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.