Calculating X-ray Attenuation (OCR A Level Physics): Revision Note

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:

$\frac{intensityofemergentX-raybeamfrommodel}{intensityofemergentX-raybeamonmodel}$

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.

Answer:

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

$\frac{intensityofemergentX-raybeamfrommodel}{intensityofemergentX-raybeamonmodel}=\frac{I}{I_0}=e^{-\mu x}$

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