of the Atom
27.1 Discovery and Properties of the
Electron
In the late 19th century, discharge tubes were
made that emitted “cathode rays.”
27.1 Discovery and Properties of the
Electron
It was found that these rays could be deflected
by electric or magnetic fields.
27.1 Discovery and Properties of the
Electron
By accelerating the rays through a known
potential and then measuring the radius of their
path in a known magnetic field, the charge to
mass ratio could be measured:
(27-1)
The result is
27.1 Discovery and Properties of the
Electron
Cathode rays were soon called electrons.
Millikan devised an experiment to measure the
charge on the electron by measuring the
electric field needed to suspend an oil droplet
of known mass between parallel plates.
27.1 Discovery and Properties of the
Electron
The mass and charge of each droplet were
measured; careful analysis of the data showed
that the charge was always an integral multiple
of a smallest charge, e.
27.1 Discovery and Properties of the
Electron
The currently accepted value of e is:
Knowing e allows the electron mass to be
calculated:
27.2 Planck’s Quantum Hypothesis;
Blackbody Radiation
All objects emit radiation whose total intensity is
proportional to the fourth power of their
temperature. This is called thermal radiation; a
blackbody is one that emits thermal radiation
only.
27.2 Planck’s Quantum Hypothesis;
Blackbody Radiation
The spectrum of blackbody radiation has been
measured; it is found that the frequency of peak
intensity increases linearly with temperature.
27.2 Planck’s Quantum Hypothesis;
Blackbody Radiation
This figure shows
blackbody radiation
curves for three
different temperatures.
Note that frequency
increases to the left.
27.2 Planck’s Quantum Hypothesis;
Blackbody Radiation
This spectrum could not be reproduced using
19th-century physics.
A solution was proposed by Max Planck in 1900:
The energy of atomic oscillations within atoms
cannot have an arbitrary value; it is related to the
frequency:
The constant h is now called Planck’s
constant.
27.2 Planck’s Quantum Hypothesis;
Blackbody Radiation
Planck found the value of his constant by fitting
blackbody curves:
Planck’s proposal was that the energy of an
oscillation had to be an integral multiple of
hf. This is called the quantization of energy.
27.3 Photon Theory of Light and the
Photoelectric Effect
Einstein suggested that, given the success of
Planck’s theory, light must be emitted in small
energy packets:
(27-4)
These tiny packets, or particles, are called
photons.
27.3 Photon Theory of Light and the
Photoelectric Effect
The photoelectric
effect: If light strikes a
metal, electrons are
emitted. The effect does
not occur if the
frequency of the light is
too low; the kinetic
energy of the electrons
increases with
frequency.
27.3 Photon Theory of Light and the
Photoelectric Effect
If light is a wave, theory predicts:
1. Number of electrons and their energy should
increase with intensity
2. Frequency would not matter
27.3 Photon Theory of Light and the
Photoelectric Effect
If light is particles, theory predicts:
• Increasing intensity increases number of
electrons but not energy
• Above a minimum energy required to break
atomic bond, kinetic energy will increase
linearly with frequency
• There is a cutoff frequency below which no
electrons will be emitted, regardless of
intensity
27.3 Photon Theory of Light and the
Photoelectric Effect
The particle theory assumes that an electron
absorbs a single photon.
Plotting the kinetic energy vs. frequency:
This shows clear
agreement with the
photon theory, and
not with wave
theory.
27.3 Photon Theory of Light and the
Photoelectric Effect
The photoelectric effect is how “electric eye”
detectors work. It is also used for movie film
soundtracks.
27.4 Energy, Mass, and Momentum of a
Photon
Clearly, a photon must travel at the speed of
light. Looking at the relativistic equation for
momentum, it is clear that this can only
happen if its rest mass is zero.
We already know that the energy is hf; we can
put this in the relativistic energy-momentum
relation and find the momentum:
(27-6)
27.4 Compton Effect
Compton did experiments in which he
scattered X-rays from different materials. He
found that the scattered X-rays had a slightly
longer wavelength (and less energy) than the
incident ones, and that the wavelength
depended on the scattering angle:
(27-7)
27.4 Compton Effect
This is another effect that is correctly predicted
by the photon model and not by the wave
model.
27.4 Photon Interactions; Pair Production
Photons passing through matter can undergo
the following interactions:
1. Photoelectric effect: photon is completely
absorbed, electron is ejected
2. Photon may be totally absorbed by electron,
but not have enough energy to eject it; the
electron moves into an excited state
3. The photon can scatter from an atom and lose
some energy
4. The photon can produce an electron-positron
pair.
27.4 Photon Interactions; Pair Production
In pair production, energy, electric charge, and
momentum must all be conserved.
Energy will be conserved
through the mass and kinetic
energy of the electron and
positron; their opposite
charges conserve charge;
and the interaction must take
place in the electromagnetic
field of a nucleus, which can
contribute momentum.
27.5 Wave-Particle Duality; the Principle of
Complementarity
We have phenomena such as diffraction and
interference that show that light is a wave,
and phenomena such as the photoelectric
effect and the Compton effect that show that
it is a particle.
Which is it?
This question has no answer; we must
accept the dual wave-particle nature of light.
27.5 Wave-Particle Duality; the Principle of
Complementarity
The principle of complementarity states that
both the wave and particle aspects of light are
fundamental to its nature.
Indeed, waves and particles are just our
interpretations of how light behaves.
27.6 Wave Nature of Matter
Just as light sometimes behaves as a
particle, matter sometimes behaves like a
wave.
The wavelength of a particle of matter is:
(27-8)
(p=mv)
This wavelength is called the deBroglie
wavelength and is extraordinarily small.
27.6 Wave Nature of Matter
The wave nature of matter becomes more
important for very light particles such as the
electron.
27.6 Wave Nature of Matter
Electron wavelengths can easily be on the
order of 10-10 m; electrons can be diffracted by
crystals just as X-rays can.
27.8 Early Models of the Atom
It was known that atoms were electrically neutral,
but that they could become charged, implying
that there were positive and negative charges
and that some of them could be removed.
One popular atomic model
was the “plum-pudding”
model:
27.8 Early Models of the Atom
This model had the atom consisting of a bulk
positive charge, with negative electrons buried
throughout.
27.8 Early Models of the Atom
Rutherford did an experiment that showed that
the positively charged nucleus must be
extremely small compared to the rest of the
atom. He scattered alpha particles – helium
nuclei – from gold foil and observed the
scattering angle. He found that some of the
angles were far larger than the plum-pudding
model would allow.
27.8 Early Models of the Atom
The only way to account for the large angles
was to assume that all the positive charge was
contained within a tiny volume – now we know
that the radius
of the nucleus
is 1/10000 that
of the atom.
27.8 Early Models of the Atom
Therefore, Rutherford’s
model of the atom is
mostly empty space:
27.9 Atomic Spectra: Key to the Structure
of the Atom
A very thin gas heated in a discharge tube emits
light only at characteristic frequencies.
27.9 Atomic Spectra: Key to the Structure
of the Atom
An atomic spectrum is a line spectrum – only
certain frequencies appear. If white light passes
through such a gas, it absorbs at those same
frequencies.
27.9 Atomic Spectra: Key to the Structure
of the Atom
The wavelengths of electrons emitted from
hydrogen have a regular pattern:
(27-9)
This is called the Balmer series. R is the
Rydberg constant:
27.9 Atomic Spectra: Key to the Structure
of the Atom
Other series include the Lyman series:
And the Paschen series:
27.9 Atomic Spectra: Key to the Structure
of the Atom
A portion of the complete spectrum of hydrogen
is shown here. The lines cannot be explained by
the Rutherford theory.
27.10 The Bohr Atom
Bohr proposed that the possible energy states
for atomic electrons were quantized – only
certain values were possible. Then the spectrum
could be explained as transitions from one level
to another.
27.10 The Bohr Atom
Bohr found that the angular momentum
was quantized:
(27-11)
27.10 The Bohr Atom
An electron is held in orbit by the Coulomb
force:
27.10 The Bohr Atom
Using the Coulomb force, we can calculate the
radii of the orbits:
(27-13)
(27-12)
27.10 The Bohr Atom
The lowest energy level
is called the ground
state; the others are
excited states.
27.11 de Broglie’s Hypothesis Applied to
Atoms
De Broglie’s hypothesis is the one associating
a wavelength with the momentum of a particle.
He proposed that only those orbits where the
wave would be a circular standing wave will
occur. This yields the same relation that Bohr
had proposed.
27.11 de Broglie’s Hypothesis Applied to
Atoms
These are circular
standing waves for
n = 2, 3, and 5.
Chapter 30
Nuclear Physics and
Radioactivity
30.1 Structure and Properties of the
Nucleus
Nucleus is made of protons and neutrons
Proton has positive charge:
Neutron is electrically neutral:
30.1 Structure and Properties of the
Nucleus
Neutrons and protons are collectively called
nucleons.
The different nuclei are referred to as nuclides.
Number of protons: atomic number, Z
Number of nucleons: atomic mass number, A
Neutron number: N = A - Z
30.1 Structure and Properties of the
Nucleus
A and Z are sufficient to specify a nuclide.
Nuclides are symbolized as follows:
X is the chemical symbol for the element; it
contains the same information as Z but in a
more easily recognizable form.
30.1 Structure and Properties of the
Nucleus
Nuclei with the same Z – so they are the same
element – but different N are called isotopes.
For many elements, several different isotopes
exist in nature.
Natural abundance is the percentage of a
particular element that consists of a particular
isotope in nature.
30.1 Structure and Properties of the
Nucleus
Because of wave-particle duality, the size of the
nucleus is somewhat fuzzy. Measurements of
high-energy electron scattering yield:
(30-1)
30.1 Structure and Properties of the
Nucleus
Masses of atoms are measured with
reference to the carbon-12 atom, which is
assigned a mass of exactly 12u. A u is a
unified atomic mass unit.
30.1 Structure and Properties of the
Nucleus
From the following table, you can see that the
electron is considerably less massive than a
nucleon.
30.2 Binding Energy and Nuclear Forces
The total mass of a stable nucleus is always
less than the sum of the masses of its
separate protons and neutrons.
Where has the mass gone?
30.2 Binding Energy and Nuclear Forces
It has become energy, such as radiation or
kinetic energy, released during the formation
of the nucleus.
This difference between the total mass of the
constituents and the mass of the nucleus is
called the total binding energy of the nucleus.
30.2 Binding Energy and Nuclear Forces
To compare how tightly bound different nuclei are, we
divide the binding energy by A to get the binding
energy per nucleon.
30.2 Binding Energy and Nuclear Forces
The higher the binding
energy per nucleon, the
more stable the
nucleus.
More massive nuclei
require extra neutrons
to overcome the
Coulomb repulsion of
the protons in order to
be stable.
30.2 Binding Energy and Nuclear Forces
The force that binds the nucleons together is
called the strong nuclear force. It is a very
strong, but short-range, force. It is essentially
zero if the nucleons are more than about 10-15 m
apart. The Coulomb force is long-range; this is
why extra neutrons are needed for stability in
high-Z nuclei.
30.2 Binding Energy and Nuclear Forces
Nuclei that are unstable decay; many such
decays are governed by another force called the
weak nuclear force.
30.3 Radioactivity
Towards the end of the 19th century, minerals
were found that would darken a photographic
plate even in the absence of light.
This phenomenon is now called radioactivity.
Marie and Pierre Curie isolated two new
elements that were highly radioactive; they are
now called polonium and radium.
30.3 Radioactivity
Radioactive rays were observed to be of three
types:
1. Alpha rays, which could barely penetrate a piece
of paper
2. Beta rays, which could penetrate 3 mm of
aluminum
3. Gamma rays, which could penetrate several
centimeters of lead
We now know that alpha rays are helium nuclei,
beta rays are electrons, and gamma rays are
electromagnetic radiation.
30.3 Radioactivity
Alpha and beta rays are bent in opposite
directions in a magnetic field, while gamma rays
are not bent at all.
30.4 Alpha Decay
Example of alpha decay:
Radium-226 will alpha-decay to radon-22
30.4 Alpha Decay
In general, alpha decay can be written:
Alpha decay occurs when the strong nuclear
force cannot hold a large nucleus together.
The mass of the parent nucleus is greater
than the sum of the masses of the daughter
nucleus and the alpha particle; this
difference is called the disintegration
energy.
30.4 Alpha Decay
Alpha decay is so much more likely than other
forms of nuclear disintegration because the
alpha particle itself is quite stable.
30.4 Alpha Decay
One type of smoke detector uses alpha
radiation – the presence of smoke is enough to
absorb the alpha rays and keep them from
striking the collector plate.
30.5 Beta Decay
Beta decay occurs when a nucleus emits
an electron. An example is the decay of
carbon-14:
The nucleus still has 14 nucleons, but it
has one more proton and one fewer
neutron.
This decay is an example of an interaction
that proceeds via the weak nuclear force.
30.5 Beta Decay
The electron in beta decay is not an orbital
electron; it is created in the decay.
The fundamental process is a neutron decaying
to a proton, electron, and neutrino:
The need for a particle such as the neutrino
was discovered through analysis of energy
and momentum conservation in beta decay –
it could not be a two-particle decay.
30.5 Beta Decay
Neutrinos are notoriously difficult to detect, as
they interact only weakly, and direct evidence
for their existence was not available until more
than 20 years had passed.
The symbol for the neutrino is the Greek letter
nu (ν); using this, we write the beta decay of
carbon-14 as:
30.5 Beta Decay
Beta decay can also occur where the nucleus
emits a positron rather than an electron:
And a nucleus can capture one of its inner
electrons:
30.6 Gamma Decay
Gamma rays are very high-energy photons. They
are emitted when a nucleus decays from an
excited state to a lower state, just as photons
are emitted by electrons returning to a lower
state.
30.7 Conservation of Nucleon Number and
Other Conservation Laws
A new law that is
evident by studying
radioactive decay is
that the total number
of nucleons cannot
change.
30.8 Half-Life and Rate of Decay
Nuclear decay is a random process; the decay
of any nucleus is not influenced by the decay
of any other.
30.8 Half-Life and Rate of Decay
Therefore, the number of decays in a short
time interval is proportional to the number of
nuclei present and to the time:
(30-3a)
Here, λ is a constant characteristic of that
particular nuclide, called the decay
constant.
30.8 Half-Life and Rate of Decay
This equation can be solved, using calculus, for
N as a function of time:
(30-4)
30.8 Half-Life and Rate of Decay
The half-life is the time it takes for half the
nuclei in a given sample to decay. It is related
to the decay constant:
(30-6)
30.10 Decay Series
A decay series occurs when one radioactive
isotope decays to another radioactive isotope,
which decays to another, and so on. This
allows the creation of nuclei that otherwise
would not exist in nature.
30.10 Decay
Series
30.11 Radioactive Dating
Radioactive dating can be done by analyzing the
fraction of carbon in organic material that is
carbon-14.
30.11 Radioactive Dating
The ratio of carbon-14 to carbon-12 in the
atmosphere has been roughly constant over
thousands of years. A living plant or tree will be
constantly exchanging carbon with the
atmosphere, and will have the same carbon ratio
in its tissues.
30.11 Radioactive Dating
When the plant dies, this exchange stops.
Carbon-14 has a half-life of about 5730 years; it
gradually decays away and becomes a smaller
and smaller fraction of the total carbon in the
plant tissue.
This fraction can be measured, and the age of the
tissue deduced.
Objects older than about 60,000 years cannot be
dated this way – there is too little carbon-14 left.
30.11 Radioactive Dating
Other isotopes are useful for geologic time
scale dating.
Uranium-238 has a half-life of 4.5 x 109 years,
and has been used to date the oldest rocks on
Earth as about 4 billion years old.
Chapter 31
Nuclear Energy; Effects and
Uses of Radiation
31.1 Nuclear Reactions and the
Transmutation of Elements
A nuclear reaction takes place when a nucleus
is struck by another nucleus or particle.
If the original nucleus is transformed into
another, this is called transmutation.
An example:
31.1 Nuclear Reactions and the
Transmutation of Elements
Energy and momentum must be conserved in
nuclear reactions.
Generic reaction:
The reaction energy, or Q-value, is the sum
of the initial masses less the sum of the
final masses, multiplied by c2:
31.1 Nuclear Reactions and the
Transmutation of Elements
If Q is positive, the reaction is exothermic, and
will occur no matter how small the initial kinetic
energy is.
If Q is negative, there is a minimum initial kinetic
energy that must be available before the reaction
can take place.
31.1 Nuclear Reactions and the
Transmutation of Elements
Neutrons are very
effective in nuclear
reactions, as they nave
no charge and therefore
are not repelled by the
nucleus.
31.2 Nuclear Fission; Nuclear Reactors
After absorbing a neutron, a
uranium-235 nucleus will split
into two roughly equal parts.
One way to visualize this is to
view the nucleus as a kind of
liquid drop.
31.2 Nuclear Fission; Nuclear Reactors
The mass distribution of the fragments shows
that the two pieces are large, but usually
unequal.
31.2 Nuclear Fission; Nuclear Reactors
The energy release in a fission reaction is quite
large. Also, since smaller nuclei are stable with
fewer neutrons, several neutrons emerge from
each fission as well.
These neutrons
can be used to
induce fission in
other nuclei,
causing a chain
reaction.
31.2 Nuclear Fission; Nuclear Reactors
In order to make a nuclear reactor, the chain
reaction needs to be self-sustaining – it will
continue indefinitely – but controlled.
31.2 Nuclear Fission; Nuclear Reactors
A moderator is needed to slow the neutrons;
otherwise their probability of interacting is too
small. Common moderators are heavy water and
graphite.
Unless the moderator is heavy water, the fraction
of fissionable nuclei in natural uranium is too
small to sustain a chain reaction, about 0.7%. It
needs to be enriched to about 2-3%.
31.2 Nuclear Fission; Nuclear Reactors
Neutrons that escape from
the uranium do not
contribute to fission. There
is a critical mass below
which a chain reaction will
not occur because too
many neutrons escape.
31.2 Nuclear Fission; Nuclear Reactors
Finally, there are control rods, usually cadmium or boron,
that absorb neutrons and can be used for fine control of
the reaction, to keep it critical but just barely.
31.2 Nuclear Fission; Nuclear Reactors
Some problems associated with nuclear reactors
include the disposal of radioactive waste and the
possibility of accidental release of radiation.
31.2 Nuclear Fission; Nuclear Reactors
An atomic bomb also uses fission, but the core is
deliberately designed to undergo a massive
uncontrolled chain reaction when the uranium is
formed into a critical mass during the detonation
process.
31.3 Nuclear Fusion
The lightest nuclei can fuse to form heavier
nuclei, releasing energy in the process. An
example is the sequence of fusion processes
that change hydrogen into helium in the Sun.
They are listed here with the energy released in
each:
31.3 Nuclear Fusion
The net effect is to transform four protons into a
helium nucleus plus two positrons, two
neutrinos, and two gamma rays.
(31-7)
More massive stars can fuse heavier
elements in their cores, all the way up to iron,
the most stable nucleus.
31.3 Nuclear Fusion
There are three fusion reactions that are being
considered for power reactors:
These reactions use very common fuels –
deuterium or tritium – and release much more
energy per nucleon than fission does.
31.3 Nuclear Fusion
A successful fusion reactor has not yet been
achieved, but fusion, or thermonuclear, bombs
have been built.
31.3 Nuclear Fusion
Several geometries for the containment of the
incredibly hot plasma that must exist in a fusion
reactor have been developed – the tokamak,
which is a torus; or inertial confinement, which
is tiny pellets of deuterium ignited by powerful
lasers.
31.4 Passage of Radiation Through Matter;
Radiation Damage
Radiation includes alpha, beta, and gamma rays;
X rays; and protons, neutrons, pions, and other
particles.
All these forms of radiation are called ionizing
radiation, because they ionize material that they
go through.
This ionization can cause damage to materials,
including biological tissue.