PH253 Final exam pro tip

Pro tip: a problem might look on first sight just like one you've seen, but you still have to read it all the way through to make sure.

I say that since I'm seeing that same mistake again & again on HW9 ... the second problem was nearly like one from last year, but the second part was different in a crucial way. By "different" I mean "not even remotely close."

Let's recap: when you see a familiar-looking problem tomorrow, it might be a trap. Make sure I haven't changed anything key before you just go solving stuff all willy-nilly.

And, a bonus pro-tip: don't forget your calculator. There may actually be numbers other than pi and 2 on the exam. I think a 7 got in there while I wasn't looking.

PH253: HW10 #2

Here are a couple of hints.


Hint the first.
Hint the second.

PH253: HW8 #2

Check it. Good idea to google the phrases I put in italics.

PH253: help on HW

I uploaded some new files here that will be of great utility.

UPDATE: on problem 3b, those should be x's not r's

Also, some useful bits from hyperphysics:

Hydrogen energies & levels:

http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html#c2

Spectrum:

http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html#c4

Quantum physics topics:

http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon

Schrodinger & Hydrogen concepts, Wave functions & plots:

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/schrcn.html#c1

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydcn.html#c1
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydwf.html#c1
http://hyperphysics.phy-astr.gsu.edu/hbase/hydwf.html#c1

PH253: random exam hints

Just sent this as an email to one of you:

I think the best thing to study right now would be 1) the practice problems I put out - I will use one or two of them directly on the exam, and 2) this semester's and last semester's homework problems, focusing on the shorter problems (not the really lengthy and mathematical ones). The exam questions will be easier than most HW problems, but covering similar topics.

The book doesn't have many good problems for 2.4.1-2, I have to admit. The problems on uncertainty will be like numbers 9 & 10 on the practice problems - using a de Broglie wavelength and the uncertainty principle together, but in a more or less straightforward way. If you can do those two problems, you are more or less OK on 2.4.1-2.

For Compton scattering, just read the notes I put out, and that should be enough.

For relativity, the sample problems are good.

For the Photoelectric effect, there is really only the one equation - it will have to be something like given wavelengths and voltages, find the work function ... not much else to ask.

For photons & the quantum hypothesis, questions will be like something like the HW problem finding the number of photons per second put out by a radio transmitter.

For radiation, it will be a simple example like given an acceleration, find the power radiated by a charge, or the energy radiated in a time t (E = Pt).

PH255: Writing a scientific paper

Lab reports are a real pain, and I know many of you in PH255 have been struggling with how to go about writing a lab report. Here's how I usually go about writing a paper:

PH253: HW4 hints

I'll be updating these through the evening as I finish them up. The link will be persistent. I'll post here when they are complete.

UPDATE: barring any typos I find later, the hints are about as complete as they are going to get.

PH253: HW3 hints

I'm starting a file of HW3 hints. Right now, there are hints for the first three problems, I will be updating it tonight and tomorrow to add more. Probably by class time tomorrow it will be as complete as it's going to get ... the URL will not change as I update the file. If you like, check here to look at the time stamp and see if it has been updated since you lacked looked.

UPDATE: the hints are probably about as complete as they are going to get. A little something for each of the 9 problems.

PH253: HW 2.1

For problem 1 on HW2,  you'll find this interesting. (Note the 'dot' notation to signify derivatives with respect to time.)

PH253: homework 2 hints

Check it. As will be our habit, we'll fully work some of the problems in class, and at least set up the rest. This homework is mathematically challenging in a few places, but I'll try to spend a little extra time on the most difficult spots

(Also, notice that in the notes on radiation I've included some example problems toward the end ...)

Tomorrow, we'll deal with accelerating charges and figure out where radiation comes from. In the notes I've written up, we'll start with 1.2.2 (Charges that start and stop) and try to get as far as the equation of motion for oscillating charges (1.3.5). Thursday, we'll continue from where we left off and finish off the rest.

Again, I will probably skip some of the details in the notes to focus on the most important results. I tried to be as thorough as possible in the notes so you could see how everything we need can be derived from what we already saw in PH105 and PH106.

PH253: HW1 hints

Tuesday, we'll set up most of the homework problems, time permitting. Thursday, we'll set up the remaining problems. Until then, below the fold are some hints on how to get started. I would agree that this HW is conceptually difficult, and requires a good knowledge of calculus in some spots. Later HW sets will be less conceptually challenging, but the math will not let up, sadly.

Also, keep in mind I may have asked some of the same problems last semester, if you dig around the HW directory ... you may also try ph102.blogspot.com. Questions I've asked before, somewhere, sometime, have a * next to them below.

Lastly, the PH102 notes I posted previously will be enough to get you through Tuesday's and Thursday's lectures. Though some of the derivations are missing, the basic results are there. For Thursday's lecture, check out the beginning of the chapter called "Magnetism" for a derivation of B from E.

PH253: Last-minute cramming

Anyone who told you last-minute studying is not helpful never tried it. (A good night's sleep is still good, when you can get it.)

• Understand how to find the equilibrium spacing, given a potential U(r). Remember how to find the maximum force?
• Understand how a set of spectral lines splits in a magnetic field (HW8 #2).
• Choose your problems carefully! Some are traps, to be safely sprung only by the most mathematically adept ... (that is, some problems are very tedious unless you are a math savant).
• You did quite a bit of work with hydrogen wave functions. Remember it.
• HW5 #7: all physicists love the harmonic oscillator to a fault. You will see it in every PH course, this one included.

PH253: HW9 hints

Copious hints on HW9 below the fold ...

PH253: hints on HW6-7, #1

There is one big issue with this problem: there are lots of shiny numbers that you're just dying to plug in to messy equations. Resist! It is a trap!

PH253: more practice problems

UPDATE 5: some typos fixed, particularly one in problem 10 just above equations 36-39. The sentence fixed was "The muon has both kinetic energy and rest energy, and we can write its total energy in terms of ..." The prior version said "... write its total kinetic energy ..." which is incorrect.

UPDATE 4:  all problems should have solutions now. I also realized that partial derivatives are beyond the stated math prereq, so you can ignore problem 11 ... something like that will not be on the exam.
UPDATE 3:  answers for all but 11 are included and some typos in the problems fixed.
UPDATE 2:  answers for all but questions 6, 8, 11 are there.
UPDATE: answers for about half the problems are up now. Should have the rest done in an hour or so.

Here you go. These are much closer to real exam problems. Read the general comments as well: one or two of these problems might just show up on the exam with little or no modification.

Answers & some solutions will follow later today.

UPDATE: I scratched the first problem (density and so forth) on further reflection.

Formula sheet (quick draft)

Here's a rough draft of the formula sheet for the exam, to give you an idea. I have not yet proofread it carefully, nor checked to be sure that I don't want to add or subtract a few things. It is unlikely to change noticeably, but just a heads-up. Any odd integrals/derivatives you need for specific problems will be provided within the problem itself, you will not be expected to memorize arcane calculus formulas (just basic ones).

At least a day or two before the exam, I will post an updated version if there is one. What you see so far is a good indication of what you do and don't need to put on your own formula sheet, however.

If you notice any typos/errors/odd omissions, please let me know.

Homework 4 hints

Most of the homework should make sense after Tuesday's lecture, if not already. Here are some hints to get you started.

1) Write w as a function of k and differentiate. Re-write the derivative in terms of p (substituting for k), and use the relativistic form of momentum to get everything in terms of c and v. Should work itself out.

2) The dropped ball will have some random horizontal velocity due to uncertainty, which gives a spread in x. Get the momentum uncertainty from this initial uncertainty in x, which gives you the velocity uncertainty. The final uncertainty in horizontal position is then governed by normal mechanics - final position is initial position plus velocity times the time required to fall a distance H. Once you have an expression for the final spread in x, differentiate with respect to initial uncertainty to minimize. We'll go over this in class, it is sneaky.

3) Plug and chug. Momentum is (gamma)mv, plug that in de Broglie. Simplify, and define the Compton wavelength to be h/mc.

4) The uncertainty relationship gets you momentum uncertainty from a given position uncertainty. Best-case scenario: the position has its minimum uncertainty value (Delta)x. Get E in terms of x, differentiate, and plug the extremal x value back into your energy equation.

5) There is an extremely good chance that these lines correspond to the emission spectrum of a simple element. If you figure out which one, subsequently figuring out all the combination is far easier.

6) The de Broglie wavelength is h/mv. The average velocity from kinetic theory is:

\langle v \rangle = \sqrt{\frac{3k_BT}{m}}

There go you. Note that the mass of a helium atom is about 4 atomic mass units. Also note that this is a problem from your text, i.e., the numerical answer is in the back of the text.
7) Huh. Nearly what we did in lecture :-) You may also find the MIT course 8.04 Open Course Ware (OCW) interesting. What's different about the helium ion?

8) We'll go over this one in class. Again related to the MIT 8.04 OCW.

PH253: Homework 3 hints

Here are a few hints to get you going, I'll post some more later tonight.

#1 - really just unit conversion ...
#2 - if you use energy & momentum conservation, you should come to a ridiculous conclusion. For instance, if you write the energy and momentum of the electron in terms of gamma, try solving for the electron's velocity ...
#3 - conserve momentum. The velocity will be very small (but measurable with the Mossbauer effect, which we'll get into later).
#4 - there is only one thing different compared to normal Compton scattering. It is that easy.
#5 - Rewrite the Compton equation substituting energy in place of wavelength appropriately. The energy difference E_i - E_f will be a function of E_i and E_f, and that is OK. Proportional to both, in fact.
#6 - just do what I suggested in class ;-)
#7 - from frequency and speed, you can get wavelength. The total energy per unit time is just power, which is the energy per photon times the number of photons per second. It is a stupidly large number of photons.
#8 - plot + regression ("trend line" in business-speak). Note that the slope of the stopping potential (y) versus frequency (x) gives you h/e, not just h! Multiply the slope by e=1.6e-19 to get h in familiar units.
#9 - you can use your result from #5. If the electron is initially at rest, its energy is just its rest energy. You want to find the change in energy divided by the incident photon energy. As we discussed in lecture, the energy shift should be much larger percentage-wise for higher energy incident photons.

PH253: stray HW2 hints

#1 - That's not a typo, it really is hc^2, not hc. There is a difference of a factor 4/c when you talk about energy or power, but here we are worried about intensity. The rest really is just math ...

#2 - Still just math ... but note that the constant 'sigma' you find here is not the same as the Stefan-Boltzman constant of number 7. Again there is a factor 4/c to convert between energy and intensity.

#3 - Just the Wien displacement formula, nothing more.

#4 - We'll talk about this in Thursday's lecture if you're having problems.

#5 - Using a fixed wavelength of 641nm, just calculate I(T) for both temperatures, using the formula from #1 and take the ratio.

#6 - Circular motion + electric force gets you velocity. Acceleration on a circular path is determined by velocity and radius (given). Kinetic energy comes from velocity, and power is energy divided by time. I'll field questions on this in lecture, there are a few steps involved.

#7 - The rate of heat loss is just the power emitted as thermal radiation, which you know to be P = A(sigma)T^4, where A is area and sigma is the Stefan-Boltzman constant. Power loss is due to thermal emission by the human, but the human is also absorbing thermal power due to the temperature of the surroundings (over the same surface area). Power lost minus power absorbed is the net power loss, which is the rate of heat loss.

PH253: HW2 #1

If you're a programmer, this may help with the first problem, as will this.

At some point in the problem, you have to find the root of an equation numerically. You can do this by any means necessary, including a graphical solution. Code solutions will please me though.