Attenuation of Beta Particles

Background

In this experiment we will study the attenuation of beta particles in aluminium, using a radioactive source and a Geiger counter detector.

The source used is strontium-\(90\) which undergoes \(\beta^{-}\) decay into yttrium-\(90\) with decay energy \(0.546\) MeV and half-life \(28.79\) years.

Each decay emits an electron (\(\mathrm{e}^{-}\)) and an electron anti-neutrino (\(\mskip 1.5mu \overline{\mskip-1.5mu \nu_{\mathrm{e}}\mskip-1.5mu }\mskip 1.5mu \)). Neutrinos have negligible probability of interacting with matter. Electrons, however, lose kinetic energy as they interact electromagnetically with matter. So, they can only travel a certain distance, or range, before they come to rest.

Theory

The absorption of \(\beta\) rays is given approximately by Beer’s Law

\begin{equation} I_{x}=I_{0}\,\exp\left(\mu\,x\right)\nonumber \\ \end{equation}

where:

  • \(I_{x}\) is the intensity after passing through an absorber of thickness \(x\);

  • \(I_{0}\) is the initial intensity at the source;

  • \(\mu\) is the linear absorption coefficient.

Thus, a plot of \(\ln I_{x}\) against \(x\) theoretically results in a straight line whose negative slope gives \(\mu\).

In practice the linear absorption coefficient \(\mu\) will vary widely from one absorber material to another. However, the quantity \(\mu/\rho\) is approximately constant for all types of absorbers and hence the use of this quantity, the mass absorption coefficient (\(\mu_{m}\)) is to be preferred. This necessitates expressing the thickness of absorber not in units of length, but in g cm\({}^{-2}\). Beer’s exponential absorptions law becomes

\begin{equation} I_{x}=I_{0}\,\exp\left[-(-\mu/\rho)(\rho x)\right]\nonumber \\ \end{equation}

where \(\rho\) is the density of absorber, and

\begin{equation} \ln I_{x}=\ln I_{0}-(\mu_{m})(\rho x)\nonumber \\ \end{equation}

Hence a plot of \(\ln I_{x}\) against thickness, expressed as \((\rho x)\) results in a straight line whose slope gives the mass absorption coefficient (\(\mu_{m}\)).

A typical absorption curve is illustrated in Figure 1. It shows two main regions of interest - the sloping beta absorption component, A, and a more penetrating component, B.