Answer to Question #174081 in Physics for Sam

Question

9. X-rays are used to images a bone in a patient ‘s leg. the X-rays have an intensity of 30.0Wm-2 when incident on the bone. 

The attenuation coefficient of bone (μ) is given by μ=2.5cm-1. Find the intensity of the X -rays at a depth of 0.69cm beneath the surface of the bone.

Answer 1

The intensity $I$ of the beam at the depth $x = 0.69cm$ is given by the following equation (see https://www.spectroscopyonline.com/view/tutorial-attenuation-x-rays-matter):

$$I = I_0e^{-\mu x}$$

where $I_0 = 30W/m^2$ is the initial intensity, $\mu = 2.5cm^{-1}$ is the linear attenuation coefficient. Thus, obtain:

$$I = 30\cdot e^{-2.5\cdot 0.69} \approx 5.35W/m^2$$

Answer. $5.35W/m^2$.