Question 5

Describe, in terms of X-ray photons, the attenuation mechanism of photoelectric absorption.

A parallel beam of X-rays is incident normally on a uniform bone sample.

The variation of the intensity $I$ of the X-rays with depth $x$ in the bone is shown below.

$Graph showing intensity I of X-rays in 10^3\text{ W m}^{-2} versus depth x in cm. The vertical axis ranges from 0 to 5.0, with gridlines every 0.1 units. The horizontal axis ranges from 0 to 1.5 cm with gridlines every 0.05 cm. The curve starts at (0, 5.0) and decreases exponentially, passing exactly through the point (1.2, 2.0).$

The bone has a uniform structure between $x = 0$ and $1.2\text{ cm}$ .

Use the graph to determine the attenuation coefficient $μ\mu$ in $cm−1\text{cm}^{-1}$ of the bone.

Use the graph to determine the exposure time $t$ for the total radiant energy incident per $cm2\text{cm}^2$ at a depth of $cm1.2\text{ cm}$ to be $J4.8\text{ J}$ .

Beyond $1.2\text{ cm}$ , the bone is replaced by a denser material having a larger attenuation coefficient than the value calculated in (i). Describe the key features of the gradient and shape of the continuation of the curve of $I$ versus $x$ beyond $1.2\text{ cm}$ .