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AP Physics Chapter 27 Quantum Physics


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Title: AP Physics Chapter 27 Quantum Physics

AP Physics Chapter 27Quantum Physics
Chapter 27 Quantum Physics
  • 27.1 Quantization Plancks Hypothesis
  • 27.2 Quanta of Light Photons and the
    Photoelectric Effect
  • 27.3 Quantum Particles The Compton Effect
  • 27.4 The Bohr Theory of the Hydrogen Atom
  • 27.5 Omitted

Homework for Chapter 27
  • Read Chapter 27
  • HW 27.A p.861-862 16, 18, 19-27.
  • HW 27.B p.863- 42, 43, 52, 54-58, 61, 63, 64.

27.1 Quantization Plancks Hypothesis
Some History on the Atomic Nucleus
J.J. Thomson Model After discovering the
electron in 1897, Sir J.J. Thomson proposed a
model of an atom in 1904. This model later came
to be known by different names such as the
plum-pudding and watermelon models.
In this model the pudding was the positive charge
of the atom and electrons were embedded in it
like plums. The total positive charge was equal
in magnitude to the total negative charge of the
electrons. Hence the atom was a neutral particle.
Rutherfords Model In 1911, Ernest Rutherford
performed an experiment to observe the scattering
of alpha particles by a thin gold foil. (Alpha
particles consist of two protons and two
neutrons). Based on the plum pudding model,
Rutherford expected very little scattering
because of the large momentum for alpha
particles. He was surprised to observe that some
alpha particles scattered through large angles
and in fact some of them had back scattered. This
was completely inconceivable on the basis of the
plum-pudding model.
This remarkable experimental result let
Rutherford to revise the atomic model. He could
explain the result of his alpha scattering
experiment by the nuclear model. According to the
nuclear model the positive charge of the atom and
most of its mass is concentrated in a very small
volume at the center of the atom. This part of
the atom came to be called the nucleus of the
atom. The electrons revolve around the nucleus in
orbits similar to the planets going around the
This model has since been further refined but the
basic idea of a tiny atomic nucleus at the center
of outer electrons still holds true.
The Electromagnetic Spectrum
Visible Light Spectrum
Max Planck (1858-1947) A German physicist
considered to be the founder of quantum theory,
and thus one of the most important physicists of
the twentieth century. Planck was awarded the
Nobel Prize in Physics in 1918.
One of the problems scientists had at the end of
the nineteenth century was how to explain thermal
radiation. thermal radiation the continuous
spectra of radiation emitted by hot objects.
Maximum intensity shifts to shorter wavelengths
(higher frequencies) with increasing
temperature. blackbody an ideal system that
absorbs and emits all radiation that falls on
A blackbody can be approximated by a small hole
leading to an interior cavity in a block of
Intensity vs. Wavelength Curves for the Thermal
Radiation from an Idealized Blackbody at
Different Temperatures
  • The location of maximum intensity shifts to
    shorter wavelengths with increasing temperature.
  • The wavelength shift obeys
  • Weins displacement law
  • ?maxT 2.90 x 10-3 mK
  • where ?max is the wavelength of radiation (in
    meters) at which maximum intensity occurs and T
    is the temperature of the body (in kelvins).

Example 27.1 What is the most intense color of
light emitted by a giant star of surface
temperature 4400 K? What is the color of the star?
Classical theory predicts the intensity of
thermal radiation is inversely related to the
emitted wavelength. I ? 1 ?4 Thus
the intensity of the radiation would become
infinitely large as the wavelength approaches
zero. This was known as the ultraviolet
catastrophe. In contrast, Planks quantum theory
predicts the observed radiation distribution.
Max Planck successfully explained the spectrum of
blackbody radiation by proposing a radical
hypothesis. According to Plancks hypothesis, the
energy of the oscillating atoms emitting the
radiation have only discrete, or particular,
amounts of energy rather than a continuous
distribution of energies. The energy is E
hf where E is the energy h is
Plancks constant (6.63 x 10-34 Js)
f is the frequency of the oscillation

On Gold Sheet
  • According to Plancks hypothesis energy is
    quantized, or occurs in only discrete amounts. A
    more specific way to represent his hypothesis is
  • En n(hf) for n 1,2,3,
  • The smallest possible amount of energy occurs
    when n 1.
  • E1 hf.
  • All other permitted values of energy are
    integral multiples of hf.
  • The quantity hf is called a quantum of energy.
  • Blackbody Radiation Applet

  • Check for Understanding
  • Which scientist is credited with the discovery of
    the electron?
  • Albert Einstein
  • Count Rutherford
  • Robert Milikan
  • Max Planck
  • J.J. Thomson

Answer e
  • 2. Which scientist is credited with the discovery
    of the atomic nucleus?
  • a) Albert Einstein
  • Count Rutherford
  • Robert Milikan
  • Max Planck
  • J.J. Thomson

Answer b
Check for Understanding 3.
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27.2 Quanta of Light Photons and the
Photoelectric Effect
  • photon a particle of light
  • Photons have no mass, but they can transfer
    energy to or from electrons.
  • Summary of Subatomic Particles
  • The mass of a proton and neutron equals one
    atomic mass unit, or amu.
  • The electron-volt (eV) is a useful unit of
    energy for subatomic particles. One eV is equal
    to the amount of energy needed to change the
    potential of an electron by one volt.
  • 1 eV 1.6 x 10-19 J

Name Mass Charge
Proton 1.67 x 10-27 kg 1 amu Positive
Neutron 1.67 x 10-27 kg 1 amu Zero
Electron 9.11 x 10-31 kg Negative
Photon 0 Zero
The Photoelectric Effect Towards the end of the
19the century, it had been experimentally
observed that when ultraviolet light was shone on
a negatively-charged electroscope, the charged
leaves fell closer together the electroscope
discharged. This was the beginnings of the path
to understanding what we now call the
photoelectric effect. When light shines on any
metal surface, the surface can release electrons.
If light were composed of waves, then eventually
any wavelength of light should be able to build
up enough energy to knock an electron free.
However, scientists had discovered that only
certain wavelengths worked with each metal and
that electrons were either emitted
instantaneously, or never emitted. They had also
noticed that shorter wavelengths worked better
than longer wavelengths. The equation for the
photoelectric effect was first explained by
Albert Einstein in 1905.
On Gold Sheet
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  • Some observations ..
  • This equation is actually just a restatement of
    conservation of energy.
  • The intensity of the light source affected the
    number of photoelectrons ejected from the surface
    since higher intensities permit more photons to
    strike the surface.
  • The frequency of the light source affected the
    kinetic energy of each photoelectron.
  • Since each photon can be absorbed by only ONE
    photoelectron (that is, there is a one-to-one
    correspondence), the energy of the photons
    directly affects the kinetic energy of the
    released photoelectrons.

  • The Experiment
  • The electrons with the maximum KE can be stopped
    from completing their journey across the
    photoelectric tub if there is a stopping
    potential set up to impede their progress. The
    formula that relates the KE of these
    photoelectrons to this stopping potential is
  • KEmax UE qVstopping or eVo
  • where Vstopping (Vo) is the stopping potential
  • q (e) is the magnitude of the charge on an
    electron, 1.6 x 10-19 coulombs
  • This formula is based on the fact that work is
    done on charged particles when they cross through
    an electric field.
  • The work done (q?V) equals the change in each
    electrons KE.

  • Incident light on the photoelectric material in
    a photocell causes the emission of electrons, and
    a current flows in the circuit.
  • The voltage applied to the tube can be changed
    by means of a variable resistor.

  • As the plots of current vs. voltage for the two
    intensities of monochromatic light show, the
    current is constant as the voltage increased.
    However, for negative voltages (by reversal of
    the battery polarity), the current goes to zero
    at a particular stopping voltage, which is
    independent of intensity.
  • As would be expected classically, the current is
    proportional to the intensity of the incident
    light the greater the intensity, the more
    energy there is to free additional electrons.

  • The minimum energy needed to free the electrons
    from the material is called the work function
  • According to energy conservation, hf Kmax ?o
    , that is, the energy of the absorbed photon goes
    into the work of freeing the electron, and the
    rest is carried off by that emitted electron as
    kinetic energy.
  • The threshold or cutoff frequency (fo ) is the
    lowest frequency, or longest wavelength, that
    permits photoelectrons to be ejected from the
    surface. At this frequency the photoelectrons
    have no extra KE (KE 0) resulting in
  • 0 hfo - ?o
  • hfo ?o or Ephoton ?o
  • fo ?o
  • h

Often the photoelectric equation is illustrated
on a graph of KE vs. frequency. On this graph,
the slope ALWAYS equals Plancks constant, 6.63 x
10-34 Js. All the lines on this type of
graph will be parallel, only differing in their
y-axis intercept (-?) and their x-axis intercept
(the threshold frequency).
(think y mxb)
f1 f2 f3
  • Photoelectric Effect Characteristics (Table 27.1
    in textbook)
  • Characteristic Predicted by wave theory?
  • The photocurrent is proportional to the yes
  • intensity of the light.
  • 2. The maximum KE of the emitted electrons no
  • is dependent on the frequency of the light
  • but not on its intensity.
  • No photoemission occurs for light with a
    frequency no
  • below a certain cutoff frequency fo regardless
  • its intensity.
  • 4. A photocurrent is observed immediately when
    the no
  • light frequency is greater than fo even if the
  • intensity is extremely low.

  • Albert Einstein received the Nobel Prize for
    Physics in 1921 for his discovery of the Law of
    the Photoelectric Effect.
  • His work ended the controversy as to whether
    light had particle properties.
  • By invoking the quantum nature of light he was
    able to explain experimental results that his
    predecessors could not explain with just the wave
    model of light.

Einsteins official portrait after receiving his
Nobel Prize in 1921.
  • Problem-Solving Hint
  • Start with the formula E hf
  • Recall from wave theory that the frequency of a
    wave is related to the wavelength by the
    formula v ?f
  • For light, the velocity is c, 3 x 108 m/s, so we
    can instead write c ?f
  • This means we can rewrite the equation for the
    energy of a photon to read
  • E hc where hc 1.24 x 103 eVnm (on your
    blue sheet)
  • ?
  • This is helpful because typically the wavelength
    in nm is given in a problem rather than
  • These formulas tell us that a photon with high
    frequency, and therefore with a small wavelength,
    is higher in energy than a photon with low
    frequency and long wavelength. So, gamma rays,
    for example, are a lot higher energy than radio
    waves because gamma rays have a higher

Example 27.2 What is the photon energy of
visible light having wavelength 632.8 nm?
Example 27.3 A metal has a work function of 4.5
eV. Find the maximum kinetic energy of the
emitted photoelectrons if the wavelength of light
falling on the metal is a) 300 nm b) 250 nm
  • Example 27.4 When light of wavelength 350 nm is
    incident on a metal surface, the stopping
    potential of the photoelectrons is measured to be
    0.500 V.
  • What is the work function of the metal?
  • What is the threshold frequency of the metal?
  • What is the maximum kinetic energy of the

  • Summary
  • Thermal radiation, typically produced by hot
    objects, has a continuous spectrum.
  • A blackbody is an ideal system that absorbs and
    emits all radiation that falls on it.
  • Weins displacement law states that the
    wavelength of maximum intensity for radiation
    from a blackbody is inversely related to its
  • Classical theory states that the wavelength of
    maximum intensity for radiation from a blackbody
    is inversely related to its temperature.
  • Plancks constant (h) is the fundamental
    proportionality constant between energy and
    frequency of thermal oscillators as well as
    frequency of a light wave and energy of the
    corresponding photons.

fo fo
  • Check for Understanding
  • A blackbody
  • absorbs all radiation incident on it
  • re-emits all radiation incident on it
  • emits thermal radiation in a continuous spectrum
  • all of these

Answer d
2. The ultraviolet catastrophe is a consequence
of a) Plancks Theory b) Classical Theory c)
Einsteins Theory d) Rutherfords Theory
Answer b
  • Check for Understanding
  • 3. Which is a true statement about the
    photoelectric effect?
  • Energy in the form of light can cause an atom to
    eject one of its electrons.
  • The frequency of light must be above a certain
    value for the ejection to occur.
  • An ejected electron has a KE of zero if the
    energy of the photon is equal to the work
  • all of these

Answer d
4. A photocurrent is observed when a) the light
frequency is above the threshold frequency b)
the energy of the photons is greater than the
work function c) the light frequency is below
the threshold frequency d) both a and b
Answer d
Check for Understanding 5.
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Check for Understanding 6.
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Homework for Chapter 27.1-2
  • HW 27.A p.861-862 16, 18, 19-27.

27.3 Quantum Particles The Compton Effect
  • In 1923, American physicist Arthur H. Compton
    (1892-1962) explained a phenomenon he observed in
    the scattering of X-rays from a graphite block by
    considering the radiation to be composed of
  • His explanation of the observed effect provided
    additional convincing evidence that, at least in
    certain types of experiments, light, and
    electromagnetic radiation in general, is composed
    of quanta, or particles of energy called
  • When X-rays of a single wavelength were
    scattered by the electrons in metal foil, the
    incident wavelength is increased in the scattered

  • The wavelength shift grew as the scattering
    angle increased. The nature of the scattering
    material did not contribute to the effect.
  • This phenomenon came to be known as the Compton
  • Compton theorized that an X-ray photon colliding
    with and electron was like billiard balls in an
    elastic collision. He reasoned that the incident
    photon would transfer some energy and momentum to
    the electron.
  • After the collision, the energy and frequency of
    the scattered photon should be decreased (Ehf)
    and its wavelength increased (? c/f).

  • He applied the principles of conservation of
    energy and momentum to develop the formula for
    the Compton effect
  • ? ? ?1 - ?o ?C (1- cos?)
  • where ?o is the wavelength of the incident
  • ?1 is the wavelength of the scattered photon
  • ?C is the Compton wavelength of the electron
  • ? is the scattering angle
  • Compton wavelength ?C h 2.43 x 10-12 m
    2.43 x 10-3 nm
  • of an electron mec
  • where h is Plancks constant
  • m is the mass of an electron
  • c is the speed of light
  • Since the Compton shift is very small, it is
    only significant for X-ray and gamma- ray
    scattering where the wavelengths are on the order
    of ?C.

  • Comptons equation correctly predicted the
    observed wavelength shift, and Compton was
    awarded a Nobel Prize in 1927.
  • Einsteins and Comptons successes in explaining
    electromagnetic phenomena in terms of quanta left
    scientists with two apparently competing theories
    of electromagnetic radiation.
  • Classically, the radiation is pictured as a
    continuous wave, and this theory satisfactorily
    explains such wave-related phenomena as
    interference and diffraction.
  • Conversely, quantum theory was necessary
  • to explain the photoelectric and Compton
  • effects correctly.
  • These two theories gave rise to a
  • description this is called the dual nature
  • of light. That is, light apparently behaves
  • sometimes as a wave and at other times as
  • photons or particles.

  • Example 27.5 X-rays of wavelength of 0.200 nm
    are scattered by a metal. The wavelength shift is
    observed to be 1.50 x 10-12 m at a certain
    scattering angle measured relative to the
    incoming X-ray.
  • What is the scattering angle?
  • What is the maximum shift possible for the
    Compton effect?

  • Summary
  • The Compton effect is the wavelength increase of
    light scattered by electrons or other charged
  • The dual nature of light means that light must
    be thought of as having both particle and wave

  • Check for Understanding
  • The Compton effect was first observed by using
  • visible light
  • infrared radiation
  • ultraviolet light
  • X-rays

Answer d
2. The wavelength shift for Compton scattering is
a maximum when a) the photon scattering angle is
90 b) the electron scattering angle is 90 c)
the shift is equal to the Compton wavelength d)
the incident photon is backscattered
Answer d
  • Check for Understanding
  • 3. A photon can undergo Compton scattering from a
    molecule as well as from a free electron. How
    does the maximum wavelength shift for Compton
    scattering from a molecule as a unit compare to
    that from a free electron?
  • ??max increases for the molecule
  • ??max decreases for the molecule
  • ??max doesnt change

Answer b. The Compton wavelength is inversely
proportional to the mass of the scattering
particle. ??max 2?C 2h ? 1 mc
4. In Compton scattering, why does the scattered
photon always have a longer wavelength than the
incident photon?
Answer From energy conservation, the scattered
photon has less energy after scattering because
the free electron receives part of the incident
energy. Since the energy of a photon is
proportional to the frequency of the light or
inversely proportional to wavelength, the
scattered photon always has a longer wavelength.
27.4 The Bohr Theory of the Hydrogen Atom
Answer When the light waves strike the
transparent material, a chain of absorptions and
reemissions occur through the material. The time
delay between each absorption and reemission
produces an average speed of light less than 3 x
108 meters per second.
  • In the 1800s, much experimental work was done
    with gas discharge tubes. (neon, hydrogen,
    mercury, etc. vapor)
  • Normally, light from an incandescent source
    (such as a light bulb) exhibits a continuous

  • When a gas is excited by heat or electricity and
    the light it emits is separated into its
    component wavelengths by a prism or diffraction
    grating, the result is a bright-line, or
    emission, spectrum, such as these of a) barium
    and b) calcium. Each atom or molecule emits a
    characteristic pattern of discrete wavelengths.

a. b. c.
  • When a continuous spectrum consisting of all
    wavelengths is passed through a cool gas, a
    series of dark lines is observed. Each line
    represents a missing wavelength a particular
    wavelength the gas has absorbed. The wavelengths
    absorbed by any substance are the same ones it
    emits when excited. This absorption spectrum of
    the Sun shows several prominent absorption lines
    the gases of the solar atmosphere produce it.

  • emission spectrum or brightline spectrum a
    series of bright lines indicating which
    wavelengths are being emitted.
  • A discrete line spectrum is characteristic of
    the individual atoms or molecules of a particular
  • Emission lines can be used to identify a
    material with a spectroscope.
  • absorption spectrum a series of dark lines
    superimposed on a continuous spectrum.
  • If white light passes through a relatively cool
    gas, certain frequencies or wavelengths are
    missing, or absorbed.
  • Absorption and emission lines for a gas occur at
    the same frequencies.
  • Hydrogen was under study because it was the
    simplest atom with one proton and one electron,
    and had a relatively simple visible spectrum.
  • The spectral lines of hydrogen in the visible
    region is called the Balmer series.

The spectral lines of hydrogen.
  • In 1913 an explanation of the spectral lines was
    given in A Theory of the Hydrogen Atom by Danish
    physicist Niels Bohr (1885-1962).
  • Bohrs Postulates
  • 1. The hydrogen electron orbits the nuclear
    proton in a circular orbit (analogous to planets
    orbiting the Sun).
  • 2. The angular momentum of the electron is
    quantized in integral multiples of Plancks
    constant, h. L nh , n1,2,3,
  • 2?
  • 3. The electron does not radiate energy when it
    is in certain discrete circular orbits.
  • 4. The electron radiates or absorbs energy only
    when it makes a transition to another orbit. hf
    Ef - Ei

  • From these assumptions, Bohr showed that the
    electron can have only certain sized orbits with
    certain energies.
  • The energy of the electron in the nth orbit is
    En -13.6 eV
  • n2
  • The radius of the orbit is rn 0.0529 n2 nm for
    n 1,2,3,
  • n is an example of a quantum number,
    specifically the principle quantum number.
  • The n 1 orbit is known as the ground state.
    Orbits with n gt 1 are called excited states.
  • The energy of the electron in any state is En,
    and the energy needed to completely free the
    electron from the atom in that state is En,
    which is called the binding energy.

Electron Excitation and Emission Simulation
rn 0.0529 n2 nm for n 1,2,3, where En is
the energy level of the electron n an integer
(quantum number) rn is the radius of the
electron orbit
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  • The Bohr theory predicts that the hydrogen
    electron can occupy only certain orbits that
    having discrete radii. Each allowed orbit has a
    corresponding energy level. The lowest energy
    level (n1) is the ground state those above
    (ngt1) are excited states.
  • The orbits are shown at the left, with orbital
    radius plotted against the 1/r electrical
    potential of the proton. The electron in the
    ground state is deepest in the potential well,
    analogous to the gravitational potential well.

  • An electron generally does not remain in an
    excited state for long. It decays, or makes a
    transition to a lower energy level, in a short
    time. The time an electron
  • spends in an excited state is called the lifetime
    of the excited state.
  • If an electron makes a downward transition for
    ni to nf state, a photon is released and its
    energy is equal to the energy difference between
    the final and initial states
  • ?E Ef Ei 13.6 1 1 eV
  • nf2 ni2
  • The wavelength of the photon is then
  • ? hc 1.24 x 103 eVnm
  • ?E ?E

  • Hydrogen Spectrum
  • For transitions with nf 1, the spectrum series
    is called the Lyman series (all ultraviolet).
  • For transitions with nf 2, the spectrum series
    is called the Balmer series (visible if ni
    3,4,5, and 6).
  • For transitions with nf 3, the spectrum
    series is called the Paschen series (infrared).

  • In fluorescence, an electron that has been
    excited by absorbing a photon returns to the
    ground state in two or more steps. At each step a
    photon is emitted each with less energy (longer
    wavelength) than the absorbed light.

Some mineral are fluorescent.
Fluorescent pigment.
A fluorescent butterfly.
  • Example 27.6 What are the orbital radius and
    total energy of an electron for a hydrogen atom
  • the ground state and
  • the second excited state?

Example 27.7 The electron of a hydrogen atom
makes a transition from the fourth excited state
to the first excited state. What are the energy
and wavelength of the emitted photon?
  • Summary
  • The Bohr theory of the hydrogen atom treats the
    electron as a classical particle in circular
    orbit around the proton, held in orbit by the
    electric attraction force.
  • The angular momentum of the electron is
    quantized in integral numbers of Plancks
    constant, h.
  • The ground state of a hydrogen atom is the state
    of lowest energy for the atomic electron (in the
    smallest orbit, n1). Excited states have greater

  • Check for Understanding
  • In his theory of the hydrogen atom, Bohr
    postulated the quantization of
  • energy
  • centripetal acceleration
  • light
  • angular momentum

Answer d
2. An excited hydrogen atom emits light when its
electron a) makes a transition to a lower
energy level b) is excited to a higher energy
level c) is in the ground state
Answer a
Check for Understanding
Bohr was able to arrive at a formula for the
energy of a single electron atom (hydrogen or a
helium ion) in the nth orbit
Check for Understanding
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Homework for Chapter 27.3-4
  • HW 27.B p.863- 42, 43, 52, 54-58, 61, 63, 64.

Chapter 27 Formulas
(No Transcript)
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