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Attenuation of Beta Particles

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-\(90\) (\({}^{90}\)Sr) which has an activity of \(5\,\mu\)Ci^{1}^{1}The curie (Ci) is an old-fashioned but convenient measure of radioactivity and indicates the number of decays per unit time. The more modern SI unit of radioactivity is the becquerel (Bq), which corresponds to \(1\) decay per second. The conversion between the two units is \(1\,\mu\textrm{Ci}=37,000\,\textrm{Bq}=37\,\textrm{kBq}\). Strontium-\(90\) 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 (\(\mkern 1.5mu \overline{\mkern-1.5mu \nu_{\mathrm{e}}\mkern-1.5mu }\mkern 1.5mu \)). 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.

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:

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

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

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\(\mu\) 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.

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