PHYS3343 - MODERN PHYSICS
SPRING 2006 - EXAM 1
NAME : ______
A. The exam is closed book and closed notes.
B. A calculator is allowed to be used during the exam, but its memory must be cleared prior to opening the exam.
C. Academic Honesty Policy:
I agree to adhere to the standards of academic honesty at my institution during the exam. Since TECP students may be taking the exam at different times, I will not discuss the exam with any other student on any TECP campus prior to 5:00 PM on Friday March 10, 2006 unless I obtain permission from my course instructor.
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Student Signature (Required for Exam to be Graded)
1. ______( 25 points) 2. ______( 15 points)
3. ______( 15 points) 4. ______( 20 points)
5. ______( 16 points) 6. ______( 15 points)
7. ______( 20 points) 8. ______( 20 points)
9. ______( 20 points) 10. ______( 20 points)
11. ______( 24 points) 12. ______( 25 points)
13. ______( 20 points)
TOTAL ______(255 points)
GRADE______
1. The MGH-Northeast Proton Therapy Center at Massachusetts General Hospital,
MGH, in Boston will use an accelerator to produce a 230 MeV proton beam to kill both benign and malignant tumors in patients. As chief design physicist for ACME corporation (a subsidiary of Roadrunner International), you have been asked to supply answers for the following questions to your boss, Dr. Wiley E. Coyote, for his meeting with the hospital representative, Porky Pig.
A. What is the total energy of the proton beam?
B. What is the linear momentum of the proton?
C. What is the proton's wavelength?
1. Continued
D. Draw a graph of the bremsstrahlung x-ray intensity as a function of wavelength and label the cut-off wavelength.
E. If the proton beam strikes a lead plate at the end of the accelerator beamline, what is the shortest wavelength of x-ray that can be emitted.
2. Under ideal conditions the normal human eye will record a visual sensation at
550 nm if as few as 100 photons are absorbed per second. What power level does this correspond to?
3. If a photon has the same energy as the rest mass of an electron, what are the photon's
A. frequency
B. wavelength
C. Linear momentum
4. For Thomson's and Rutherford's model of the atom, you are to 1) draw a picture of the model, 2) describe the experimental facts that the model explains, and 3) describe any problems with the model
A. Thomson's Model
4. Continued
B. Rutherford's Model
5. Answer the following questions for the Bohr model of the hydrogen atom.
A. Write the individual assumptions in the Bohr model
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B. Prove that the allowed orbits in the Bohr model correspond to constructive interference of the electron wave.
5. Continued
C. What is the wavelength of radiation emitted by the hydrogen atom during an electron transition from the 2nd excited state to the ground state?
6. A muon traveling toward the earth at a speed of 0.99c appears to an observer on earth to live for a time of 8 ms before decaying.
A. What is the muon's half-life (time before decaying) according to the muon?
B. How far does the muon travel before it decays as seen by an observer on earth?
7. Consider the un-normalized probability distribution function
A. Calculate assuming that x is a continuous variable.
7. Continue
B. Calculate , assuming that x is a discrete variable that can only
take on integer values (…., -4, -2, 0, 2, 4, 6, …).
8. An electron in Chromium (atomic number 24) makes a transition from the n = 2
state to the n = 1 state without emitting a photon. Instead the excess energy is transferred to an outer electron in the n = 4 state which is ejected by the atom. This process is called an Auger process. Use the Bohr theory to
A. draw the energy diagram for Chromium.
8. Continued
B. to find the kinetic energy of the ejected electron.
9. Choose one of the following six famous experiments (Photoelectric effect, Michaelson-Morely interferometer, Davisson-Germer, Thomson's e/m, Franck- Hertz, or Geiger-Marsden). Indicate which experiment you are drawing, draw the
experimental setup, explain the function of each major piece of equipment, and the outcome of the experiment.
10. Two light sources are used in the photoelectric experiment to determine the work
for a particular metal surface. When a green light from a mercury lamp
(l = 546.1 nm) is used, a retarding potential of 1.70 V reduces the photocurrent to zero.
A. Based on this measurement, what is the work function for this metal?
B. What stopping potential would be observed when using yellow light from a helium discharge tube (l = 587.5 nm)?
11. A photon undergoing Compton scattering has an energy after scattering of 80
keV, and the electron recoils with an energy of 25 keV.
A. Find the wavelength of the incident photon.
B. Find the angle at which the photon scatters.
11. Continued
C. Find the angle at which the electron recoils.
12. Given the velocities of two particles in Reference Frame O shown below,
what is the relative speed of the particles?
13. Short Answers
A. Give three processes by which photons will interact with matter and explain how the processes differ.
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B. List at least two experimental observations that Bohr’s model correctly predicts.
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13. Continued
C. Give at least two problems with the Bohr model either philosophically or with its in ability to predict some experimental result.
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D. A heated object puts out 500 Watts of thermal energy and has a peak in its spectrum at 2.898 mm when the object is at 1000 K. What can be said about the power radiated by the object and the peak wavelength if the object is heated to 2000 K.
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13. Continued
E. Explain the assumption that Einstein made in solving the Photoelectric effect problem and how his explanation differs from the classical physics explanation.
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PHYS3443 EQUATIONS & CONSTANTS
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3) 4)
5) 6)
7) 8)