CIE A Level Physics (9702) 2019-2021

Revision Notes

27.4.3 Attenuation of X-rays in Matter

Attenuation of X-rays in Matter

  • 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, 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

Worked example: Attenuation of X-rays in matter

Attenuation_of_X-rays_in_Matter_Worked_Example_-_Attenuation_of_X-rays_Question, downloadable AS & A Level Physics revision notes

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

Attenuation of X-rays in Matter Worked Example equation 2

Step 3:           

Substitute in values and calculate the ratio

Attenuation of X-rays in Matter Worked Example equation 3

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 2:           

Write out the equation for attenuation for two media and rearrange

Attenuation of X-rays in Matter Worked Example equation 4

Step 3:           

Substitute in values and calculate the ratio

Attenuation of X-rays in Matter Worked Example equation 5

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

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