X-ray attenuation
Medical Imaging - OCR A-Level Physics
Worked Example
An X-ray beam of intensityThe powerThe rate of energy transfer. Measured in watts (W). transmitted per unit area perpendicular to the wave direction. Measured in W m⁻². Proportional to amplitude squared. 5.0 × 10⁴ W m⁻² passes through 3.0 cm of tissue with a linear attenuationThe reduction in intensityThe powerThe rate of energy transfer. Measured in watts (W). transmitted per unit area perpendicular to the wave direction. Measured in W m⁻². Proportional to amplitude squared. of radiation (such as X-rays) as it passes through a material, due to absorption and scattering. coefficient of 0.20 cm⁻¹, followed by 1.5 cm of bone with μ = 0.60 cm⁻¹. Calculate the transmitted intensityThe powerThe rate of energy transfer. Measured in watts (W). transmitted per unit area perpendicular to the wave direction. Measured in W m⁻². Proportional to amplitude squared..
Show Solution
1
Apply attenuationThe reduction in intensity of radiation (such as X-rays) as it passes through a material, due to absorption and scattering. through tissue first
$I_{1} = I_{0} e^(-\mu_{1}x_{1}) = 5.0 \times 10⁴ \times e^(-0.20 \times 3.0).$
2
$I_{1} = 5.0 \times 10⁴ \times e^(-0.60) = 5.0 \times 10⁴ \times 0.549 = 2.74 \times 10⁴\;\text{W}\;\text{m}⁻^{2}.$
3
Then apply attenuationThe reduction in intensity of radiation (such as X-rays) as it passes through a material, due to absorption and scattering. through bone
$I_{2} = I_{1} e^(-\mu_{2}x_{2}) = 2.74 \times 10⁴ \times e^(-0.60 \times 1.5).$
4
$I_{2} = 2.74 \times 10⁴ \times e^(-0.90) = 2.74 \times 10⁴ \times 0.407 = 1.11 \times 10⁴\;\text{W}\;\text{m}⁻^{2}.$
5
Alternatively in one step
I = I₀ e^(-(μ₁x₁ + μ₂x₂)) = 5.0 × 10⁴ × e^(-(0.60 + 0.90)) = 5.0 × 10⁴ × e^(-1.50) = 1.1 × 10⁴ W m⁻².
Answer
Transmitted intensity ≈ 1.1 × 10⁴ W m⁻².