Experimental Data Analysis Lab

PHYS 391 - Fall 2017
Labs 2a - Brownian Motion, 2b - Counting Statistics

Updated 26 September, 2017 13:21

Do EITHER Lab, but not BOTH

Lab Goals

For Lab 2a: Brownian Motion: The goals of this lab are to explore the statistical properties of Brownian motion and confirm the diffusion relation. Learning how to perform video-based data analysis as well as understanding device calibration is also part of this lab.

For Lab 2b: Counting Statistics: The goals of this lab are to explore the statistical properties of coutning events in a random process. This process, radioactive decays of nuclei, is observable via its emission of ionizing radiation that can be observed using a Geiger-Muller tube and associated electronics.

Formal Lab Writeup (for both Lab 2a or Lab 2b)

This will be one of the few labs of the term where I ask for a formal lab writeup. This lab writeup should include 5 sections, as follows:

1: Abstract (write last!): 2 terse paragraphs. PP1 speaks to what you are trying to do, with a sentence or two about theory background and a few more sentences about the experiment(s). PP2 speaks to results, described in general.

2: Introduction & Background: more detail here. Start with the theoretical background for experiments, but PLEASE don't just reiterate what is in the lab handout! This section would describe lab goals in some detail, and SHOULD include an diagram or drawing of the experimental setup, with labels, etc.

3: Results: This section should give example tables or plots of data (but not all of it, please). It should address data 'quality indicators' (such as |(mean(delta_x))^2| vs. |mean(delta_x^2)|, and speak to how data quality was improved through lab procedures.

4: Analysis: Here we expect to see comments on significant tables and plots, including 'secondary' plots that are derived from computationally-reduced data (for example, a Time Evolution plot). One should state values here (e.g. various estimates of D and k_B. This section is where errors should be propogated and example calculations for error given.

( It is fine to subdivide the prevous two sections (3: and 4:) according to the assigned parts of the lab, for example data calibration: estimating D, estimating k_B, and doing 'Time Evolution'.)

5: Conclusions: Restate main findings (e.g. values for k_B, lessons learned from Time Evolution analysis). Give general impressions as to where procedures could be improved, suggest some 'next time' improvements.

In general:

Lab 2a (Brownian Motion) :

Manifest

Background Reading

See also the Brownian motion simulator for a more direct demonstration of how kinetic collisions with thermal molecules leads to Brownian motion.

General Instructions

The lab handout, linked above, gives detailed instructions for this lab. There are two main tasks for this lab, which can be done separately.

The first task is to collect data with the USB microscope which demonstrates Brownian motion of silicon microspheres in water. This data will be in the form of a time-lapse series of frames which can be saved as a movie. In addition to a chunk of raw data, some calibration data (observing a calibration plate of known dimension) is also necessary. This first step should be performed during your lab time with the equipment provided and TA supervision. Working with a lab partner is encouraged.

Here's another movie made 10-24-14 at 40x for you to peruse. Download it in order to see it, as it doesn't 'play well' in Firefox and other browsers.

I've included, here, a link also to a movie taken with 100x magnification. If you had problems in lab with spheres on slides not showing much motion, please use the movie linked in the paragraph above or the 100x movie to do your analysis. You'll need to determine scaling for the 100x movie, I didn't manage to make an image of the calibration slide with the setup. Be sure to check the number of pixels in the 100x movies to ensure it makes sense given the 40x movie linked above (paragraph) was taken with an OMAX microscope at maximum resolution. Given the size of the 100x movie, I don't think the same can be said about it. In other words, buyer beware!

The second task is analyzing this data in MATLAB to elucidate the statistical properties of Brownian motion. This second task should be done on your own.

Lab 2b (Counting Statistics) :

Lab Manifest

General Instructions

The lab handout, linked above, gives detailed instructions for this lab. There are four main tasks for this lab, which can be done separately.

The first task is to measure background levels with the Geiger counter and establish that the distribution of events seen in a given time interval follows a Poisson distribution. The second task is to verify the Gaussian approximation with width given by sqrt(n) by increasing the counting rate using a radioactive source. Third, we want to verify the inverse square law for the flux of particles through the detector. Finally, the attenuation of ionizing radiation through material will be measured.

Code Assignment

There is no explicit code assignment for this lab, although I do ask you to overlay a Poisson distribution on a histogram of data. This may be a bit tricky to figure out, so use your Pratap book if necessary (section 6.1.5 may be of some help). Also, you need to perform some linear fits to extract parameters with uncertainties. The linfit.m function should save you having to write your own function for this.

Errata

For reference, the Users Guide and Extended Users Manual for the Digital Radiation Monitors are available from Vernier.

Code Assignment for Either Lab

Please submit any matlab code you used for these analyses in a (compressed) zip file, emailed to the instructor. All information about what you have done should be included in your lab notebook.