Medical physics

• Echo depth is \(ct/2\) and the echo is attenuated both ways; \(\lambda_{\min}\) depends on \(V\) only; each annihilation photon carries \(m_ec^2\), not \(2m_ec^2\).

• 24.1.1 I can understand — understand that a piezo-electric crystal changes shape when a p.d. is applied across it and that the crystal generates an e.m.f. when its shape changes
• 24.1.2 I can understand — understand how ultrasound waves are generated and detected by a piezoelectric transducer
• 24.1.3 I can understand — understand how the reflection of pulses of ultrasound at boundaries between tissues can be used to obtain diagnostic information about internal structures
• 24.1.4 I can define — define the specific acoustic impedance of a medium as Z = ρc, where c is the speed of sound in the medium
• 24.1.5 I can use — use I_R/I₀ = (Z₁ − Z₂)²/(Z₁ + Z₂)² for the intensity reflection coefficient of a boundary between two media
• 24.1.6 I can recall — recall and use I = I₀e−μx for the attenuation of ultrasound in matter
• 24.2.1 I can explain — explain that X-rays are produced by electron bombardment of a metal target and calculate the minimum wavelength of X-rays produced from the accelerating p.d.
• 24.2.2 I can understand — understand the use of X-rays in imaging internal body structures, including an understanding of the term contrast in X-ray imaging
• 24.2.3 I can recall — recall and use I = I₀e−μx for the attenuation of X-rays in matter
• 24.2.4 I can understand — understand that computed tomography (CT) scanning produces a 3D image of an internal structure by first combining multiple X-ray images taken in the same section from different angles to obtain a 2D image of the section, then repeating this process along an axis and combining 2D images of multiple sections
• 24.3.1 I can understand — understand that a tracer is a substance containing radioactive nuclei that can be introduced into the body and is then absorbed by the tissue being studied
• 24.3.2 I can recall — recall that a tracer that decays by β+ decay is used in positron emission tomography (PET scanning)
• 24.3.3 I can understand — understand that annihilation occurs when a particle interacts with its antiparticle and that mass–energy and momentum are conserved in the process
• 24.3.4 I can explain — explain that, in PET scanning, positrons emitted by the decay of the tracer annihilate when they interact with electrons in the tissue, producing a pair of gamma-ray photons travelling in opposite directions
• 24.3.5 I can calculate — calculate the energy of the gamma-ray photons emitted during the annihilation of an electron-positron pair
• 24.3.6 I can understand — understand that the gamma-ray photons from an annihilation event travel outside the body and can be detected, and an image of the tracer concentration in the tissue can be created by processing the arrival times of the gamma-ray photons

Units, significant figures and working are part of the physics. Give a calculated answer to the same number of significant figures as the least precise data, or one more; keep full precision in the working and round only at the end; write the unit with every final answer. A fifth of the qualification is experimental: Papers 3 and 5 test AO3 only, and their questions may be set in contexts outside the syllabus content, so the practical work in this chapter is set out as method, recording, graphs and uncertainties rather than as theory.

• “The echo came back after time t, so the boundary is at depth ct, and its intensity has fallen by e−μd.” Correct The pulse goes to the boundary and back. Depth \(d = ct/2\), and the echo is attenuated over a path of \(2d\): by \(e^{-2\mu d}\), on top of the reflection coefficient at the boundary.
• “IR/I0 = (Z1 − Z2)/(Z1 + Z2).” Correct For intensity the ratio is squared: \((Z_1 - Z_2)^2/(Z_1 + Z_2)^2\). It is given on the Data and formulas sheet; copy it exactly. It has no unit and never exceeds 1.
• “\(I = I_0e^{-\mu x}\) is on the formula sheet.” Correct It is not. The syllabus says recall and use it, for ultrasound (24.1.6) and for X-rays (24.2.3). The reflection coefficient is the only Topic 24 equation the sheet prints.
• “A bigger tube current or a tungsten target gives X-rays of shorter minimum wavelength.” Correct \(\lambda_{\min} = hc/(eV)\) depends on the accelerating p.d. only. The current changes how many X-rays there are (the intensity), not their maximum energy.
• “Contrast is how bright or how sharp the image is.” Correct Contrast is the difference in exposure (blackening) between different areas of the image. It is good when neighbouring tissues have very different attenuation coefficients.
• “Each annihilation photon has 2mec2 = 1.02 MeV.” Correct 2mec2 is the total, shared between two photons. Each has \(m_ec^2\) = 8.20 × 10−14 J = 0.512 MeV from Data-sheet values.
• “The PET tracer gives out the gamma rays that are detected.” Correct The tracer emits positrons (β+ decay). The gamma-ray photons come from each positron annihilating with an electron in the tissue.
• “A steady p.d. across the crystal produces ultrasound.” Repair A steady p.d. changes the crystal's shape once. An alternating p.d., at the crystal's resonant frequency, makes it vibrate and send out ultrasound.
• “Depth = speed × echo time.” Repair The pulse goes there and back: \(d = ct/2\).
• “The gel is a lubricant so the probe slides easily.” Repair It excludes air. Z of air is far smaller than Z of skin, so an air gap reflects 99.9% of the ultrasound; gel has Z close to skin's and lets almost all of it in.
• “IR/I0 = (Z1 − Z2)/(Z1 + Z2) = −0.65 for soft tissue into bone.” Repair For intensity the ratio is squared: 0.652 = 0.42. An intensity ratio can never be negative.
• “For an echo from depth d, the attenuation factor is e−μd.” Repair The path is 2d, so \(e^{-2\mu d}\).
• “A tungsten target or a larger tube current gives a shorter λmin.” Repair \(\lambda_{\min} = hc/(eV)\) depends only on the accelerating p.d. The current changes the intensity.
• “Contrast is how bright the image is.” Repair Contrast is the difference in exposure (blackening) between areas of the image.
• “A CT scan is one X-ray image viewed in 3D.” Repair Many images of one section from different angles are combined into a 2D image of the section; this is repeated along an axis, and the 2D images are combined into a 3D image.
• “The PET tracer emits gamma rays.” Repair It emits positrons (β+ decay); the gamma rays come from their annihilation with electrons.
• “Each annihilation photon has 2mec2, about 1.02 MeV.” Repair The total is 2mec2; each photon has mec2, 0.512 MeV from the Data-sheet values.

• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.
• Two exponentials, one rule for the units. In \(I = I_0e^{-\mu x}\) the product \(\mu x\) has no unit, so put \(x\) in metres when \(\mu\) is in m−1, or both in centimetres. For an echo the distance in the exponent is the path there and back, \(2d\).
• Interleave with the chapters that use this one. Topic 25 (astronomy and cosmology) uses the same photon and intensity ideas at the scale of stars: when you reach it, re-answer “why is intensity power per unit area?”. When you revise Topic 23, re-answer “why does \(I = I_0e^{-\mu x}\) have the same shape as radioactive decay?”; when you revise Topic 22, re-derive \(\lambda_{\min} = hc/(eV)\). Recalling a topic inside a new context is worth more than another pass over this chapter on its own; at A Level, Paper 4 assumes the whole of the AS content, so nothing here is ever finished with.

• Cambridge International AS & A Level Physics 9702 has five components. Topic 24 is A Level content, so it is examined in Papers 4 and 5. A Level content: examined in Paper 4 (A Level structured, which also requires the AS content) and, as practical context, Paper 5. AS Level candidates take Papers 1, 2 and 3; A Level candidates take all five, either staged over two years (Papers 1–3 in year one, Papers 4 and 5 in year two) or together in one series. Examinations are available in the June and November series, and in March in India.
• Across both the AS Level and the A Level the assessment objectives are weighted AO1 40% (knowledge and understanding), AO2 40% (handling, applying and evaluating information) and AO3 20% (experimental skills and investigations). AS candidates are graded a–e; A Level candidates A*–E. The Data and formulas sheet is printed as page 2 of Papers 1 and 2 and as pages 2 and 3 of Paper 4: it gives the constants and a short list of formulas. Every other equation in this chapter is one the syllabus says you must recall, and this chapter says which is which.
• There is no multiple-choice item on Topic 24: it is A Level content. Most of its outcomes begin “understand”, so a Paper 4 question asks you to describe how a transducer generates and detects ultrasound, explain why gel is used or why two photons leave in opposite directions, define specific acoustic impedance or state what contrast means, and describe the three steps of CT.
• \(Z = \rho c\); the reflection coefficient, which the Data and formulas sheet gives; \(I = I_0e^{-\mu x}\), which you must recall; \(\lambda_{\min} = hc/(eV)\) from \(E = hf\); and the photon energy \(m_ec^2\). Echo depth \(ct/2\) and the location \(s = c\Delta t/2\) come from speed = distance/time.
• A Paper 5 analysis question can give readings of intensity against thickness and ask you to plot \(\ln I\) against \(x\), add error bars, draw a worst acceptable line and find \(\mu\) with its uncertainty. Echo timing with an oscilloscope, \(t\) against \(d\), is the laboratory version of the pulse-echo method.
• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.