Define attenuation coefficient.

X-rays are used in dentistry to reveal decay inside teeth. In a research study, a tooth is partially filled with a new glass-based material to replace decayed tissue. X-ray photographs are taken of the tooth.

A parallel beam of X-rays is incident on the tooth. X-rays emerging at A have travelled through enamel and filling only, X-rays emerging at B have travelled through enamel and tooth tissue only.

(i) Show that the ratio \(\frac{{{\rm{intensity of X - rays at A}}}}{{{\rm{intensity of X - rays at B}}}}\) is approximately 3×10^–7.

(ii) The X-ray exposure time is such as to enable fine detail in the enamel to be revealed by X-rays emerging at B. Suggest, with reference to the ratio in (b)(i), why the contrast at B is much greater than the contrast at A.

A complete dental record of all the teeth in a patient’s mouth requires about 20 separate X-ray exposures. Image intensifiers are now used in dentistry to allow a single image to be made of all the teeth with one exposure. Outline the advantages of this for the patient.

The table shows data about the acoustic impedance of some materials that would be involved in the transmission of ultrasound through a tooth.

Without carrying out a calculation, outline two reasons why ultrasound is not used to detect the presence of decay inside a tooth.

\(\mu \) in I=I₀e^-μx;
all symbols defined;

or

the probability per unit length/metre;
of a photon being absorbed;

(i) \({I_A} = {I_0}{{\rm{e}}^{\left[ { - {\mu _e}2x - {\mu _{\rm{f}}}y} \right]}}\) or \({I_B} = {I_0}{{\rm{e}}^{\left[ { - {\mu _e}2x - {\mu _{\rm{t}}}y} \right]}}\);
\(\frac{{{I_{\rm{A}}}}}{{{I_{\rm{B}}}}} = \frac{{{{\rm{e}}^{\left[ { - {\mu _e}2x - {\mu _{\rm{f}}}y} \right]}}}}{{{{\rm{e}}^{\left[ { - {\mu _e}2x - {\mu _{\rm{t}}}y} \right]}}}}\);
\( = {{\rm{e}}^{\left[ { - \left[ {6.3 - 0.3} \right]2.5} \right]}}\);
=3.1×10^-7;
Do not apply a marking penalty if attenuation effect of enamel is ignored, as it is the same for both rays.
Award first and second marking point by implication if only the correct working of the third marking point is shown.
Approximate answer is given in the question, so look for working and at least two significant figures in the final answer (3.059...).

(ii) intensity ratio is very small / intensity for A is much less than at B;
so if the contrast is correct for B, it cannot be correct for A / A will be underexposed so contrast will be poor;

or

compared to B, the much smaller intensity for A is due to the filling;
for A, small changes in enamel attenuation coefficient will be insignificant compared to that of the filling, so contrast is poor;

quicker procedure;
less dose overall / safer;

acoustic impedance difference between decayed and good tissue is very small so reflection will be weak;
the acoustic impedance of tissue/decayed tissue is much smaller than for enamel so contrast would be poor;
difficult to get ultrasound signal into tooth given mismatch between acoustic impedance of air and enamel;
there will be a strong internal reflection when reflection from tissue is incident on enamel from inside;