| Date | November 2016 | Marks available | 2 | Reference code | 16N.3.HL.TZ0.19 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Show that | Question number | 19 | Adapted from | N/A |
Question
The linear attenuation coefficient μ of a material is affected by the energy of the X-ray beam and by the density ρ of the material. The mass absorption coefficient is equal to \(\frac{\mu }{\rho }\) to take into account the density of the material.
The graph shows the variation of mass absorption coefficient with energy of the X-ray beam for both muscle and bone.
Show that the attenuation coefficient for bone of density 1800 kg m–3, for X-rays of 20 keV, is about 7 cm–1.
The density of muscle is 1200 kg m–3. Calculate the ratio of intensities to compare, for a beam of 20 keV, the attenuation produced by 1 cm of bone and 1 cm of muscle.
Suggest why more energetic beams of about 150 keV would be unsuitable for imaging a bone–muscle section of a body.
Markscheme
reads value on graph at 20 keV as 4 «cm2 g–1»
«4 cm2 g–1 × 1800 kg m–3 × \(\frac{{1000}}{{1000000}}\) = » 7.2 «cm–1»
Ensure that the calculation has right POT conversion.
Answer must be to at least two significant figures.
ALTERNATIVE 1
(finds intensity ratios for muscle and bone separately)
Watch for ECF
for muscle: obtains μ = 0.96 cm−1
Allow answers in the range of 0.90 to 1.02 cm–1.
\(\frac{I}{{{I_0}}}\) = e−μx so for muscle 0.38
Allow answers in the range of 0.36 to 0.41.
Allow answers in dB. Muscle -4dB, Bone -30 or -31dB
for bone: \(\frac{I}{{{I_0}}}\) = 7.5 × 10−4 «if μ = 7.2 is used»
OR
9.1×10−4 «if μ=7 is used»
ALTERNATIVE 2
for muscle: obtains μ = 0.96 cm−1
Allow answers in the range of 0.90 to 1.02 cm–1.
\(\frac{{{I_{{\rm{MUSCLE}}}}}}{{{I_{{\rm{BONE}}}}}} = \frac{{{e^{ - 0.96}}}}{{{e^{ - 7.2}}}}\)
Frequently the POT will be incorrect for MP1. Allow ECF from MP1 to MP2.
Allow +/- 26 or 27dB
Award [2 max] if μ=960 as they will get \(\frac{{{I_{{\rm{MUSCLE}}}}}}{{{I_{{\rm{BONE}}}}}}\) = 0.
ratio is about 500 «513»
Allow range 395 to 546
If 7 used, ratio is about 420, if 7.2 is used, ratio is about 510
Allow answer IBONE/IMUSCLE from a range 0.0017 to 0.0026.
similar absorption so poor contrast
