Cambridge International AS & A Level · 24 · structured
X-ray production, contrast and CT reconstruction
X-ray production, contrast and CT reconstruction · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 11
- Topics
- 4
- Answer
- Complete
Electrons in an X-ray tube are accelerated through 60.0 kV into a metal target. Use e=1.60×10⁻¹⁹ C, h=6.63×10⁻³⁴ J s and c=3.00×10⁸ m s⁻¹. For a separate simplified imaging comparison, two 2.00 cm paths have constant intensity attenuation coefficients 0.200 cm⁻¹ (soft tissue) and 0.800 cm⁻¹ (bone).
- (a)
Explain how electron bombardment produces X-rays and calculate the minimum possible wavelength using the accelerating voltage.
4 marks - (b)
Recall the exponential intensity attenuation relation and calculate the transmitted fraction along each imaging path. Use the results to explain image contrast without assuming a particular display's black/white convention.
4 marks - (c)
Describe how a CT scanner obtains a two-dimensional section and then a three-dimensional internal image.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Explain how electron bombardment produces X-rays and calculate the minimum possible wavelength using the accelerating voltage.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
Accelerated electrons lose energy through interactions and deceleration in the metal, producing X-ray photons (with much energy also becoming heat).
- 2
The maximum energy of one photon occurs if one electron's full kinetic energy eV is transferred to it.
- 3
E_max=eV=1.60×10⁻¹⁹×60000=9.60×10⁻¹⁵ J.
- 4
λ_min=hc/E_max=2.07×10⁻¹¹ m.
(b)
Recall the exponential intensity attenuation relation and calculate the transmitted fraction along each imaging path. Use the results to explain image contrast without assuming a particular display's black/white convention.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
Use I=I₀e^(−μx) with cm and cm⁻¹ consistently.
- 2
Soft tissue: I/I₀=e^(−0.200×2.00)=0.670.
- 3
Bone: I/I₀=e^(−0.800×2.00)=0.202.
- 4
Differential attenuation gives different detected intensities, producing contrast. The displayed light/dark mapping is a separate display choice.
(c)
Describe how a CT scanner obtains a two-dimensional section and then a three-dimensional internal image.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
Measure X-ray transmission through the same section from many angular directions.
- 2
Computer processing combines those projections to reconstruct the attenuation distribution in a two-dimensional slice.
- 3
Acquire and reconstruct slices at different positions along an axis, then combine them into a three-dimensional volume.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- (a) Accelerated electrons lose energy through interactions and deceleration in the metal, producing X-ray photons (with much energy also becoming heat).
- (a) The maximum energy of one photon occurs if one electron's full kinetic energy eV is transferred to it.
- (a) E_max=eV=1.60×10⁻¹⁹×60000=9.60×10⁻¹⁵ J.
- (a) λ_min=hc/E_max=2.07×10⁻¹¹ m.
- (b) Use I=I₀e^(−μx) with cm and cm⁻¹ consistently.
- (b) Soft tissue: I/I₀=e^(−0.200×2.00)=0.670.
- (b) Bone: I/I₀=e^(−0.800×2.00)=0.202.
- (b) Differential attenuation gives different detected intensities, producing contrast. The displayed light/dark mapping is a separate display choice.
- (c) Measure X-ray transmission through the same section from many angular directions.
- (c) Computer processing combines those projections to reconstruct the attenuation distribution in a two-dimensional slice.
- (c) Acquire and reconstruct slices at different positions along an axis, then combine them into a three-dimensional volume.
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