David Sang and Graham Jones Solutions for Chapter: Medical Imaging, Exercise 3: Questions

3 Use the equation $I=I_0{\mathrm{e}}^{-\mu x}$ to show that the half thickness $x_{1/2}$ is related to the attenuation coefficient $\mu$ by:
$x_{1/2}=\frac{\ln 2}{\mu }$.

An X-ray beam transfers $400 \mathrm{J}$ of energy through an area of $5.0{ \mathrm{cm}}^2$ each second. Calculate its intensity in ${\mathrm{Wm}}^{-2}$.

An X-ray beam of initial intensity $50 \mathrm{W}{ \mathrm{m}}^{-2}$ is incident on soft tissue of attenuation coefficient $1.2{ \mathrm{cm}}^{-1}$. Calculate its intensity after it has passed through a $5.0 \mathrm{cm}$ thickness of tissue.