Answer to Question #174077 in Physics for Sam

Question

5. X-rays hit a lead block with an intensity of 200Wm-2. Lead has a linear attenuation coefficient of 27 cm-1. Calculate the intensity of the X-rays 15mm into the lead block.

Answer 1

The intensity $I$ of the beam at the depth $x = 15mm = 1.5cm$ is given by the following equation (see https://www.spectroscopyonline.com/view/tutorial-attenuation-x-rays-matter):

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

where $I_0 = 200W/m^2$ is the initial intensity, $\mu = 27cm^{-1}$ is the linear attenuation coefficient. Thus, obtain:

$$I = 200\cdot e^{-27\cdot 15} \approx 5.2\times 10^{16}W/m^2$$

Answer. $5.2\times 10^{16}W/m^2$.