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Uncertain Principles

Physics, Politics, Pop Culture

Friday, January 03, 2003

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?

Posted at 12:11 PM | link | follow-ups | 4 comments

Snow on the Thruway from Schenectady to Buffalo

It's snowing. Again.

Depending on whose numbers you believe (I got a haircut this morning, and the forecasts quoted by people coming in had increased from "ten to twelve inches" to "sixteen to twenty-one inches" by the time I left, though the radio station I have on in my office is still saying "ten to eighteen"), we're getting either "a whole lot of snow" or "way too goddamn much" snow.

And, with classes starting Monday, I pretty much have to stay at work this afternoon, to get ready. It's going to be a fun ride home, that's for sure.

Global warming, my ass.

Posted at 11:56 AM | link | follow-ups | no comments

Thursday, January 02, 2003

Rugby Mentality, I'll Have It 'Til I'm Dead

Back in the halcyon days of my mis-spent youth, I spent several years playing rugby. While it's been a couple of years since I last played, it's left its mark in many ways: I make sure to channel-surf past Fox Sports World on a regular basis, just in case they have a game on; I have a pair of nagging shoulder injuries that act up from time to time; I have a bone-deep loathing of bourbon whiskey, particularly Jim Beam; and I know a large number of off-color drinking songs.

Which isn't necessarily a bad thing, as at least I have a mental image to go with Terry Pratchett's frequent references to "the hedgehog song" (it's probably not the same one he's thinking of, but the basic idea is the same), even though I catch myself humming "I Don't Want to Join the Army" in the lab from time to time (Obligatory In-Joke: "This song is not a rebel song..."). But among those songs is one that consists entirely of dirty limericks, strung together with an odd Mexican-themed chorus. Among the verses is:

A newlywed couple named Kelly
Got stuck belly to belly
It seems in their haste
They used wallpaper paste
Instead of petroleum jelly

Having spent the last two days removing ugly wallpaper from the new house (a process which involves using steam to loosen the glue, allowing you to peel the paper off the wall, getting the newly viscous glue all over everything), I suspect I'd be happier not knowing this one particular song.

Posted at 4:50 PM | link | follow-ups | 3 comments

Tuesday, December 31, 2002

This Is Spilifantrr

A few random sports-related items:

Anyway, you get the idea. Lots of sports news, not so much blogging time.

Posted at 9:11 AM | link | follow-ups | 4 comments

Monday, December 30, 2002

Pining for the Fjords

I spent an hour or two yesterday scraping paint off the living-room ceiling in our new house. Whoever painted it last did a stunningly bad job, through a combination of general incompetence and really cheap paint. My parents (old hands at this DIY stuff) had come up to help with general fix-it activities, and shortly after my father started poking at some peeling paint on the ceiling, a three-by-four foot sheet of paint came off the ceiling. That's not a unit error-- the piece of paint that came down was just about the size of Kate...

So I spent a bunch of time scraping paint off the ceiling. It came off in huge irregular strips, leaving behind vague blobby shapes like creeping eldritch horrors in a Lovecraft story, or some sort of white-on-off-white map of imaginary continents. It was still a tedious job, though the task was somewhat lightened by viewing the scraper as the implacable hand of God (or geological forces, for the atheists in the audience), re-arranging the landscape. Scrape-- there goes the Iberian peninsula. Scrape-- so much for Scandawegia, pity about the fjords... Even that got old pretty fast...

Eventually, we ended up clearing the paint from about half the room-- one or two areas were oddly tenacious, but most of the paint on the end of the room by the fireplace wound up in the trash. There's a ragged line midway across the room, where the old paint stayed up a little better. Spackling and sanding that to eliminate the impression of a spreading blight will no doubt provide much of this afternoon's entertainment.

And then there are the myriad offenses against good taste perpetrated by the previous owners, such as painting the brick fireplace a sort of dingy cream color. Though one can hardly blame them for covering up the pea-green paint applied by the owners before them-- when the Interior Desecrators book comes out, I fully expect to see an earlier incarnation of my living room therein. It's a small comfort, while removing the paint through a combination of chemical stripper, power tools, and brute force, to know that the curses I'm heaping on the heads of those responsible will insure them an endlessly interesting afterlife...

I could go on, but, well, there's too much else to do. There's plenty of stuff I'd like to blog about, and I'll probably be writing posts in my head as I scrape, sand, and spackle the walls, but I have no idea how much of it will get posted. And the fun is just beginning...

Posted at 12:13 PM | link | follow-ups | 4 comments

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