Outline why the fracture in a broken bone can be seen in a medical X-ray image.

The diagram shows X-rays incident on tissue and bone.

The thicknesses of bone and tissue are both 0.054 m.

The intensity of X-rays transmitted through bone is I_b and the intensity transmitted through tissue is I_t.

The following data are available.

Mass absorption coefficient for bone = mass absorption
coefficient for tissue = 1.2 × 10^–2\(\,\)m²\(\,\)kg^–1
Density of bone = 1.9 × 103 kg\(\,\)m^–3
Density of tissue = 1.1 × 103 kg\(\,\)m^–3

Calculate the ratio \(\frac{{{I_{\text{b}}}}}{{{I_{\text{t}}}}}\).

the large uniform magnetic field applied to the patient.

the radio-frequency signal emitted towards the patient.

the non-uniform magnetic field applied to the patient.

bone and tissue absorb different amounts of X-rays
OR
bone and tissue have different attenuation coefficients

so boundaries and fractures are delineated in an image

[2 marks]

\(\frac{{{I_{{\text{bone}}}}}}{{{I_{{\text{tissue}}}}}} = \frac{{{I_0}{{\text{e}}^{ - {\mu _{\text{b}}}x}}}}{{{I_0}{{\text{e}}^{ - {\mu _{\text{t}}}x}}}} = {{\text{e}}^{ - \left( {{\mu _{\text{b}}} - {\mu _{\text{t}}}} \right)x}}\)

\(\frac{{{I_{{\text{bone}}}}}}{{{I_{{\text{tissue}}}}}} = {{\text{e}}^{ - 1.2 \times {{10}^{ - 2}} \times \left( {1.9 - 1.1} \right) \times {{10}^3} \times 5.4 \times {{10}^{ - 2}}}}\)

\(\frac{{{I_{{\text{bone}}}}}}{{{I_{{\text{tissue}}}}}} = 0.60\)

[3 marks]

to split the energy level of protons in the body
OR
to cause protons in the body to align with the field / precess at Larmor frequency

[1 mark]

to force/excite protons that are in the spin up/parallel state

into a transition to the spin down/antiparallel state

[2 marks]

the emitted radio frequency signal has a frequency that depends on the magnetic field

with a gradient field different parts of the body have different frequencies and so can be identified

[2 marks]