Airport Security X-ray Imaging · AI Generator #GEN-21B28CD0

Physics · modern-physics

Problem

Modern airport security scanners use X-rays with energy

E = 120\;\text{keV}

to image luggage contents. The scanner creates images by detecting how much X-ray intensity is absorbed when the beam passes through different materials. A particular scanner requires that at least

25\%

of the original X-ray intensity must reach the detector to create a usable image. A passenger's suitcase contains a steel laptop computer with thickness

t = 8.0\;\text{mm}

. Steel has a mass density of

\rho = 7800\;\text{kg/m}^3

and a mass attenuation coefficient of

\mu/\rho = 0.85\;\text{cm}^2/\text{g}

for

120\;\text{keV}

X-rays. Will the X-ray scanner be able to create a usable image when the beam passes through the laptop? The intensity of X-rays after passing through a material follows the Beer-Lambert law:

I = I_0 e^{-\mu x}

, where

\mu

is the linear attenuation coefficient and

x

is the thickness.

Intuitive explanation

X-ray absorption follows an exponential decay law, and you need to connect the material's properties to find how much intensity survives. The key is converting the mass attenuation coefficient (which compares absorption per unit mass) into a linear attenuation coefficient by multiplying by density—this tells you how strongly the steel itself absorbs the beam. Then apply Beer-Lambert to see if enough intensity reaches the detector for a usable image.

Intuitive explanation

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