Show All Work for Partial Credit, and Have a Nice Break
While cleaning things up for the new term, I realized that I never did post my final exam from last term (Relativity and Quantum). Here it is. Scores ranged from a 52 to a 98, and the distribution was a little top-heavy, but not too bad. On the whole I was pretty happy with it, and with the class in general. Student survey responses were also generally positive, which is nice, as I pushed the class a little bit (one commenter called it "The hardest class I've ever taken"), and I was worried that they'd feel frustrated.
Physics 19 Final Exam, Fall 2002
1) Superman is exactly 2.00 m (a little over 6'6") tall, and, as everybody knows, is capable of flying (horizontally) faster than a speeding bullet.
a) A speeding bullet travels at approximately 500 m/s. If Superman flies through a physics lab at this speed, how much would Superman's height decrease, according to an observer in the lab frame? (HINT: this question asks for the change in height, not his full height.)
b) A witness to one of Superman's exploits swears that, as the Man of Steel flashed by him, he was 5'8" (173 cm) tall. This would require Superman to be moving quite a bit faster than a speeding bullet. What speed would be needed?
c) As Superman swooped in to save the day in part b, moving from west to east, Lex Luthor simultaneously detonated bombs on all four sides of a 100 m square parking lot. In what order do the bombs go off according to Superman (who is in the exact center of the lot at the time)? (Be sure to explain your answer.)
d) How much time passes between the first and last explosions, according to Superman?
2) A physicist decides to use a photoelectric cell as a source of electrons with a maximum kinetic energy of 1.00 eV. When he shines light with a wavelength of 723 nm on the cell, the stopping potential measured is 0.2 V.
a) What wavelength should he use to get the desired 1.00 eV electrons?
b) What is the work function of the metal in the cell?
c) He rigs up a small lamp to shine the appropriate light on the cell, at an intensity of 0.05 W/m2, and finds that 14,500 electrons per second are emitted from the plate. An hour later, however, the battery on the lamp has started to die, and the light intensity drops to 0.025 W/m2. What is the maximum kinetic energy of the electrons emitted now? (Be sure to explain your answer.)
d) How many electrons per second are emitted now?
3) Using semiconductor manufacturing techniques, it's possible to make a structure called a "quantum dot" which is a fair approximation of an infinite square well potential. A scientist studying the properties of quantum dots prepares one with a length L, and starts putting electrons into it. Each electron put into the "dot" goes into the lowest energy state available.
a) What is the energy of the first electron placed into the "dot"?
b) Neglecting interactions between the electrons, what is the energy of the 17th electron placed into the "dot"?
c) What is the normalized wavefunction for the 17th electron placed into the "dot"?
d) Part b) specifically says "neglecting interactions between the electrons." What interactions would need to be considered, and what effect would you expect them to have on the answer to part b)? Be as specific as possible, and explain your answer.
Short Answer
4) A diode laser works by putting electrons into the conduction band of a semiconductor, and letting them drop down into the valence band, emitting a photon on the way.
a) What is the minimum value for the band gap of the semiconductor in a diode laser operating at 811 nm?
b) What change in the band gap is needed to increase the wavelength by 1 nm?
5) A hydrogen atom is in the 7f level. How many degenerate sublevels are there in this state?
6) Would you expect Xenon-100 (Xe has atomic number 54) to be stable? Why or why not? If it is unstable, what sort of particles would you expect it to emit?
7) You send a friend to the store to get 1000 atoms with a half-life of 2.5 minutes. He shows up with only 127 atoms. How long did it take him to get back from the store?
8) A particle has a wavefunction given by:
Y(x) = 0 for x < -1 = A(x^4 - 1) for -1 < x < 1 = 0 for x > 1
What is the value of A that properly normalizes this wavefunction?
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