Attenuation of X-rays in Matter (CIE A Level Physics)

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

• Where:
  • I₀ = the intensity of the incident beam (W m^-2)
  • I = the intensity of the emergent 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

Absorption of X-rays by different materials

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

Step 3:           

Substitute in values and calculate the ratio

Part (b)

Step 1:           

Write out the known quantities

Linear absorption coefficient for muscle, μ_m = 0.20 cm^-1

Linear absorption coefficient for bone, μ_b = 12 cm^-1

Distance travelled through the muscle, x_m = 4.0 cm

Distance travelled through the bone, x_b = 4.0 cm

Step 2:           

Write out the equation for attenuation for two media and rearrange

Step 3:           

Substitute in values and calculate the ratio

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