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Quantum Physics
Physics at the End of the 1900's
Discovery of the Electron
At the end of the nineteenth century, studies were being conducted in which electricity is
discharged through rarefied gases. In one experiment, a very high voltage was applied to
the electrodes of an almost completely evacuated glass tube fitted with electrodes. A dark
space was observed to originate at the cathode and extend to the anode at the opposite
end and that the far end of the tube would glow. The stream could be deflected by
magnetic or electric fields. This stream was given the name cathode rays.
In 1897, J.J. Thomson directly measured the q/m (the charge to mass ratio of the cathode
rays). He used a high voltage to accelerate the cathode rays and passed them through an
electric field produced between two charged parallel plates. A pair of coils produced a
magnetic field. The deflection of the particles in the presence of only an electric field or
in the presence of only a magnetic field were consistent with the paths of a negativelycharged particle. In the absence of an electric field, the magnetic force on the particles
(F=qvB) bends the rays into a circle, whose radius could be measured. Since F = ma,
qvB = mv2/r
or
q/m = v/Br
Next, the electric field was adjusted so that no deflection due to the magnetic field
occurred. Thus, the electric field force (E = F/q) is equal to the magnetic field
force (F = qvB).
qvB = Eq or v = E/B
Combining this with the previous equation yields,
q/m = E/(B2r)
This beam of particles is now called electrons. Robet A. Millikan, in his famous
oil-drop experiment, determined the charge q of an electron to be 1.6 x 10-19 J.
Quantum Theory
Another question concerned the spectrum of light emitted by hot objects. An
incandescent light bulb emits a wide spectrum of frequencies. The higher the
temperature of the light bulb, the "whiter" it appears. The spectrum of light
produced doesn't depend upon the material, but the temperature. The total
intensity of the radiation is proportional to the fourth power of its Kelvin
temperature.
Blackbody radiation is that emitted by an idealized blackbody (a body that
absorbs all radiation falling on it). In 1900, Max Planck explained the spectrum of
the light produced by an incandescent body. He proposed that the atoms of the
material didn't radiate electromagnetic waves continuously, but only at discrete
values. He proposed that energy was quantized; it is not a continuous quantity.
This energy was related to the frequency by E=hf. His quantum hypothesis
suggests that the energy can only be whole number multiples of hf, or nhf, where
n=1,2,3,....
Photoelectric Effect and the Photon Theory of Light
In 1887, Hertz' experiments confirmed Maxwells' theory of light. Seemingly,
Maxwell's electromagnetic theory of light explained all of optics.
The wave theory of light did not explain the photoelectric effect. When light is
shone on a metal surface, a current is developed, implying that the light causes
electrons to be emitted from the surface. The electron flow depends upon the
frequency of the light used, not the intensity of the light. This is called the
photoelectric effect.
In 1905, Albert Einstein proposed a revolutionary theory of light, explaining the
photoelectric effect. In his theory, light consists of discrete bundles of energy
called photons. Einstein won the Nobel Prize for his theory in 1921.
Theories of light:
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Newton's theory - light consists of particles called corpuscles; this theory
only explained reflection
Wave theory of light (Maxwell's theory) - light behaves like a wave; this
explained all the properties of light such as reflection, refraction,
diffraction, and interference; it did not explain the photoelectric effect or
radiation produced by an incandescent light
Quantum theory - light has a dual nature; when light is transmitted
through space or matter, it behaves like a wave; when light is emitted or
absorbed, it behaves like a particle called a photon
Maxwell's theory of light as an electromagnetic wave:
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
a changing electric field will produce a magnetic field
a changing magnetic field will produce an electric field
A magnetic field is produced in empty space by a changing electric field.
Maxwell hypothesized that if a changing magnetic field produces an electric field,
the electric field must also be changing. Maxwell found that the net result of these
interacting fields was the production of a wave of magnetic and electric fields
traveling through space at a speed of 3 x 108 m/s. Thus, light is an electromagnetic
wave.
Photoelectric Effect
A photocell is used in the experiment. When placed in the dark, the galvanometer
reads zero. When light shines on a metal plate in the photocell, the galvanometer
detects a current. When a variable voltage is used and the terminals reversed, a
point is reached where no current is detected. This voltage is measures the
maximum kinetic energy of the ejected electrons (or photoelectrons). The current
flow does not depend upon the intensity of the light used, but upon the frequency
of the light used.
Maxwell's wave theory predicts that as the intensity of light is increased, the
current flow should increase. The frequency should not affect the maximum
kinetic energy of the photoelectrons. According to this theory, the electric field of
the electromagnetic wave exerts a force on the electrons in the metal and some are
ejected from the surface.
Einstein's photon theory predicts that only the frequency of the light used affects
the maximum kinetic energy of the photoelectrons. As the intensity of light is
increased, no change is seen in the maximum kinetic energy of the photoelectrons.
No photoelectrons are ejected until a minimum value of energy is reached, no
matter how great the intensity. After this point, the maximum kinetic energy of
the photoelectrons increases linearly as the frequency of light used increases.
Once photoelectrons are ejected, increasing the intensity of light for a given
frequency results in a higher measured current. More photoelectrons are ejected,
but their maximum kinetic energy still remains the same (stopping potential).
Photoelectric cell experimental results
http://lectureonline.cl.msu.edu/~mmp/kap28/PhotoEffect/photo.htm
Photoelectric Effect Virtual Lab
http://lectureonline.cl.msu.edu/~mmp/kap28/PhotoEffect/photo.htm
Photoelectric Effect Computer Lab
http://www.blackgold.ab.ca/ict/Division4/Photoelectric Effect 2.htm
Anther good photoelectric effect applet http://www.ifae.es/xec/phot2.html
The above graph shows the appearance of the KEmax vs. frequency of light used
graph for the photoelectric effect. Notice, the unit of energy used for the y-axis is
eV and that of the horizontal axis is Hertz (or sec-1). The slope of the graph is E/f.
In this graph, this does not equal h, Planck's constant. For it to equal h, energy
would need to be in Joules. How to convert your slope for this graph to the correct
units that will give you a slope that is equal to h: slope = eV/f. Remember, eV is
the same thing as dividing your energy in J by q. With a graph with these axes, if
you multiply your slope by q, you will have a value for h.
Photon the particle nature of light; discrete bundles of energy; the energy of a
photon depends upon the frequency of light used; a photon has no rest mass
E=hf
E = hc/ 
momentum of a photon: p = E/c = hc/c = h/
AP Free Response and Multiple Choice Questions: Almost every AP test, you
are asked to calculate the momentum of a photon, whether as part of a freeresponse question or as a multiple choice question. Since you need to know the
frequency to do so, you are usually asked to initially calculate frequency of the
photon knowing the voltage in free response questions.
Important general information for the AP test - Multiple Choice and Free
Response:
1. Be able to calculate the energy in Joules of electrons accelerated by a
given voltage. Remember-voltage is equivalent numerically to energy in
electron Volts. If you multiple voltage by charge (if it's an electron you
simply multiply by the elementary charge), then you have energy of the
electron in Joules. You can calculate the speed of the electron by setting
this energy in Joules (kinetic energy) equal to 1/2 mv2. You can calculate
the de Broglie wavelength of the electron once you know its speed.
2. Be able to calculate the energy of light knowing its wavelength or
frequency.
3. Since frequency is directly proportional to the color of light, be able to
predict which color of light has the greatest or the least energy.
Threshold frequency (fo) the minimum frequency of light that results in the
emission of photoelectrons
Planck's constant (h)
h = 6.626 x 10-34J sec
Work function the minimum amount of work needed to eject an electron from
the surface
E = h fo
Stopping potential (Vo) equivalent to the maximum kinetic energy of the
ejected photoelectrons (KEmax)
Photoelectric equation
KEmax = hf - hfo
KEmax = eVo
Electron volt (eV) voltage in volts is equivalent to the magnitude of the energy
in electron volts. The electron volt is an easier unit to use than Joules. An electron
volt can be easily converted into Joules.
1 eV = 1.6 x 10-19J
Rate of Emission of Photons from a Given Source of Light For a given
frequency, the number of photons emitted is proportional to the intensity of the
light, or the power (P) of the source.
number of photons emitted per second = P/hf
Free Response Questions on the AP Exam Dealing with the Photoelectric
Effect:
1. You need to be familiar with the terminology-work function, threshold
frequency, and stopping potential.
2. You may be given experimental data to interpret by graphing KE vs f.
From this graph, you will be asked to determine Planck's constant (it's the
slope!). You also may be asked to determine the work function from a
graph of experimental data. You may be asked to draw the graph of KE vs
f for a different metal knowing its threshold frequency.
3. Free response questions that only deal with the photoelectric effect are not
very common. They were more common in the past. You are usually given
the stopping potential and the minimum frequency of light at which
photoelectrons are ejected and asked to calculate the work function of the
material and the energy (or frequency/wavelength)of the light irradiated
on the surface.
4. You may be asked to calculate both the energy of the ejected
photoelectrons and their speed.
Multiple Choice Questions on the AP Exam Dealing with the Photoelectric
Effect:
1. Be able to interpret KE vs f graphs. Know what a KE vs f graph for the
photoelectric effect should look like.
2. Be able to interpret intensity of the irradiated light vs f graphs. Know what
an intensity vs f graph should look like.
3. Understand that the photoelectric effect supports the particle theory of
light.
4. Know what the maximum speed of ejected photoelctrons depends upon.
5. Know what an experimenter should do to increase the number of
photoelectrons ejected per second.
Experimental proofs that light behaves like a particle:
1. Photoelectric effect
2. Compton effect (1923) - X-rays that irradiate a substance lose energy
when they strike the substance (the wavelengths of the X-rays that are
scattered by striking the substance are longer, or lower in energy). The
beam can be considered to be a stream of photons with energy hf and
momentum h/. These photons collide like billiard balls with the free
electrons in the target, losing some of their kinetic energy, producing
longer wavelengths.
3. Pair production - a photon disappears in the process of creating electron/
positron pairs; rest mass is created from pure energy according to
Einstein's E = m c2. If an electron collides with a positron, the pair
annihilate each other and their energy appears as that of photons.
4. Atomic Spectra
o Light that is emitted or absorbed by an atom occurs in a spectrum
of sharply defined wavelengths, or spectral lines. These spectra are
a characteristic of the atom.
The dual nature of light is a very abstract concept that cannot be visualized. We
cannot imagine light as a combination of a wave and a particle. When we do an
experiment, we must think of light as a wave or as a particle -- not as a
combination.
Early atomic models:
1. Plum pudding model(approximately 1890's)
o atom was visualized as a homogeneous sphere of positive charge in
which were randomly located tiny negative charges--like plums in
a pudding
2. Rutherford model (1911)
Rutherford's gold foil experiment applet
http://micro.magnet.fsu.edu/electromag/java/rutherford/index.html
o
Rutherford's gold foil experiment (1911) contradicted the plum
pudding atomic model
o Rutherford bombarded a piece of gold foil with a beam of positive
charges called alpha particles. An alpha particle has a charge of +2.
o the plum pudding model predicted that there should be little alpha
particle deflection
o experimental results indicated that the majority of the alpha
particles passed through the foil unaffected and some of the alpha
particles were deflected at very great angles
o Rutherford concluded that the majority of the atom was empty
space
o He also concluded that the alpha particle deflection could only be
explained if the positive charge and the almost of the mass of the
atom was located in a tiny central core.
o Rutherford proposed that the electrons were orbiting the central,
massive core like planets around the sun.
o Problems with model:
1. Cannot explain atomic spectra - the model predicts that
light will be emitted in a continuous spectra.
2. Predicts that atoms are unstable - electrons in circular orbits
around the nucleus would be centripetally accelerated.
Accelerating electric charges emit energy. The electrons'
energy would decrease, causing the electrons to spiral into
the nucleus.
o Support for model:
1. The radius of an average atom is one Angstrom, or 1 x 10-10
m.
2. The radius of a nucleus is 1 x 10-14 m to 1 x 10-15 m.
3. Bohr model (1913)
o Bohr hypothesized that electrons moved around the nucleus in
orbits, but only certain orbits were allowed. Electrons in each orbit
would contain a definite amount of energy and could move in the
orbit without radiating energy.
o Light was emitted only when an electron jumped from one possible
orbit to another. When this occurs, a photon of energy is emitted or
absorbed whose energy was given by "hf".
hf = Eupper - Elower
o
o
Bohr proposed that allowed orbits have quantum numbers (n) of 1, 2, etc.
The lowest energy level, or ground state, corresponded to n=1. Both the orbits and the
energy are quantitized.
The energy of a quantum level (n) of a hydrogen atom is given by: (For
other atoms,Eatom=EnZ2. The energy has a negative value becuase it represents the
minimum amount of energy that is required to remove an electron from that orbital.
Applet that shows how atomic emission spectra are formed from energy
transitions
http://zebu.uoregon.edu/nsf/emit.html
Binding energy or ionization energy The minimum energy required to remove
an electron from its ground state.
AP Multiple Choice Questions Dealing with Energy Level Transitions:
1.
These are very commonly asked types of multiple choice
questions.
2.
You will be given an energy level diagram. The energy of each
level from ground state to ionization state will be marked. You may be
asked to predict what energies of photons will be emitted when irradiated
with photons of a range of energies.
3.
When given the energy level diagram of an atom with the energies
of each quantum level labeled, predict possible photon energies emitted
when an electron is excited to one of the quantum levels.
AP Free Response Questions Dealing with Energy Level Transistions
4.
You may be asked to complete an energy level diagram. You are
told what wavelength of light is absorbed and what wavelengths of light
are emitted.
5.
You are given an energy level diagram from ground state to
ionization state for hydrogen. A situation is described where hydrogen
becomes excited from absorbing an electron. Two photons are emitted, but
they only give you the energy of one photon in eV. You will be asked to
calculate the wavelength of the photon of known energy. You will be
asked to calculate the energy and frequency of the other photon emitted.
You will be asked to draw arrows on the energy level diagram showing
these transitions.
6.
o
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You may be asked to calculate the kinetic energy and de Broglie
wavelength when a photon (with energy greater than 13.6 eV) interacts
with ground state hydrogen.
7.
An atom of known ground state energy is said to only absorb two
given wavelengths of light. You will be asked to calculate the photons'
energies and to complete an energy level diagram.
8.
You may be asked to calculate the wavelength for a transition from
one energy level to another and asked if the emission line would be
visible.
Line spectra:
Balmer (1885) showed the wavelengths for the four visible lines of
hydrogen gas can be given by: This Balmer series involves transitions to n=2
where R is the Rydberg Constant, R = 1.097 x 107 / m
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o
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o
Later experiments showed similar series of lines. The Lyman series
involve transitions to n=1 and fit the formula
The Paschen series involves transitions to n=3 and fit the formula
Success of the model:
It explains why atoms emit line spectra and accurately predicts for
hydrogen the wavelengths of the emitted light.
It accurately explains absorption spectra - photons of just the right
energy are required to knock an electron from a lower to a higher energy level.
It accurately predicts the ionization energy for hydrogen.
Problems with the Bohr model:
0.
4.
Bohr assumed that electrons that move in a circle do not radiate
energy even though they are accelerating.
1.
Bohr's model could not explain how electrons moved from one
energy level to another.
2.
His model could not explain why there was a stable ground state or
why orbits were quantitized.
3.
The model only worked for hydrogen.
Quantum mechanical view of the atom:
o
Electrons do not have well-defined orbits, but instead exist as an electron
cloud, a region of high probablility of finding an electron. Electron clouds can be
thought of as an electron wave spread out in space.
o
The state of an electron corresponds to four quantum numbers
0.
n The principal quantum number which can only have whole
number values and corresponds to the old Bohr theory for energy levels.
1.
l The orbital quantum number can have values from 0 to n-1. It
is related to the magnitude of the angular momentum of the electron.
2.
ml The magnetic quantum number is related to the direction of
the electron's angular momentum. It can have integer values ranging from
-l to ,i>+l
3.
ms The spin quantum number can only have two values, +1/2
and -1/2.
The Wave Nature of Matter
In 1923, Louis de Broglie proposed that matter also behaved like a wave. He based his
argument upon the symmetry of nature. If light acted like both a wave and a particle, then
matter should also act like a particle and like a wave. He proposed that the wavelength of
a material particle should be related to its momentum just as the wavelength of a photon
is related to its momentum (p=h/).
de Broglie wavelength is given by
=h/mv
We can measure the wavelength of a particle but we do not know what is
"waving." We do not know what quantity in a matter wave corresponds to the
electric field in an electromagnetic wave.
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According to de Broglie's hypothesis, electrons have a wave nature,
providing an explanation for Bohr's model of the atom.
de Broglie proposed that the electrons in orbit around the nucleus are
actually resonant standing waves.
The electron can be envisioned as a circular standing wave that closed on
itself. If the wavelength of the wave was such that the wave did not close
in upon itself, destructive intereference would occur.
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The only allowable standing waves contain a whole number of
wavelengths.
Experimental proof came in 1927. A stream of electrons were passed
through a double slit and allowed to fall on a screen. The electron stream
produced a diffraction pattern that would be expected of a wave.
AP Multiple Choice & Free Response Questions Dealing with the Wave
Nature of Matter:
1. You may be asked to perform an easy calculation. In other words, if you
know what accelerating potential is required to produce electrons with a
certain wavelength, what accelerating potential would be required to
produce electrons with another wavelength?
2. Be able to recognize a graph of de Broglie wavelength vs linear
momentum.
3. Know what experimentally supports the wave nature of matter.
4. Predict how the de Broglie wavelength of an electron would change with a
change in its momentum.
5. Calculating the de Broglie wavelength of an electron is usually
incorporated into free response questions dealing with transitions between
energy levels in a hydrogen atom.
Davisson-Germer Experiment (1927)
Davisson and Germer discovered electron diffraction which is strong
experimental support for the wave nature of matter.
1. The experiment: http://zebu.uoregon.edu/nsf/emit.html
o A beam of electrons was directed at the surface of nickle crystals.
They wanted to observe how many electrons were reflected from
the surface at various angles.
o They expected that even the smoothest surface would look rough
to an electron. The expected diffuse reflection.
2. Observations: http://zebu.uoregon.edu/nsf/emit.html
o The electrons were reflected in almost the same way that X-rays
would be reflected. In other words, they were diffracted.
o The accelerating voltages were used to determine the speeds of the
electrons.
o The speeds of the electrons were used to calculate their de Broglie
wavelengths.
3. Conclusion:
o The angles at which strong reflections occurred were the same
angles at which X-rays with the same wavelength would be
reflected.
o Electrons diffracted as if they were a wave.
Compton Scattering http://zebu.uoregon.edu/nsf/emit.html
Compton scattered X-rays from various materials. He found that the scattered
light had a lower frequency than the incident light, indicating a loss of energy. He
used the photon theory of light to explain how the incident photons collided with
the electrons of the material. He applied the laws of conservation of energy and
momentum to such collisions and found that the predicted energies of the
scattered photons agreed with experimental results. After the collision, the change
in wavelength of the photon is given by  = (h/mc)(1 - cos).
where mo is the rest mass and  is the angle of the scattered photon. ' is the
wavelength of the scattered photon and  is the wavelength of the incident
photon.
The quantity h/moc = 0.00243 nm is called the Compton wavelength of the
electron.
The recoil energy of the scattered electron is equal to the loss of energy of the
photon. Thus, KEe = (hc/) - (hc/')
X-rays
Production: (Roentgen in 1895) When electrons are accelerated by a high voltage
in a vacuum tube and strike a glass or metal surface within the tube, X-rays are
emitted.
Nature of X-rays: http://zebu.uoregon.edu/nsf/emit.html
1. Charge is zero http://zebu.uoregon.edu/nsf/emit.html
2. They diffract, proving that they are waves.
3. They are a form of electromagnetic radiation.
The wavelength of an X-ray can be calculated by determining the energy in Joules
of the accelerating voltage. This energy can be used to calculate the frequency of
the X-ray and then the wavelength of the X-ray.
http://zebu.uoregon.edu/nsf/emit.html
Quantum Mechanics
In 1925, Schrodinger and Heisenberg independently worked out a new theory,
quantum mechanics. An important aspect of the theory is the Heisenberg
Uncertainty Principle. http://zebu.uoregon.edu/nsf/emit.html
Heisenberg Uncertainty Principle - a particle's momentum and position cannot
both be known precisely at the same time http://zebu.uoregon.edu/nsf/emit.html
One form of the uncertainty principle states that both the position x and the
momentum p of an object cannot be measured precisely at the same time. The
products of the uncertainties, (p)(x) can be no less than h.
http://zebu.uoregon.edu/nsf/emit.html
Quantum Physics Sample Problems
1. The threshold frequency of sodium is 5.6 x 1014 Hz. It is irradiated with light of
8.6 x 1014Hz frequency. What is the energy of the ejected photoelectrons is J and
in eV?
2. The stopping potential of a photocell is 3.2 V. Calculate its energy in J.
3. 240 nm light is used to irradiate zinc. Its threshold wavelength is 310 nm. What is
the energy of the ejected photoelectrons?
4. The work function for cesium is 1.96 eV. It is irradiated by 425 nm light. What is
the energy of the ejected photoelectrons in eV? What is the speed of the ejected
photoelectrons if the mass of an electron is 9.11 x 10-31 kg?
5. A 7 kg bowling ball rolls down an alley with a speed of 8.5 m/s. What is its
deBroglie wavelength?
6. An electron (mass = 9.11 x 10-31kg) is accelerated by 150 V. Find the speed of the
electron. What is its deBroglie wavelength?
7. Repeat for an electron accelerated by 250 V.
8. For the hydrogen atom, find the energy of the first and second energy levels.
What energy is given off by a photon dropping from the second to the first level?
9. Calculate the frequency of this photon. Calculate its wavelength.
Quantum Physics Homework
Photoelectric Effect
1. The threshold frequency of tin is 1.2 x 1015Hz. What is the threshold wavelength?
What is the work function of tin? Ans: 250 nm; 4.97 eV
2. In number one, if 167 nm light falls on tin, what is the kinetic energy of ejected
photoelectrons? Ans: 2.47 eV
3. In number one, what is the speed of the ejected photoelectrons? Ans: 9.31 x 105
m/s
4. The threshold frequency of a given metal is 6.7 x 1014Hz. It is illuminated by 350
nm light. What is the kinetic energy of the ejected photoelectrons? Ans: 0.78 eV
5. In number four, the metal is illuminated by 550 nm light. What is the kinetic
energy of the ejected photoelectrons? Ans: 0 eV
6. The work function of iron is 4.7 eV. What is the threshold wavelength of iron?
Ans: 264 nm
7. If the iron is exposed to 150 nm light, what is the kinetic energy of the ejected
electrons? Use work function of iron given in number 6. Ans: 3.58 eV
8. In number 7, what is their speed? Ans: 1.12 x 106m/s
de Broglie Wavelength
1. What is the de Broglie wavelength of a deuteron of mass 3.3 x 10-27kg that moves
with a speed of 2.5 x 104m/s. Ans: 8.03 x 10-12m
2. What is the de Broglie wavelength of a proton (mass=1.67 x 10-27kg) moving at 1
x 106m/s? Ans: 3.97 x 10-13m
3. An electron is accelerated across a potential difference of 54 V. Find the
maximum velocity of the electron. Ans: 4.36 x 106m/s
4. What is the de Broglie wavelength of the electron in number three? Ans: 1.67 x
10-10m
5. The kinetic energy of an electron is 13.65 eV. Find the velocity of the electron.
Calculate its de Broglie wavelength. Ans: 2.19 x 106m/s; 0.332 nm
6. An electron has a de Broglie wavelength of 400 nm. What is its velocity? Ans:
1,818 m/s
Atomic Models
1. An electron in a mercury atom drops from 8.82 eV to 6.67 eV above its ground
state. What is the energy of the photon emitted? What is its frequency? Ans: 2.15
eV; 5.19 x 1014Hz
2. What energy is associated with the second, third, fourth, fifth, and sixth energy
levels in the hydrogen atom? Ans: -3.4 eV; -1.51 eV; -0.85 eV; -0.54 eV; -0.38
eV
3. Using the values calculated in number 2, determine the following energy
differences for the hydrogen atom: E6 - E5 and E5 - E3. Ans: 0.16 eV; 0.97 eV
4. Using the values calculated in number three, determine the frequencies of light
emitted by the photon given off in the energy changes. Ans: 3.86 x 1013Hz; 2.34 x
1014Hz
5. Determine the wavelengths of the emitted photons in number four. Ans: 7772 nm;
1282 nm
AP Physics B - Modern Physics Objectives
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Students should be know the properties of photons and understand the
photoelectric effect so they can:
1. Relate the energy of a photon in joules or electron-volts to its wavelength
or frequency.
2. Relate the linear momentum of a photon to its energy or wavelength, and
apply linear momentum conservation to simple processes involving the
emission, absorption, or reflection of photons.
3. Calculate the number of photons per second emitted by a monochromatic
source of specific wavelength and power.
4. Describe a typical photoelectric effect experiment, and explain what
experimental observations provide evidence for the photon nature of light.
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5. Describe qualitatively how the number of photoelectrons and their
maximum kinetic energy depend on the wavelength and intensity of the
light striking the surface, and account for this dependence in terms of a
photon model of light.
6. When given the maximum kinetic energy of photoelectrons ejected by
photons of one energy or wavelength, determine the maximum kinetic
energy of photoelectrons for a different photon energy or wavelength.
7. Sketch or identify a graph of stopping potential versus frequency for a
photoelectric-effect experiment, determine from such a graph the
threshold frequency and work function, and calculate an approximate
value of h/e.
Students should understand the concept of energy levels for atoms so they can:
1. Calculate the energy or wavelength of the photon emitted or absorbed in a
transition between specified levels, or the energy or wavelength required
to ionize an atom.
2. Explain qualitatively the origin of emission or absorption spectra of gases.
3. Given the wavelengths or energies of photons emitted or absorbed in a
two-step transition between levels, calculate the wavlength or energy for a
single-step transition between the same levels.
4. Write an expression for the energy levels of hydrogen in terms of the
ground-state energy, draw a diagram to depict these levels, and explain
how this diagram accounts for the various "series" in the hydrogen
spectrum.
Students should understand the concept of the DeBroglie wavelength so they can:
1. Calculate the wavelength of a particle as a function of its momentum.
2. Describe the Davisson-Germer experiment, and explain how it provides
evidence for the wave nature of electrons.
Students should understand the nature oand production of x-rays so they can
calcualte the shortest wavelength of x-rays that may be produced by electrons
accelerated through a specified voltage.
Students should understand Compton scatterying so they can:
1. Describe Compton's experiment, and state what results were observed and
by what sort of analysis these results may be explained.
2. Account qualitatively for the increase of photon wavelength that is
observed, and explain the significance of the Compton wavelength.
Students should understand the significance of the mass number and charge of
nuclei so they can:
1. Interpret symbols for nuclei that indicate these quantities.
2. Use conservation of mass number and charge to complete nuclear
reactions.
3. Determine the mass number and charge of a nucleus after it has undergone
specific decay processes.
4. Describe the process of alpha, beta, and gamma decay and write a reaction
to describe each.
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5. Explain why the existence of the neutrino had to be postulated in order to
reconcile experimental data from beta decay with fundamental
conservation laws.
Students should know the nature of the nuclear force so they can compare its
strength and range with those of the electromagnetic force.
Students should understand nuclear fission so they can:
1. Describe a typical neutron-induced fission and explain why a chain
reaction is possible.
2. Relate the energy released in fission to the decrease in rest mass.
AP Quantum Physics Sample Problems
1. A helium neon laser emits light of 632.8 nm wavelength. What is the energy of
the photon in this beam? What is its momentum? Ans: 1.96 ev or 3.14 x 10-19 J;
1.05 x 10-27 kg m/sec
2. A magnesium surface has a work function of 3.68 eV. Electromagnetic waves
with a 215 nm wavelength strike the surface and eject photoelectrons. Calculate
the energy of the photoelectrons in Joules and in electron volts. Ans: 2.09 eV;
3.35 x 10-19 J
3. A metal has a threshold frequency of 5.6x 1014 Hz. If 8.6 x1014 Hz frequency light
illuminates the metal, what is the maximum kinetic energy of the ejected
photoelectrons? Ans: 1.24 eV
4. When light falls on a photoelectric surface, the stopping potential that prevents
the electrons from flowing across a photocell is 3.5 V. What is the maximum
speed of the photoelectrons? Ans: 1.11 x 106 m/s
5. With what speed will the fastest photoelectrons be emitted from a surface whose
threshold wavelength is 600 nm, when the surface is illuminated by 400 nm light?
Ans: 6 x 105 m/s
6. In a photoelectric experiment, light is incident on a metal surface. Photoelectrons
are ejected, producing a current. A reverse potential is applied and adjusted until
the current drops to zero (this is called the stopping potential). This data is
collected for stopping potentials (listed first) for four different frequencies (listed
second): 0, 2 x 1014 Hz; 0.9 V, 4 x 1014 Hz; 2 V, 7 x 1014 Hz; and 3 V, 9.3 x 1014
Hz. Determine an experimental value for Planck’s constant. What is the work
function of the metal? Ans: 6.47 x 10-34 J sec; 1.294 x 10-19 J (0.83 eV)
7. 120,000 V is applied across two electrodes in an X-ray tube, producing electrons
at the cathode which produce photons at the anode. What is the frequency of the
photons produced? What is the momentum of the photons produced? Ans: 2.9 x
1019 Hz; 6.4 x 10-23 kgm/s
8. In the previous problem, a photon with this maximum energy collides elastically
(hint: remember energy is conserved!) with an electron at rest. This collision
produces a scattered photon with frequency of 1.8 x 1019 Hz and causes the
electron to recoil. Calculate the kinetic energy of the recoiled electron. What is
the speed of the recoiled electron? What is the de Broglie wavelength of the
recoiled electron? Ans: 7.3 x 10-15 J; 1.3 x 108 m/s; 5.75 x 10-12 m