Calculating X-ray Attenuation(OCR A Level Physics)

Author

Katie M

Expertise

Physics

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 transmitted 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

Worked example

A student investigates the absorption of X-ray radiation in a model arm. A cross-section of the model arm is shown in the diagram.

Parallel X-ray beams are directed along the line MM and along the line BB. The linear absorption coefficients of the muscle and the bone are 0.20 cm-1 and 12 cm-1 respectively.

Calculate the ratio:

for a parallel X-ray beam directed along the line

a) MM

b) BB

and state whether the X-ray images are sharp, or have good contrast.

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, 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

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

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