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Question 23M.3.HL.TZ2.15

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Date May 2023 Marks available [Maximum mark: 10] Reference code 23M.3.HL.TZ2.15
Level HL Paper 3 Time zone TZ2
Command term Calculate, Compare, Determine, Explain, Show that, State Question number 15 Adapted from N/A
15.
[Maximum mark: 10]
23M.3.HL.TZ2.15

The X-ray attenuation coefficient values for bone and muscle at an energy of 100 keV are shown.

Bone attenuation coefficient = 0.348 cm−1
Muscle attenuation coefficient = 0.173 cm−1

(a)

Show that the half-value thickness of bone when using X-ray energies of 100 keV is approximately 2 cm.

[1]

Markscheme

ln 20.348

OR

1.99 «cm» ✓

 

Allow 2.0 «cm»

A monochromatic X-ray beam of energy 100 keV and intensity I0 is incident on muscle of thickness 4.0 cm.

(b)

Calculate, in terms of I0, the final beam intensity that emerges from the muscle.

[2]

Markscheme

II0 = e−0.173×4 ✓

= 0.50 ✓

 

Award [2] for BCA

An X-ray beam of energy 100 keV and intensity I0 is directed at a section of the upper leg that can be modelled using 4.0 cm of muscle, 2.0 cm of bone and then 4.0 cm of muscle as shown.

(c)

Determine, in terms of I0, the final beam intensity that emerges from this section of the upper leg.

[2]

Markscheme

Imuscle × Ibone × Imuscle = 123 ✓

I = 0.125 I0 ✓

 

Award [2] for BCA

Watch for ECF from (b)

Allow ECF from MP1

Additional attenuation coefficient values for bone and muscle are shown for X-ray energies of 1 keV and 10 keV.

 

Energy of X-rays
/ keV 		Bone attenuation
coefficient / cm−1 		Muscle attenuation
coefficient / cm−1
1 7260 3910
10 55.9 56.2

 

(d)

Compare, with reference to contrast and sharpness, the final images formed when X-rays of 1 keV or 10 keV are incident on the same muscle–bone–muscle section of the upper leg.

[2]

Markscheme

more contrast with 1 keV OR less sharp with 1 keV

correct explanation for one of them, i.e.

«more contrast with 1 keV» as coefficients have greater ratio OR

«less sharp with 1 keV» as the X-rays will be scattered more ✓

 

Accept reverse argument in each case for 10 keV.

(e)

Other medical imaging techniques include ultrasound and nuclear magnetic resonance (NMR) imaging.

(e.i)

State one difference between an A scan and a B scan in ultrasound medical imaging.

[1]

Markscheme

A scan is one dimensional ✓

B scan is two dimensional ✓

B scan computed from multiple images ✓

(e.ii)

Explain how position information is obtained in nuclear magnetic resonance (NMR) imaging.

[2]

Markscheme

gradient field is added to initial strong magnetic field ✓

varies linearly across/along the patient ✓

the flip/Larmor frequency varies linearly across the patient «hence position of proton frequency known» ✓