University of California San Diego Physics Worksheet finish question number 14, 15, 16, 17total 4 questionshow all work…………………… Quantum Phy

University of California San Diego Physics Worksheet finish question number 14, 15, 16, 17total 4 questionshow all work…………………… Quantum Physics 2D
Key Homework Ch. 12,13,14
Oct., 2018
These problems are to be worked on in discussion. They contain most of the physics concepts needed to solve other
problems. The other problems have solutions that can be used to help you with these more basic problems. The solutions
to these problems are intentionally not given so you can learn to really solve things yourself.
For each part of a problem,
1. state the physics principle (in words) that you will use to solve the problem,
2. write down the best formulas from the formula sheet to answer the problem,
3. then write an algebraic expression for the answer based on the formulas,
4. and finally compute a numerical result if that is possible.
The text in blue is provided to help you get started on the problem. Don’t expect similar text on the quiz. Do be ready
to find the formulas needed on the formula sheet which is on Tritoned and will be provided with the quiz.
1. For free particles with complete translation symmetry, any energy is allowed. For bound states with no translation
symmetry, only quantized energies are allowed. In solids, it is often found that there are bands of allowed energies
separated by bands of energy with no allowed states. In crystals, the size of the gap between allowed Energy bands
determines the characteristics of the solid in many ways.
It was predicted that solids with crystalline structure would have energy bands.
a) What symmetry is responsible for these solutions with energy bands?
b) Write the form of the solutions giving the energy bands. What characterizes the two factors in these solutions?
c) What band structure do insulators have?
d) What band structure do intrinsic semiconductors have?
e) What band structure do metals have?
f) How are quantum metals expected to be different from the classical theory of metals?
2. The resistivity of most metals increases with increasing temperature, whereas the resistivity of an intrinsic semiconductor
decreases with increasing temperature.
a) What explains this behavior for metals?
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b) What explains this behavior for intrinsic semiconductors?
c) What basic difference between a metal and an intrinsic semiconductor accounts for this basic difference?
3. Many parameters of crystals are dependent on the band gap.
a) From the optical absorption spectrum of a certain semiconductor, one finds that the longest wavelength of radiation
absorbed is 1.40 µm. What is the band gap for this semiconductor? Explain how the band gap gives rise to this
behavior.
b) What band gap would be needed to make blue (450 nm) LEDs? Explain why.
c) Most of the sun’s radiation has wavelengths shorter than 1000 nm. For a solar cell to absorb all of this, what band
gap ought the material have? Explain your reasoning.
d) The band gap in Germanium is 0.72 eV. When used as a photon detector, roughly how many electrons can be made
to jump from the valence to the conduction band by passage of a 760 keV photon that loses all its energy in the
crystal?
4. A p-type semiconductor has positive charge carriers but is electrically neutral. Similarly an n-type semiconductor has
negative charge carriers but is electrically neutral. When they are put in contact (making a diode), statistical forces cause
some of the charge carriers to migrate to the opposite semiconductor. The charge carriers move until an E-field is created
to stop the migration. This E-field creates a depletion region near the junction where there are no charge carriers. If
a forward voltage is applied to the diode, the voltage needs to be large enough to move charge carriers back into the
depletion region before and current can flow through the diode. If a backward voltage is applied to the diode, that voltage
just increases the depletion region and no significant current flows. Are these statements about the PN junction in a
diode true or false?
a) Electrons from the p-region diffuse across the junction into the n-region.
b) An electric field is created in the region of the junction.
c) In the region around the junction there are very few holes in the P region.
d) There is a voltage drop across the junction that opposes current in the forward direction of the diode.
5. The standard bipolar transistor has an emitter, a base, and a collector. It operates basically as a current amplifier, where
a small base-emitter current controls a much larger emitter-collector current.
a) Explain generally how the bipolar transistor works.
b) What are the major differences between the operation of a Field Effect Transistor (FET) and a Bipolar transistor?
c) Explain generally how a FET works?
6. Which best describes how a p-n junction operates as a solar cell?
a. Incoming photons heat up the semiconductor, thus promoting electrons into the conduction band, leaving behind a
hole in the valence band. The junction E-field pushes the electron and hole in opposite directions causing a current
to flow.
b. Incoming photons are absorbed by an electron near the junction, promoting it from the valence band to the conduction
band and leaving behind a hole in the valence band. The junction E-field pushes the electron and hole in opposite
directions causing a current to flow.
c. Incoming photons strike electrons pushing them in some direction. The diode formed by the junction only allows
current to flow in the backward direction, thus producing a net current.
d. The photodiode works like a Field effect transistor, with a field provided by EM wave from incoming light, causing
the junction to become conducting, causing a current to flow.
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e. The Electric field in the EM wave pushes electrons back and forth across the junction, but the diode only allows
current to flow forward, causing a net current to flow.
7. Diodes can emit light.
a) In a light emitting diode, what must be done electrically to cause the diode to emit light? How is the light emitted?
b) What feature of the band gap is needed to make the LED emit light without much energy going into heat?
c) Is the light from an LED produced primarily by spontaneous emission or stimulated emission?
d) What feature of the LED determines the color of the light?
e) What addition to an LED is needed to make a laser diode?
f) Is the light from a laser diode produced primarily by spontaneous emission or stimulated emission?
8. Find the radius of the nucleus of
238 U.
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9. Assume that Uranium, as it occurs naturally, consists of two stable isotopes, 238 U and 235 U. What is the abundance
235 U if the mean atomic weight is 238.02891 u and the masses of the two isotopes are 238.05079 u and 235.04393 u
respectively?
10. Using the atomic mass of 235.04393 u for
235 U,
what is its binding energy per nucleon?
11. Tritium has an average lifetime of 17.79 yr. What percentage of the 3 H nuclei in a Tritium sample will decay during a
period of 10 years?
12. What is the binding energy per nucleon for 3 H (Tritium) with an atomic mass of 3.0160492?
13.
the most copious isotope of Thorium with half-life of 14.1 × 109 yr., decays by α emission followed by β − emission
followed again by β − emission, then followed by 4 consecutive α emissions. What (still radioactive) isotope is produced?
232 Th,
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14. Consider a hydrogen atom with the electron in the 2p state. The magnetic field at the nucleus produced by the orbiting
electron has a value of 12.5 (2.5)T. The proton can have its magnetic moment aligned in either of two directions
perpendicular to the plane of the electron’s orbit. Because of the interaction of the proton’s magnetic moment with the
electron’s magnetic field, there will be a difference in energy between the states with the two different orientations of the
proton’s magnetic moment. Find that energy difference in electron volts.
15. A freshly prepared sample of a certain radioactive isotope has an activity of 10000 Bq. After an elapsed time of 4 hours,
its activity is 7000 Bq. How many atoms of the isotope were contained in the freshly prepared sample?
16. We wish to accurately date some bones estimated to be 30000 years old using Carbon-14 dating.
• If a sample has an activity of 0.1 Becquerels, how many decays can be measured per day?
• To get an activity of 0.1 Becquerels due to decays of 14 C, how big a sample of carbon from the bones is needed (in
kilograms)? The lifetime of 14 C is 8267 years, and the fraction of carbon (atoms), in a living organism, which are
14 C, is 1.3 × 10−12 . The average mass of Carbon is 12.010 U per atom (or grams per mole).
17. How does the sun produce energy?

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