Physics B
Modern Physics
Notes Packet
Name:________________
Quantum Physics
What is meant by the term “quantized”?
Which has more energy in its photons, a red laser
or a green laser? Why?
When are we likely to use quantum physics, as
opposed to Newton’s Laws, for example?
The “electron-volt” (eV)
When is it useful?
How do we convert from eV to Joules?
Light as a wave
Draw a picture of a wave of light. Indicate the
wavelength.
Sample Problem (similar to 30.10)
What is the frequency and wavelength of a
photon whose energy is 4.0 x 10-19J?
How do we relate the speed of light to its
frequency and wavelength?
Equation:
Sample Problem
The bonding energy of H2 is 104.2 kcal/mol.
Determine the frequency and wavelength of a
photon that could split one atom of H2 into two
separate atoms. (1 kcal = 4186 J).
Light as a particle
When does light behave like a particle? What
particle characteristics does it possess?
Calculating photon energy.
Equation:
Sample Problem
How many photons are emitted per second by a
He-Ne laser that emits 3.0 mW of power at a
wavelength of 632.8 nm?
Which has more energy in its photons, a very
bright, powerful red laser or a small key-ring red
laser? Why?
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Absorption Spectrum
What does an absorption spectrum look like?
Emission of photon by atom
What happens when an atom absorbs a photon?
Quantized atomic energy levels
As the energy of an atom gets more negative,
what happens to the stability of the atom?
Emission Spectrum
What does an emission spectrum look like?
What does the ionization level in the figure
represent?
Sample Problem
What does the ground state represent?
What are states between the ground state and the
ionization level called?
Can the atom exist at energy levels in between
the allowed states shown?
A. What is the frequency and wavelength of the
light that will cause the atom shown to transition
from the ground state to the first excited state?
B. Draw the transition.
Absorption of photon by atom
What happens when an atom absorbs a photon?
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Sample Problem
Photoelectric Effect
Describe what happens in the ‘photoelectric
effect.
What is meant by the term “photoelectron”.
A. What is the longest wavelength of light that
when absorbed will cause the atom whose energy
levels are shown above to ionize from the ground
state?
What is meant by the “work function”?
B. Draw the transition.
Sample Problem
Ionization level
0.0 eV
-8.0 eV
A.
Assume the atom whose energy levels are
shown above is in the second excited state.
What frequencies of light are seen in its
emission spectrum?
Ground state (lowest energy level)
-12.0 eV
Draw transitions representing the photoelectric
effect on the figure above, labeling the
following:
Energy of the photon
Work Function
Kinetic Energy of the photoelectron.
B. Draw the transitions.
Sample Atomic Transition Problems
(HW #2 at the back of the packet)
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Sample problem
Photoelectric Effect equation in
equation form:
The photoelectric equation is Kmax = hf – φ.
Suppose you shine various colors of light on a
certain metal. You measure Kmax for
photoelectrons ejected from this metal as a
function of the frequency of the incident light.
A) How will you graph this data so that you get
a linear graph?
Sample problem
Suppose the maximum wavelength a photon can have
and still eject an electron from a metal is 340 nm.
What is the work function of the metal surface?
The Photoelectric Effect experiment
Describe briefly in words.
Sample problem
Zinc and cadmium have photoelectric work
functions given by WZn = 4.33 eV and WCd =
4.22 eV.
A) If illuminated with light of the same
frequency, which one gives photoelectrons
with the most kinetic energy?
Sketch the experimental apparatus.
B) Calculate the maximum kinetic energy of
photoelectrons from each surface for 275 nm light.
Question:
Suppose you collect Kmax and frequency data for
a metal at several different frequencies. You then
graph Kmax for photoelectrons on y-axis and
frequency on x-axis. What information can you
get from the slope and intercept of your data?
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What are some strange results from the
photoelectric experiment?
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Mass and Momentum of Photons
Voltage versus current for different
intensities of light.
Number of
electrons
(current)
increases with
brightness, but
energy of
electrons
doesn’t!
Does a photon have a “rest mass”. Why or why
not?
I
I3
I2
I1
How do you calculate how much mass must be
destroyed to create a given photon?
V
Vs
Vs, the voltage needed to stop the electrons,
doesn’t change with light intensity.
That means the kinetic energy of the electrons
is independent of how bright the light is.
“Stopping
Potential”
Voltage versus current for
different frequencies of light.
Energy of
electrons
increases as
the energy of
the light
increases.
f3
f2
I
Sample problem
Calculate the mass that must be destroyed to
form a photon of 340 nm light.
f3 > f2 > f1
f1
Vs,3 Vs,2 Vs,1
“Stopping
Potential”
V
Even though it doesn’t have mass, does a photon
have momentum?
Vs changes with light frequency.
That means the kinetic energy of the
photoelectrons is dependent on light color.
How do you determine the kinetic energy of
photoelectrons from the voltage?
How would we calculate the momentum of a
photon; with what equation?
Describe Compton scattering:
Sketch a graph that might be used to analyze the
photoelectric effect.
Sample Problem
What is the momentum of photons that have a
wavelength of 620 nm?
Sample Photoelectric Problems
(HW #4 at the back of the packet)
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Sample problem
What is the momentum of photons that have a
wavelength of 620 nm?
Sample Problem
What is the frequency of a photon that has the
same momentum as an electron with speed 1200
m/s?
Sample problem
What is the wavelength of a 2,200 kg elephant
running at 1.2 m/s?
Sample Problems
S-115b, S-113 (at back of packet)
Wave-Particle Duality
What does this term mean?
Nuclear Physics
Draw the symbolic representation of a typical
nucleus, and label the parts of the figure.
When is this phenomenon most pronounced?
Energy:
Particle:
Photon:
Momentum:
Particle:
Photon:
What is meant by the word isotope?
What do isotopes of an element have in
common?
Wavelength:
Particle:
Photon:
What differs between isotopes?
What is the wavelength of a particle called?
Examples of isotopes:
What did the Compton scattering experiment
prove?
Nuclear Particles
What did the Davisson-Germer experiement
prove?
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List the two nuclear particles, or nucleons, and
draw their symbols.
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Nuclear reactions
Neutrino and Anti-Neutrino
List three nuclear decay reactions, and describe
the nuclear decay particle emitted from each.
Definition:
When are neutrinos and antineutrinos produced?
Gamma Radiation, γ
Sample alpha decay
Definition:
Sample beta decay
Calculation of energy released in nuclear
reactions
1.
2.
Sample positron decay
3.
4.
5.
Add up the mass (in atomic mass units) of the
reactants. You can find the mass in Appendix E of
your textbook.
Add up the mass (in atomic mass units) of the
products.
Find the difference between reactant and product
mass. The missing mass has been converted to
energy.
Convert to kg ( 1 u = 1.66 x 10-27 kg)
Use E = mc2 to calculate energy released.
Fission
Definition:
Sample Problem
Complete the reaction and identify the type of
decay.
234
90
Th →
230
88
Ra+...
When does fission occur?
Sample fission reaction
Sample Problem
Find the identity of X in the reaction and identify
the type of decay.
x→
234
91
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Pa+ -10 e
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Sample problem
Mass defect
Complete the following reaction, and calculate
the energy released.
Definition:
235
92
1
U+ 01 n → 132
51 Sb+5 0 n+...
Sample problem
What is the mass defect of 12C in atomic mass
units? How does this relate to mass in kg and
energy in eV and J?
Fusion
Definition:
When does fusion occur?
Sample fusion reaction
Sample problem
You fuse a free proton with a free neutron to
form a deuterium nucleus. How much energy is
released?
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Ionization level
Problem 1
0.0 eV
Third excited state
Using the diagram at right, show the following, using arrows to represent
transitions:
a) The transition of the atom from the ground state to the second excited
state by absorption of one photon. Calculate the wavelength and
frequency of the photon.
Second excited state
-3.0 eV
First excited state
-5.5 eV
Ground state (lowest energy level)
b) The transition of the atom from the ground state to the second excited
state by absorption of two photons. Calculate the wavelengths and
frequencies of these photons, and label the order in which they must be
absorbed.
-1.0 eV
-11.5 eV
Ionization level
0.0 eV
Third excited state
Second excited state
-1.0 eV
-3.0 eV
First excited state
-5.5 eV
Ground state (lowest energy level)
-11.5 eV
Problem 2
Using the diagram shown, draw all emissions representing the transition of the
atom from the third excited state to the ground state. Calculate the frequency of
all photons emitted. You must consider single and multiple-step transitions.
Ionization level
0.0 eV
Third excited state
Second excited state
-1.0 eV
-3.0 eV
First excited state
-5.5 eV
Ground state (lowest energy level)
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-11.5 eV
Problem 3
It is observed that a certain atom in the ground state ionizes in a single transition when 129 nm light is shown upon
it, but it will not ionize in a single transition at longer wavelengths. It is also observed that the same atom in its
ground state will absorb 250 nm, 175 nm, and 140 nm photons.
A) Draw an energy level diagram for this atom. Use electron-volts (eV) as your energy unit. Clearly label the
ground state, ionization level, and each excited state.
B) On the energy level diagram you have constructed above, show one way that the atom can ionize in a twostep transition. Label each step of the transition with the frequency of the photon associated with that step.
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A080 B3. In a photoelectric experiment, radiation of several different frequencies was made to shine on a metal
surface and the maximum kinetic energy of the ejected electrons was measured at each frequency. Selected results
of the experiment are presented in the table below:
Maximum Kinetic
Frequency (Hz)
Energy
of Electrons (eV)
0.5 x 1015
No electrons ejected
1.0 x 1015
1.0
15
3.0
1.5 x 10
15
a.
2.0 x 10
5.0
On the axes below, plot the data from this photoelectric experiment.
b.
Determine the threshold frequency of the metal surface.
c.
Determine the work function of the metal surface.
d.
When light of frequency 2.0 x 1015 hertz strikes the metal surface, electrons of assorted speeds are ejected from
the surface. What minimum retarding potential would be required to stop all of the electrons ejected from the
surface by light of frequency 2.0 x 1015 hertz?
e.
Investigation reveals that some electrons ejected from the metal surface move in circular paths Suggest a
reasonable explanation for this electron behavior.
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(S-116 Bb7—10 points) A monochromatic source emits a 2.5 mW beam of light of wavelength 450 nm.
a. Calculate the energy of a photon in the beam.
b. Calculate the number of photons emitted by the source in 5 minutes.
The beam is incident on the surface of a metal in a photoelectric-effect experiment. The stopping potential for the
emitted electron is measured to be 0.86 V.
c. Calculate the maximum speed of the emitted electrons.
d. Calculate the de Broglie wavelength of the most energetic electrons.
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S-115B b6 (10 points)
An incident gamma ray photon of wavelength 1.400 x 10-14 m is scattered off a stationary nucleus. The shift in
wavelength of the photon is measured for various scattering angles, and the results are plotted on the graph shown
below.
(a) On the graph, sketch a best-fit curve to the data.
In one of the trials, the photon is scattered at an angle of 120° with its original direction.
(b) Calculate the wavelength of this photon after it is scattered off the nucleus.
(c) Calculate the momentum of this scattered photon.
(d) Calculate the energy that this scattering event imparts to the recoiling nucleus.
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S-113 B7. (10 points) A photon of wavelength 2.0 x 10-11 m strikes a free electron of mass me
that is initially at rest, as shown above left. After the collision, the photon is shifted in
wavelength by an amount ∆λ = 2h/mec, and reversed in direction, as shown above right.
(a) Determine the energy in joules of the incident photon.
(b) Determine the magnitude of the momentum of the incident photon.
(c) Indicate below whether the photon wavelength is increased or decreased by the interaction.
Increased
Decreased
Explain your reasoning.
(d) Determine the magnitude of the momentum acquired by the electron.
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