Motivation and Courses:
Many advanced laboratory courses involve a sequence of unique experiments, where students rotate through a series of experiments. At Queen's University, we are aiming to have students do significant open-ended experimental projects, so we want preparatory experiments that we can deploy to all students at once, giving the support needed to allow the project to be both ambitious and successful. We have designed an experiment that we ran for 40 students at a time in fall 2017 which addresses the following learning outcomes:
- Learn the basics of radioactivity and work safely with radioactive sources;
- Understand and perform particle counting and spectroscopy experiments;
With secondary learning outcomes:
- Continue to use software for non-linear curve fitting
- Understand calibration of instruments
- Use and modify simple op-amp amplifiers in experiments
- Compare a model to data
Background:
This lab is intended to function as a first introduction to particle physics. You will use a silicon semiconductor detector, a customizable charge and voltage amplifier, and the Red Pitaya STEMlab device to investigate the alpha decay of an 241Am radioactive source and alpha particle energy loss in air and through mylar films. The full instructions for the Fall 2017 lab are available\cite{knobel2017}.
Theory and Model:
Ionizing radiation produced from radioactive decay takes the form of photons (x-rays and gamma rays), electrons (beta particles), positrons, fission fragments and alpha particles. Alpha particles (\(\alpha\)), the ionized nuclei of a helium atom, are both heavy and highly charged, so they interact strongly with matter, ionizing the atoms of the material they pass through. Thus alpha particles lose energy quickly, and the ~ MeV particles emitted from typical radioactive sources can be stopped by a sheet of paper or a few centimetres of air. This energy loss can be described by the stopping power \(S\left(E\right)=-\frac{dE}{dx}\), where \(E\) is the energy and \(x\) the distance traversed in a medium. Often the mass stopping power is used, where the mass stopping power is divided by the material density. Bethe derived a classical relativistic formula describing the stopping power\cite{Knoll2010}:
\(S=\frac{4\pi e^4z^2}{m_ev^2}NB\),
\(B\ =Z\left[\ln\frac{2m_ev^2}{I}-\ln\left(1-\frac{v^2}{c^2}\right)-\frac{v^2}{c^2}\right]\)
where \(c\) is the speed of light, \(v\) the speed of the particle, \(z\) the charge of the alpha particle (ie. 2), \(Z\) the atomic number of the absorber atoms, and \(N\) the atomic density in the target material. The mean ionization potential of the absorber atoms \(I\) is typically taken from tables, though it is approximately \(I\approx\left(10\, \mathrm{eV}\right)Z\), allowing a quicker approximation. For non-relativistic particles, only the first two terms in \(B\) are important. Since the energy loss of the alpha particles is approximately \(S \propto 1/v^2\), so that as the particle slows down, the energy loss increases, meaning that near the end of the particle's track \(S\) increases to a peak before dropping as the particle bonds with electrons - the so-called Bragg peak. More precise models of stopping power include the quantum nature of the stopping material and higher order terms, and these are tabulated through the ASTAR webpage at \cite{nist}.