In these experiments, you are dealing with extremely small "signals" which would not be directly measurable; therefore, clever techniques are needed in order to amplify the effects of "small perturbations". You'll want to note that such techniques are irreversible. Careful consideration of technique and uncertainty will enhance your experience.
We'll all watch a brief movie on this topic, showing Jim Smith, who lives nearby, performing, during his younger days, this now-classic experiment on Time Dilation and Mu-Mesons. [While he made use of a mountain, last year's class suggested launching a high-altitude balloon from our quad....] During your viewing, make detailed notes in your lab notebook. I will collect and examine these notes.
After I return your (graded) notebooks, with comments, you will read through more detailed article describing the experiment, from the American Journal of Physics [D. H. Frisch, J. H. Smith, Am. J. Phys., 31, 342 (1963)]. After a careful reading, you'll be further prepared to begin doing science. Learn from how the authors have tried their best to consider any possible sources of error that they could think and, in particular, how they have tried to estimate the magnitude and direction of skew you might expect to be associated with each source of error they could think of. Scientific work often involves performing tests in order to track down the magnitudes and signs of various sources of error. Also, you should try to make it a personal habit, to incorporate at least some numerical work on both the random and potential systematic errors associated with your measurements and calculated results (in order to quantify your level of confidence in your conclusions - which you should try to make as high as possible!). Towards this end, everyone will write a summary of the arguments used in this paper. This summary should provide an outline of how the authors use scientific method and, in particular, how they deal with possible systematic and random errors. You'll want to be brief, but thorough!
While you may have used "Data Studio" software in our Introductory Physics courses, professional work requires that you be able to report statistical uncertainties for each of your fitting parameters (something that last year's software is not set up to do). This year, we introduce you to software packages that allow syntactic programming, e.g. for custom fits involving complicated functional forms, and also provide access to the more complete statistical reporting we now require.
Outside of the scheduled meeting time, you should practice your skills with both LabVIEW and with Igor Pro.
During this (three week) round, you may do one or more of the following labs (or propose your own alternative, as described at the end of this page). The lab constitutes a hefty chunk of your course grade, so I'm hoping that this is something you'll enjoy putting significant effort into.
Only those who try to actually complete their work during the first week are likely to develop a significant, satisfying body of work over the course of the round. [Once you do complete a lab, the goal is to extend that work in the subsequent weeks.]
Although these experiments do demonstrate some concepts that may be new to you, they invariably rely upon principles which you have already learned. Use your introductory text!! You are to use the sorts of physics that you already know in order to think through how your equipment is intended to operate, to plan your measurements, and to consider what can be learned. Importantly, the entire process should be documented in your lab notebook.
[On the use of references: Please provide a clear citation in your notebook, guiding your reader to the location in a text where you found useful information. Moreover, please note that it is far from sufficient to merely provide a citation: in your notebook, you must work through the key arguments and derivations that you have extracted from your references. Finally, a failure to provide proper citation constitutes plagarism.]
You can't easily measure ultra-small currents, right? So if you have,
say, thirty electrons passing by a detector each minute ... is that a measurable
current? For this lab, you'll want to figure out the operation of a
Geiger tube. Last week, after asking yourself how you might measure "single quanta," you examined a Geiger tube, puzzled over how it might work, and then did an experiment, mapping out the Geiger plateau. If you want to read a lot more about how Geiger tubes work, here are notes from the Univ. of Michigan (which has a Physics Department with a concentration in Nuclear Engineering & Radiological Sciences). They go into much more detail than we need for our purposes, but some of you may want to take a gander.
Your work can be extended in any number of ways (e.g., Radioactive Dating, etc.). There are many related articles available to you in the literature [e.g., "An experiment to measure range, range straggling, stopping power, and energy straggling of alpha particles in air," by P. J. Ouseph, Andrew Mostovych, Am. J. Phys. 46, 742 (1978)], and you might enjoy an online search of what's been published in this particular journal.
As a class, you will use a Geiger detector in an experiment aimed at determining (indirectly) the speed of something moving a good fraction of the speed of light!!! -- That is, if you had less energetic beta particles (as might be the case if you used an isotope other than Chlorine-36), then it wouldn't take as much aluminum to shield your detector. In other words, the "range" of the particle traveling through aluminum is a measure of its energy. This PHYS 106-style procedural is only a prompt for you to write, in your lab notebook, thoughts on "How do we judge a model""
Corrections: The apparatus is such that one can never have “zero” absorber thickness between the source and the counting system. Always present in the system are:
the Geiger tube’s end window, equivalent to about 1 mg/cm^2 of absorber;
the source cover, equivalent to about 1 mg/cm^2; and
the intervening air, which amounts to about 1 mg/cm^2 per centimeter of thickness. (The air thickness must be measured and corrections for these three things taken into account. Although the tables we supply for this lab make it easy, it should be clear in your records what is raw data and where corrections have been introduced.)
A browser search immediately reveals the dependence of range upon energy of a charged particle moving through matter. If your measured Range for the beta particles from a particular radioactive source turns out to be less than 1200 mg/cm2, then you can use the "empirical relation" below (found by accelerating electrons through known voltages, in the way you did in PHYS 106):
Energy = Exp[ 6.63 - 3.2376 Sqrt[ 10.2146 - Log[MeasuredRange] ] ]
where MeasuredRange is the numerical value of your measured range based on the CORRECTED total absorber thickness, in mg/cm^2, and the result will be the energy, in MeV.
To find the speed from the energy, see the final slide in Piazza Note @36, then go tell someone not in Physics how large a speed you were able to experimentally determine.
You can't "see" an electron, right? Well, no - not directly. On the other hand, you can set up systems that allow you to see the "trajectory" of very tiny particles.
Have you ever heard of a cloud chamber? The idea is to create an environment which is supersaturated with vapor (i.e., a system near an instability), so that even a tiny particle passing through will create an amplified, measurable "contrails" of the sort airplanes sometimes leave in the sky. You should read and think carefully about what it means and takes to create supersaturated conditions; without sufficient understanding, your chances of success are significantly diminished. Many designs have been suggested for the construction of cloud chambers. Can you get one to work? It's up to you to learn what's needed to make it happen!
By studying the effect of fields (e.g., a magnetic field) upon the "tracks", one can begin to learn about the nature of the particles that create these tracks.
If you'd prefer to "cut to the chase", we already have photos of particle tracks taken under well-documented conditions from a research-grade (bubble) chamber. Careful analysis is aided by several experimental tools.
Want to clearly see that the experimental relationship between energy and momentum requires relativity?
This lab also uses a Geiger counter, but here it is incorporated into something like the mass spectrometers you encountered in your earlier coursework. You'll need to sort out some of the set-up and the experiment on your own (using what you learned in PHYS 106).
[You should also do a citation search on Jack G. Couch, Terry K. Dorries, Am. J. Phys. 50, 917 (1982). Although this is not quite your experiment, it is close enough to make for good reading!]
1) American Journal of Physics: this journal has many articles that are "pitched" at your level (and some that are not).
2) Review of Scientific Instruments: a cutting-edge research-level journal, with extremely advanced articles; you should nevertheless feel encouraged to enter into conversation!
Again, the laboratory portion of this course is designed to offer flexibility: those interested in finding their own experiments to do, or apparatus to build, will find encouragement and opportunity.