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# 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-$$90$$ ($${}^{90}$$Sr) which has an activity of $$5\,\mu$$Ci11The 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.

## Theory

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

$$I_{x}=I_{0}\,\exp\left(\mu\,x\right)\nonumber \\$$

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

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

where $$\rho$$ is the density of absorber, and

$$\ln I_{x}=\ln I_{0}-(\mu_{m})(\rho x)\nonumber \\$$

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.