AQA A-Level Physics Paper 3 (3BB), June 2025: Question 2

11 marks · Hard difficulty · Extended Answer

Calculate the decay and extraction of technetium-99m from a molybdenum-99 generator and compare MUGA and TTE heart imaging techniques.

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Question

Question 2 features a graph (Figure 3) plotting activity in GBq against time in hours (from 0 to 50 hours) for a molybdenum-technetium generator. A dashed curve shows the decreasing activity of 99Mo starting at about 74 GBq at t=0, and a solid curve shows the activity of 99mTc rising from 0 to a peak of about 51 GBq at 24 hours, dropping to 0 upon extraction, and repeating the cycle up to 48 hours. Part 02.1 asks to show that approximately 6 × 10^15 nuclei of 99Mo decay between t = 0 and t = 24 hours given the decay constant is 2.8 × 10^-6 s^-1 (2 marks). Part 02.2 states 90% of 99Mo decays into 99mTc and asks to estimate the number of 99mTc nuclei extracted at t = 24 hours (3 marks). Part 02.3 presents an extended question comparing a MUGA scan using 99mTc with a TTE ultrasound scan of the heart, focusing on imaging mechanism, common advantages, and comparative strengths and weaknesses (6 marks).
Question text

02 Technetium-99m (99mTc) is produced from the decay of molybdenum-99 (99Mo).

In hospitals, 99mTc is extracted from a molybdenum-technetium generator.

99Mo is put into the generator at time t = 0

As 99Mo decays, the amount of 99mTc increases to a maximum at t = 24 hours.

99mTc is extracted from the generator at regular intervals.

At each extraction, the activity of 99mTc in the generator falls to zero and then

increases again.

Figure 3 shows how the activities of 99Mo and 99mTc in the generator vary with t when

extractions are made at t = 24 hours and t = 48 hours.

Figure 3

activity of 99Mo

activity of 99mTc 7

02.1 Show that about 6 × 1015 nuclei of 99Mo decay between t = 0 and t = 24 hours.

decay constant for 99Mo = 2.8 × 10−6 s−1

[2 marks]

02.2 90% of the 99Mo nuclei decay to form 99mTc nuclei. The other 10% decay to form

different nuclei.

Estimate the number of 99mTc nuclei that are extracted from the generator

at t = 24 hours.

[3 marks]

8 number =

02.3 Information about heart function can be obtained from a multi-gated acquisition

(MUGA) scan or from a transthoracic echocardiogram (TTE) scan.

Heart specialists use these scans to diagnose a range of heart conditions.

In a MUGA scan, a patient is injected with a compound containing 99mTc which binds

to red blood cells.

Using images of the red blood cells, a precise reading can be made of blood flow rate

through the heart.

A TTE is an ultrasound scan of the heart.

Images of the heart are seen on a monitor as a transducer is moved across

*07*the surface of the patient’s chest.

Compare the MUGA method of investigating heart function with the TTE method of

investigating heart function.

In your answer you should:

• outline how an image of the red blood cells is obtained during a MUGA scan

• explain the advantages that a MUGA scan and a TTE scan have in common

• compare the strengths and weaknesses of a MUGA scan and a TTE scan.

[6 marks]

Mark scheme

Show the mark scheme The mark scheme provides criteria for parts 02.1 to 02.3. For 02.1, marks are awarded for reading activities (74 and 58 GBq) and using A = λN or ΔN = N0(1 - e^-λt) or graphical area integration to calculate 5.7 × 10^15 nuclei. For 02.2, Method 1 calculates 99mTc decayed and subtracts from 0.9 × 6 × 10^15 to find (1.4 to 2.4) × 10^15; Method 2 uses half-life of 6 hours to find λ and calculates N = A/λ = 51 GBq / λ giving 1.50 to 1.63 × 10^15. For 02.3, a level of response grid (up to 6 marks) covers three main areas: Area 1 (how MUGA image is obtained with gamma camera and collimator), Area 2 (common advantages: non-invasive, moving 2D images, no general anaesthetic), and Area 3 (strengths and weaknesses: MUGA is quantitative and more accurate vs TTE being cheaper, non-ionising, and subjective).

Question Answers Additional comments/Guidance Mark AO

02.1 Max one from Expect to see 74 (× 109) − 58 (× 109) (= 16 × 109) 2 AO2

• Reads off activities of 74(× 109) and 58 (× 109) from Condone consistent power of ten errors where attempt

the graph (and calculates the difference) (1) to find difference is seen

Condone one other error in read offs where their

difference is calculated.

Expect to see one of

• Use of A = −λN to find number of nuclei at t=0 / 74×109

• (N=) (= 2.64 × 1016) (a)

t =24 / difference between t=0 and t =24 (2) 2.8×10−6

58 × 109

• (N=) (= 2.07 × 1016) (b)

2.8 ×10−6

16 × 109

• (N=) −6 (c)

2.8 ×10

• 74(× 109) − 58 (× 109) = 2.8 (× 10-6) × N (d)

• 16 (× 109) = 2.8 (× 10-6) × N (e)

• Use of N = N 𝑒𝑒−𝜆𝜆𝑡𝑡 (3)

0 16 16

• Finding difference of 2.64 × 10 and 2.07 × 10

seen (f)

−𝜆𝜆𝑡𝑡 difference in activity

• Use of (∆)N = N0 (1 − 𝑒𝑒 ) (4) • Condone one error in -6 (g)

2.8 ×10

condone power of ten errors in (d) and (e) and (f)

For Use of in (3) is by substitution of N (or N0) and t = 24

• determines area under 99Mo graph between t = 0 and (× 602) , condone N (1.82 x1016) from A = 51 GBq.

t = 24 hours. (5) For (3) N = 2.64 (× 1016) / N= 2.07 (× 1016) t = 24 (× 602)

For (4) N = 2.64 (× 1016) t = 24 (× 602)

allow area of a trapezium: expect base 24 × 3600 and

parallel sides 74 × 109 and 58 × 109

5.7 × 1015

allow counting squares: expect 325 to 400 small squares

(13 to 16 large squares) x by area of one square

for MP2 accept > 2 sf, rounding to 5.7 × 1015

Must see MP1 to award MP2

02.2 Method 1: for number in range 3.0 to 3.7 × 1015 3 1 × AO2

calculates number of 99mTc (that have decayed between t = 2 × AO3

0 and t = 24) 1 For allow use of (0.9 ×) 6 × 1015 − their number

99m of 99mTc

use of (0.9 ×) their 02.1 − their number of Tc (that have

decayed between t = 0 and t = 24) 2 for 3 must see use of 0.9 in a valid difference

calculation

number of 99mTc extracted in range 1.4 to 2.4 × 1015

for 1 evidence for half-life of 6(.0) hours seen in

working; expect λ = 3.2 × 10−5 (s−1 ) based on half-

Method 2: use of recognisable half-life to determine the life = 2.2 × 104 s

decay constant for 99mTc ln 2

1 allow substitution of half-life in hours, eg λ =

6(.0)

use of activity at t = 24 hours and a decay constant to for substitution of A in range 50(× 109) to

99m 2

determine number of Tc extracted 2 ( 9 )

9 51×10

52(.2) (× 10 ), eg N =

their λ

allow PoT on activity in MP2

number of 99mTc extracted in range 1.50 to 1.63 × 1015 15

3 for allow 2 sf in range 1.5 to 1.6 × 10

Where no other mark is scored, Max 1 for:

attempt to find area (under 99mTc curve)

• 215 to 255 small squares (or 8 to 10 large)

• allow area of triangle and trapezium

• finds area of one small square = 1.4 × 1013

Question Answers Additional comments/Guidance Mark 11 AO

02.3 Mark Criteria In each area, a partial response covers one bullet point 6 2 × AO2

while a detailed response covers at least two.

All three areas covered in some detail. Area 1: How images obtained (MUGA scan) 4 × AO3

66 marks can be awarded even if there is an error • (99m)Tc is used as a tracer OR (99m)Tc is a gamma-

and/or parts of one aspect missing. emitter (do not award if annihilation mentioned)

All three areas covered, at least two in detail. • the imaging device is a gamma camera

5 Whilst there will be gaps, there should only be an (mentioning a detector / scanner insufficient)

occasional error. • details of gamma camera (collimator,

photomultiplier, dynodes)

Two areas successfully discussed, or one discussed treat as neutral: (99m)Tc quickly removed from body (in

and two others covered partially. Whilst there will be about 24 hours) / has a short (effective) half-life

4 several gaps, there should only be an occasional

Area 2: Common advantages

error. • both are non-invasive

One area discussed and one discussed partially, or all • both generate (2D) images that provide an

3 three covered partially. There are likely to be several animated view of the functioning heart or wtte

errors and omissions in the discussion. • no need to anaesthetise patient

Only one area discussed or makes a partial attempt at • both are outpatient procedures

2 two areas. • patients do not have to remain still / allow ‘both

may be used during stress testing’

1 Only one area covered and that partially. 'can be used if patient has pacemaker' is neutral

Area 3: Strength and weakness

0 No relevant comments • MUGA provides (both) quantitative (and

qualitative) information / MUGA is more accurate /

TTE provides only qualitative information / MUGA

image intensity is related to number of red blood

cells in region

• Interpretation of TTE images may be subjective /

not reproducible

• TTE lower cost / allow ‘takes less time’

allow reverse argument

• TTE uses non-ionising radiation / no side effects /

MUGA uses ionising radiation.

’MUGA produces higher resolution images’ is neutral

Total 11

How to answer it

Radioactive Decay & Medical Diagnostics: ⁹⁹Mo–⁹⁹ᵐTc Generator and Heart Imaging

📋 What this question tests

This question integrates Nuclear Decay Physics with Medical Imaging Applications (Turn 2 Option Topic: Medical Physics):

  • Interpreting decay and growth activity curves in a parent-daughter isotope cow/generator system.
  • Applying decay equations ( A = λN and ΔN = ΔA / λ ) and unit conversions ( GBq to Bq , hours to seconds).
  • Estimating daughter nuclei yield accounting for branching ratios (90% formation).
  • Extended comparative evaluation of cardiac imaging techniques: MUGA scan (radionuclide/gamma camera) vs TTE (transthoracic echocardiogram/ultrasound).
Question 02.1 • 2 Marks

Number of Parent (⁹⁹Mo) Nuclei Decaying in 24 Hours

Calculation / "Show that" proof

📐 Step-by-Step Calculation

  1. Read activities from graph:
    At t = 0 : A₀ = 74 GBq = 74 × 10⁹ Bq
    At t = 24 h : A₂₄ = 58 GBq = 58 × 10⁹ Bq
  2. Find the change in activity:
    ΔA = 74 × 10⁹ - 58 × 10⁹ = 16 × 10⁹ Bq
  3. Relate activity to number of nuclei using A = λN :
    ΔN = ΔA / λ
    ΔN = (16 × 10⁹) / (2.8 × 10⁻⁶ s⁻¹)
  4. Calculate final value:
    ΔN = 5.71 × 10¹⁵ nuclei
    Rounds cleanly to about 6 × 10¹⁵.

✅ Mark Scheme Breakdown

[Mark 1] Method mark for either:

  • Reading activities 74 (× 10⁹) and 58 (× 10⁹) and calculating difference ( 16 × 10⁹ ), OR
  • Calculating N₀ = (74 × 10⁹) / (2.8 × 10⁻⁶) = 2.64 × 10¹⁶ and N₂₄ = (58 × 10⁹) / (2.8 × 10⁻⁶) = 2.07 × 10¹⁶ , OR
  • Using ΔN = N₀(1 - e⁻ᵝᵗ) with t = 24 × 3600 s , OR
  • Finding area under the curve between 0 and 24 h .

[Mark 2] Accurate evaluation giving 5.7 × 10¹⁵ (must give to at least 2 sig figs to show it rounds to 6 × 10¹⁵).

🧠 Exam Technique: "Show that" Questions

When the question asks to "Show that value ≈ X", never stop at the rounded value X. You must write down the unrounded or more precise calculated answer (e.g. 5.7 × 10¹⁵) to prove you carried out the calculation rather than back-calculated from the prompt!

❌ Common Errors

  • Unit Trap (Giga): Forgetting that the vertical axis is in GBq ( 10⁹ Bq ).
  • Time Trap: If using N = N₀ e⁻ᵝᵗ , using t = 24 instead of converting to seconds: t = 24 × 3600 = 86,400 s .
  • Misreading the graph coordinates at 24 hours. Each major grid block is 10 GBq with 5 subdivisions (2 GBq per small square).
Question 02.2 • 3 Marks

Estimating Number of ⁹⁹ᵐTc Nuclei Extracted at t = 24 Hours

Decay branching and daughter equilibrium estimation

📐 Recommended Method (Method 2: Activity & Decay Constant)

  1. Determine half-life or decay constant of ⁹⁹ᵐTc:
    Standard textbook value for ⁹⁹ᵐTc half-life is T₁/₂ = 6.0 hours ( 21,600 s ).
    λ_Tc = ln(2) / T₁/₂ = ln(2) / (6.0 × 3600) ≈ 3.21 × 10⁻⁵ s⁻¹
  2. Read activity of ⁹⁹ᵐTc at t = 24 hours:
    From solid curve at peak: A_Tc = 51 GBq (accept range 50 to 52 GBq ).
  3. Calculate extracted number of nuclei:
    N = A / λ = (51 × 10⁹) / (3.21 × 10⁻⁵) = 1.59 × 10¹⁵
    Acceptable range: 1.50 × 10¹⁵ to 1.63 × 10¹⁵.

📐 Alternative Method (Method 1: Formation vs Decay)

  1. Total ⁹⁹ᵐTc nuclei created in 24 h:
    N_created = 0.90 × ΔN_Mo = 0.90 × (5.7 × 10¹⁵) ≈ 5.13 × 10¹⁵
  2. Nuclei lost by decay during 24 h:
    Calculated from integrated activity under ⁹⁹ᵐTc curve between 0 and 24 h:
    Area ≈ 3.0 × 10¹⁵ to 3.7 × 10¹⁵ nuclei decayed.
  3. Subtract to find remaining nuclei:
    N_extracted = 5.13 × 10¹⁵ - 3.4 × 10¹⁵ ≈ 1.4 × 10¹⁵ to 2.4 × 10¹⁵ .

✅ Mark Scheme (Method 2)

  • [Mark 1]: Recall/use of recognisable half-life of ⁹⁹ᵐTc ( 6.0 h or 2.2 × 10⁴ s ) to find λ ≈ 3.2 × 10⁻⁵ s⁻¹ .
  • [Mark 2]: Read activity at t = 24 h ( 50 to 52 GBq ) and substitute into N = A / λ .
  • [Mark 3]: Final value in range 1.50 × 10¹⁵ to 1.63 × 10¹⁵ (or 1.4 to 2.4 × 10¹⁵ if using Method 1).

❌ Common Errors

  • Assuming no daughter decay: Simply calculating 0.90 × (6 × 10¹⁵) = 5.4 × 10¹⁵ and stopping. This completely ignores the fact that ⁹⁹ᵐTc decays rapidly with a 6-hour half-life while accumulating!
  • Half-life unit error: Calculating λ = ln(2)/6.0 = 0.1155 h⁻¹ and dividing 51 × 10⁹ s⁻¹ directly without converting hours to seconds.
Question 02.3 • 6 Marks

Comparing MUGA Scan vs Transthoracic Echocardiogram (TTE)

Extended response: Level of response question

Examiner Level Matrix:
• Level 3 (5–6 marks): All three areas covered in detail; clear, logically structured argument with correct medical physics terminology.
• Level 2 (3–4 marks): Two areas in detail, or one in detail and two partially addressed.
• Level 1 (1–2 marks): Only one area covered or fragmented general points.

Area 1: How Images are Formed in a MUGA Scan

  • Radiotracer: ⁹⁹ᵐTc is tagged to red blood cells and injected into the patient.
  • Emission: ⁹⁹ᵐTc decays via isomeric transition, emitting gamma photons (140 keV).
  • Detection (Gamma Camera):
    • Collimator: Lead honeycombed plate ensures only photons parallel to the holes reach the crystal (prevents blurring).
    • Scintillator (NaI crystal): Converts incident gamma rays into visible light flashes.
    • Photomultiplier tubes (PMTs): Convert light flashes into measurable electrical pulses.
    • Computer gating: Synchronised with ECG signal (R-wave) over multiple heart cycles to build an animated movie of cardiac cycles.

Area 2: Advantages Common to Both Scans

  • Non-invasive: Neither requires surgery or cardiac catheterisation.
  • Functional / Dynamic imaging: Both produce real-time moving (2D cine) images of the beating heart to assess wall motion and ejection fraction.
  • Outpatient procedures: No hospital overnight stay or general anaesthetic required.
  • Stress testing capability: Both can be performed at rest and during exercise/pharmacological stress to assess response under workload.

Area 3: Strengths & Weaknesses Comparison

Aspect MUGA (Radionuclide) TTE (Ultrasound)
Safety / Radiation Uses ionising gamma radiation; small dose risk. Non-ionising sound waves; completely safe, no dose limit.
Accuracy & Objectivity Highly accurate & reproducible quantitative measure of ejection fraction (count-based). Subjective; operator-dependent; geometric assumptions required.
Cost & Availability More expensive; requires radiopharmacy & gamma camera suite. Cheaper, portable bedside scanner, instantly available.
Patient Anatomy Impact Not obstructed by ribcage or lung tissue. Poor acoustic windows in obese or COPD patients (rib/lung reflection).

❌ Common Pitfalls in Question 02.3

  • Confusing MUGA with PET: ⁹⁹ᵐTc is a gamma emitter, NOT a positron (β⁺) emitter! Mentioning electron-positron annihilation causes immediate forfeiture of marks in Area 1.
  • Vague detector descriptions: Merely writing "a detector scans the body" is insufficient for A-Level. You must explicitly name the gamma camera and its key components (collimator, scintillator, PMTs).
  • Claiming MUGA has higher spatial resolution: Do NOT claim MUGA has higher spatial resolution than ultrasound (it does not; gamma cameras have relatively poor spatial resolution). Its advantage is quantitative accuracy because image brightness directly counts blood volume.

Topics

Physics · Optional topics · Practical skills · 3.8 Nuclear physics (A-level only) · 3.10 Medical physics (A-level only) · Data analysis

Question and mark scheme from the AQA A-Level Physics examination, Paper 3 (3BB), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.