2.4 Radiation Attenuation and Shielding

Understanding how radiation loses energy as it passes through a material is fundamental to designing effective shielding and ensuring safety.

The Exponential Attenuation Law

The attenuation of a beam of photons (X-rays and gamma rays) as it passes through a material is described by the **exponential attenuation law**. This law states that the intensity of a monoenergetic beam decreases exponentially with the thickness of the material.

$$I(x) = I_0 e^{-\mu x}$$

Where:

$I(x)$: The intensity of the radiation after passing through a thickness $x$ of the material.
$I_0$: The initial intensity of the radiation beam.
$\mu$: The **linear attenuation coefficient** ($cm^{-1}$), a value that depends on the energy of the radiation and the properties of the material.
$x$: The thickness of the material.

Linear and Mass Attenuation Coefficients

The linear attenuation coefficient $\mu$ is useful for a specific material, but it depends on the material's density. For a more universal value, the **mass attenuation coefficient** ($\mu/\rho$) is often used, where $\rho$ is the material's density.

This allows us to write the attenuation formula in terms of areal density ($\rho x$), which is independent of the state of the material (e.g., gas, liquid, or solid):

$$I(x) = I_0 e^{-(\frac{\mu}{\rho}) \rho x}$$

Practical Shielding Concepts

Two key concepts are used to describe the effectiveness of a shielding material:

Half-Value Layer (HVL): The thickness of a material required to reduce the intensity of a radiation beam to half of its initial value.
$$HVL = \frac{\ln(2)}{\mu} \approx \frac{0.693}{\mu}$$
Tenth-Value Layer (TVL): The thickness of a material required to reduce the intensity of a radiation beam to one-tenth of its initial value.
$$TVL = \frac{\ln(10)}{\mu} \approx \frac{2.303}{\mu}$$