Gamma Lab Writeup Info

Suggestions from Dylan for the Gamma lab report.

GammaRayAbsorptionDiscussionTopics.pdf

Gamma Lab Uncertainty

Working through these questions will help you figure out the correct error bars for lead absorption data points in the gamma ray lab.

1. In lab you confirmed that the source emits gamma rays according to a poisson distribution \[ P(k) = \frac{\lambda^k}{k!} e^{-\lambda} , \] where \(P(k)\) is the probability of measuring \(k\) counts.
(a) Show that for the poisson distribution, the average value is \(\lambda\) and the uncertainty is \(\sigma=\sqrt{\lambda}\).
(b) Show that if you measure \(N\) total counts in some time interval, the uncertainty in the measured total number of counts is \(\sigma_N = \sqrt{N}\).

2. Suppose you measure counts over a time interval \(T\) seconds long, and observe \(N\) total counts. Your measured count rate is then \(n=N/T\) counts per second. Assuming \(\sigma_N = \sqrt{N}\), show that the uncertainty in the count rate is \(\sigma_n = \frac{\sqrt{n}}{\sqrt{T}} \). (Hint: There are two ways to show this. One is by averaging over \(T\) one-second intervals. The other is by using the propagation of error formula.)

3. Let \(n=n_m-n_b\) be the difference between a measured count rate and a previously measured background count rate. You have already determined values for \(\sigma_{n_m}\) and \(\sigma_{n_b}\). Show that \(\sigma_n = \sqrt{\sigma_{n_m}^2 + \sigma_{n_b}^2 } \). When your measured count rate is small, the background uncertainty will be a significant contribution to the error bar.

4. Assume that you have measured count rates \(n_1, n_2\) and calculated uncertainties \(\sigma_{n_1},\sigma_{n_2}\) at two different thicknesses of lead. Let \( f = - \ln \frac{n_2}{n_1} \). Show that \[ \sigma_f =  \sqrt{ \left( \! \frac{\sigma_{n_1}}{n_1} \!\! \right)^{\! 2} + \left( \! \frac{\sigma_{n_2}}{n_2} \!\! \right)^{\! 2} } \; . \] This is the error bar that should appear in your plot, where the uncertainties on the right-hand side take into account the previous questions.

2nd Homework dues date.

If you have midterm tomorrow (Tuesday), then you can hand in your 2nd homework on Thursday instead of tomorrow.

Example Lab Report

Here is an example of a short lab report. First is an example of a bad report, with common mistakes labelled. Second is an example of a good version of the same report.

jellybean.pdf

Thanks to Prof. David Smith for this example.

Python Plotting Tutorial (Part 4)

Making Prettier Plots
This example shows how to add custom titles, axis labels, range limits, tickmarks, and grid lines to your plot.

Python Plotting Tutorial (Part 3)

In this part, we'll see how to define functions and plot complex functions.

Python Plotting Tutorial (Part 2)

In this part we'll cover a few miscellaneous things...

Python Plotting Tutorial (Part 1)

Here's a script which makes a simple plot in python. First look at the example, then we'll break it down line by line.

Input:


Output:


Ok, let's break it down.

Plotting Tools -- Python

We have set each of you up with an online tool for using the Python programming language. Python is easy to use, and is a powerful tool for plotting and data analysis. To log in visit:

hyperion.ucsc.edu
username: your ucsc username (i.e. username@ucsc.edu)
pwd: Winter2017

To create a new folder, click New > Folder in the top right.
To create a python script, click New > (Notebooks) Python in the top right.
To run your script, press Shift+Enter.
Please Shutdown all of your running processes before logging off or closing the window.
This system runs Python 3.

Tutorials for plotting will be coming soon.

Video related to homework on circuits.

This video is related to your homework on circuits and impedance. It focuses mainly on the basic physics of circuit analysis --how to use basic concepts related to current and voltage to analyze a circuit driven by an ac source. It includes an analysis of the amplitude and phase shift associated with the current response. Let me know if you find it helpful and please free free to ask any questions and comment here.  -Zack

Impedance Lab Instructions and Resources

For the impedance lab, we are doing things a bit differently from the lab manual. The manual contains three experiments: DC voltage source, AC impedance, and nonlinear elements. We are eliminating the first and last -- you should only include the AC impedance experiment in your reports. The other two parts are now optional exercises.

Below are some resources for this lab. The new instructions override the lab manual. However, the manual does contain useful information about resonant circuits and about extracting the component values with linear fits.

Homework due dates.

Please turn in your first homework assignment in class on January 19th or 24th.  (I would recommend 19th since that is farther away from the due date for your first lab.) It can be either of the two assignments posted, your choice. For example you may wish to choose the one that is most relevant to you at this time.
2nd homework is due Feb 7th.

Homework on Statistics

The link below will take you to a pdf with your statistics homework assignment.  Please post comments, questions, corrections... here.

https://drive.google.com/file/d/0B_GIlXrjJVn4M0xpeUsxT21rbzA/view?usp=sharing

Homework on Circuits and Impedance.

Note. Graphing, figure captions, labels and scales are an important part of this assignment.

1.  Consider a resistor and a capacitor in series driven by a voltage source.
a) First suppose that the system is in equilibrium with no current flowing and no charge on the capacitor for t less than zero. Then at t=0 the voltage jumps up to 5 volts in a very short time. Calculate and graph the voltage across the resistor and the charge on the capacitor as a function of time. Please do a sketched graph drawn by hand with sufficient care to capture what is essential and important, but ideally without excessive detail or a million points calculated. Include a figure caption for your graph as well as labels and scales on all axes.
b) Alternatively, suppose that instead of looking at the response to a step voltage, we imagine that the system is driven by the voltage source with an applied voltage of \(v(t) = V_o cos (\omega t)\). In this driven case calculate the current and the charge as a function of time for the steady state solution (ignore possible transient effects).
c) Graph the driving voltage and the current (through the resistor) as a function of time for a frequency that seems relatively low to you. Indicate the phase relationship for these in your graph.
d) Graph the driving voltage and the current (through the resistor) as a function of time for a frequency that seems relatively high to you. Indicate the phase relationship for these in your graph.
e) Do the same for an intermediate frequency. (Please draw all graphs by hand with sufficient care to capture what is essential and important.)
f) Graph the magnitude of the impedance of this system as a function of driving frequency.
Graph the phase relationship between the driving voltage and the current as a function of driving frequency. Please include a figure caption for your graph as well as labels and scales on all axes.
g) Thinking back to part a) what do you think would constitute a "very short time". Explain. You can use phrases like "characteristic time scale" in your explanation.

2. Consider a resistor and an inductor in series driven by a voltage source.
Do all the same things as in problem 1, parts a-g.

3. Discuss/explain the similarities and differences between your results from 1. and 2.

Some notes on writing lab reports.

Writing lab reports

(Usually people start with section 3 and then do the introduction and abstract last. Actually, starting with the figures and figure captions and then writing sections 3), 4) and 5), in that order, often works well.)

Special note: Figure and table captions are very important and should be cogent and readable on their own.

1) Title and abstract

 An abstract is typically 1 paragraph. Summarize what was done in the lab in a cogent manner, including major results, salient points and conclusions. It should stand alone from the rest of the report.

2) Introduction

 The introduction can provide background, context and motivation. Include an explicit statement (a paragraph or perhaps even just a sentence) of what will be done. It's usually the right place to introduce the theoretical background and concepts.

3) Apparatus and procedure

In this section, describe how you did the experiment. List the major components and describe of their functionality. Describe procedures, and their motivation. Usually, you do not include specific results in the procedures section, but you do discuss how the measurements are done and how the results obtained (for instance, in the impedance lab, you would discuss how the impedance Z is derived from your measured voltages for a given frequency).

4) Results

Present data/results clearly in written paragraphs, tables and figures. This may include both raw and derived data (e.g. for the circuits lab, the amplitudes and frequencies from the scope as well as the calculated values of impedance and/or admittance. You should not just include a series of tables and plots: there should be a narrative introducing each set of data and results, and referring to the corresponding tables and plots. Figure and table captions are very important and should be cogent and readable on their own.

5) Discussion and analysis

Discuss your results, interpret data and present your findings. This section is very important. Sometimes the boundary between results and discussion and analysis can be a bit porous.

6) Summary and conclusions

Think of the "big picture" of what your experiment and analysis is all about. Summarize what you your experiments and analysis have shown and emphasize key points of your report. Any new ideas of how to go about things?  The summary/conclusions should tie back in to the introduction. If one of your goals was to make a quantitative measurement, you can quote the (quantitative) result in the conclusion.

Welcome to Physics 133

People: Prof Zack Schlesinger, ISB 243, zacksc@gmail.com (please use this email)
office hours in class and by appointment, 831 459-3714 (email preferred for messages)

TA Dylan Kennedy, (dymkenne@ucsc.edu)  

TA Joseph Schindler, (jcschind@ucsc.edu)   

About: This is a lab class and centers on you doing three experiments and writing about them. The experiments are described in your lab book (available at the BayTree Bookstore). (The one I have says “Physics 133, UCSC, November 3, 2016” on the cover and it is green.) The three experiments are:

1. Quantum Spectra (aka Atomic Spectra)
2. Impedance
3. Gamma Ray Absorption

There are also two homework assignments. Please turn in all homework assignments and lab reports on time.

Homework due dates:  
January 19 or 24: HW1
February 7: HW2

Lab due dates:  

LAB I: report due January 31.

LAB II: report due Feb 21. 

LAB III: report due March 16.