# 27.4.3 Attenuation of X-rays in Matter

### Attenuation of X-rays in Matter

• This is why they appear white on the X-ray photograph
• When the collimated beam of X-rays passes through the patient’s body, they are absorbed and scattered
• The attenuation of X-rays can be calculated using the equation:

I = I0 e−μx

• Where:
• I0 = the intensity of the incident beam (W m-2)
• I = the intensity of the reflected beam (W m-2)
• μ = the linear absorption coefficient (m-1)
• x = distance travelled through the material (m)
• The attenuation coefficient also depends on the energy of the X-ray photons
• The intensity of the X-ray decays exponentially
• The thickness of the material that will reduce the X-ray beam or a particular frequency to half its original value is known as the half thickness

Part (a)

Step 1:

Write out the known quantities

Linear absorption coefficient for muscle, μ = 0.20 cm-1

Distance travelled through the muscle, x = 8.0 cm

Step 2:

Write out the equation for attenuation and rearrange

I = I0 e−μx Part (b)

Step 1:

Write out the known quantities

Linear absorption coefficient for muscle, μm = 0.20 cm-1

Linear absorption coefficient for bone, μb = 12 cm-1

Distance travelled through the muscle, xm = 4.0 cm

Distance travelled through the bone, xb = 4.0 cm

Step 4:

Write a concluding statement

Each ratio gives a measure of the amount of transmission of the beam

A good contrast is when:

• There is a large difference between the intensities
• The ratio is much less than 1.0

Therefore, both images have a good contrast ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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