Atomic Physics — Free IB MYP4 Physics Questions

1QuestionRelative charge and mass comparisonConcept Practice

2 marks~3 minCriterion A

The diagram below shows a helium atom with its subatomic particles labelled X, Y, and Z.

Particle properties:

Proton	relative charge $+1$	relative mass $1$
Neutron	relative charge $0$	relative mass $1$
Electron	relative charge $-1$	relative mass $\approx 0$

a

Identify the particle that has a relative charge of

+1

and a relative mass of

1

. [1]

b

A helium atom is electrically neutral. Using the relative charges of its subatomic particles, explain how a helium atom — which contains two protons — achieves an overall charge of zero. [1]

Solutions

2QuestionSubatomic particles: Proton (charge, mass, location) , Neutron (charge, mass, location), Electron (charge, mass, location)Concept Practice

2 marks~3 minCriterion D

Iodine-131 (

^{131}

I) is a radioactive isotope used in thyroid imaging. The thyroid gland absorbs iodine naturally, concentrating the isotope in thyroid tissue. Iodine-131 emits gamma radiation, which can be detected externally by imaging equipment. However, its use in medicine involves both advantages and hazards.

Outline one benefit and one risk of using iodine-131 in medical imaging. [2]

Solutions

3QuestionDefinition of an atomConcept Practice

3 marks~5 minCriterion C

The bar graph below shows the relative charges of the three sub-atomic particles found in an atom.

Proton:

+1

Neutron:

0

Electron:

-1

a

State the relative charge of a neutron. [1]

b

Using the graph, explain why a neutral atom has no overall electric charge. [1]

c

A student claims that removing one electron from a neutral atom produces a particle with a relative charge of

+2

. Evaluate this claim. [1]

Solutions

4QuestionApplications of radioactivity in medicineConcept Practice

2 marks~3 minCriterion D

Positron Emission Tomography (PET) scanning uses the radioactive tracer fluorine-18 (

^{18}

F), which is incorporated into a glucose analogue and injected into a patient. Metabolically active tissues — such as tumours — absorb the tracer preferentially. As

^{18}

F undergoes beta-plus decay, the emitted positrons annihilate with electrons, producing pairs of gamma rays detected by the scanner to construct a functional image.

Explain how the mechanism of PET scanning makes it particularly useful for detecting cancerous tissue. [1]

Identify one safety consideration that must be addressed when using PET scanning on a patient. [1]

Solutions

5QuestionDecay series (basic idea)Concept Practice

2 marks~3 minCriterion A

The diagram shows part of the uranium-238 decay series:

^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} \rightarrow ^{234}_{91}\text{Pa} \rightarrow ^{234}_{92}\text{U}

a

Deduce the type of nuclear decay occurring at each of the three steps. [1]

b

Construct a balanced nuclear equation for each step, using correct nuclide notation for the parent nucleus, daughter nucleus, and emitted particle. [1]

Solutions

6QuestionPractical uses in Sterilization/ Medical imaging/ Industrial thickness controlConcept Practice

2 marks~3 minCriterion A

Medical facilities use gamma radiation from cobalt-60 (

^{60}

Co) sources to sterilize single-use items such as syringes, surgical gloves, and wound dressings. The radiation penetrates sealed packaging, destroying microorganisms without requiring the items to be unwrapped.

a

Outline how gamma radiation sterilizes packaged medical equipment without opening the packaging. [1]

b

Identify one limitation of using

^{60}

Co gamma sources for sterilization in a hospital supply facility. [1]

Solutions

7QuestionBackground radiation: Natural sources (cosmic, rocks), Artificial sourcesConcept Practice

2 marks~3 minCriterion D

Granite bedrock releases radon gas, a radioactive decay product, which can accumulate inside buildings constructed on such geology.

a

Identify one real-world application of the knowledge that granite is a natural source of background radiation. [1]

b

Describe one societal impact that could result if this radiation source is not accounted for in building design. [1]

Solutions

8QuestionDefinition of isotopesConcept Practice

2 marks~3 minCriterion A

The diagram shows three nuclei:

Nucleus A	1 proton	0 neutrons
Nucleus B	1 proton	1 neutron
Nucleus C	2 protons	1 neutron

a

Deduce which two nuclei are isotopes of the same element. [1]

b

Explain the defining property that makes them isotopes. [1]

Solutions

9QuestionNotation of isotopes (e.g., ¹⁴C)Concept Practice

2 marks~3 minCriterion D

Archaeologists use radiocarbon dating to determine the age of organic artefacts. The method relies on the known half-life of

^{14}\text{C}

(approximately 5 730 years) and the ratio of

^{14}\text{C}

to

^{12}\text{C}

remaining in a sample.

a

Describe one real-world application of

^{14}\text{C}

in archaeology. [1]

b

Explain one limitation of this application that could affect the reliability of the age determined. [1]

Solutions

10QuestionBinding energy (qualitative)Concept Practice

2 marks~3 minCriterion A

A helium-4 nucleus (

^{4}_{2}

He) contains two protons and two neutrons packed into a diameter of approximately

10^{-15}

m.

a

Identify the fundamental force that holds the nucleons together inside the helium-4 nucleus. [1]

b

Explain why this force is necessary for the nucleus to remain stable, given that the nucleus also contains two positively charged protons. [1]

Solutions

11QuestionSafe handling of radioactive materialsConcept Practice

2 marks~3 minCriterion D

In nuclear medicine, lead-lined containers are used to store and transport radioactive isotopes such as

\text{I-131}

and

\text{Tc-99m}

within hospital environments.

a

Explain how lead-lined containers protect hospital staff and patients from radiation exposure during the handling of radioactive isotopes. [1]

b

Evaluate one limitation of using lead-lined containers as a radiation safety measure in hospitals. [1]

Solutions

12QuestionUnits of radiation (basic awareness)Concept Practice

2 marks~3 minCriterion A

A hospital records that a patient received an absorbed dose of

5 \text{ mGy}

of gamma radiation (radiation weighting factor

= 1

) during a medical imaging procedure. A second patient, undergoing a different procedure, receives the same absorbed dose from alpha particles (radiation weighting factor

= 20

).

a

Calculate the equivalent dose, in

\text{Sv}

, received by the second patient. [1]

b

Explain why using only absorbed dose to compare the health risk to both patients would be misleading. [1]

Solutions

13QuestionThomson’s plum pudding modelAssessment Practice

3 marks~5 minCriterion C

The graph below shows the predicted relative number of alpha particles detected at different scattering angles for Thomson's plum pudding model and Rutherford's nuclear model.

Using the graph and your knowledge of atomic structure, explain why the plum pudding model predicted significantly fewer alpha particles scattered at angles greater than 90° compared to the results Rutherford actually observed. [3]

Solutions

14QuestionAtomic number (Z) and mass number (A)Assessment Practice

5 marks~8 minCriterion A

A mass spectrometer analyses element X and detects three isotopes:

Peak 1	$m/z = 84$	relative abundance $= 0.5\%$
Peak 2	$m/z = 86$	relative abundance $= 9.9\%$
Peak 3	$m/z = 88$	relative abundance $= 89.6\%$

a

Calculate the weighted average atomic mass of element X using:

\bar{A} = \frac{\sum (m/z \times \text{relative abundance})}{\sum \text{relative abundance}}

Show all working. [2]

b

Deduce the identity of element X from your result and state its atomic number

Z

. [1]

c

The three peaks all share the same atomic number

Z

yet differ in mass number

A

. Analyse how this is possible, and explain why the most abundant isotope does not necessarily determine the value of

Z

. [2]

Solutions

15QuestionEnergy levels and electron transitionsAssessment Practice

8 marks~12 minCriterion B

When a hydrogen atom's electron drops to a lower energy level, it emits a photon whose wavelength reveals the energy difference between those levels.

Lyman series (transitions to

n = 1

):

n = 2 \to 1

: 121.6 nm,

\quad n = 3 \to 1

: 102.6 nm,

\quad n = 4 \to 1

: 97.2 nm,

\quad n = 5 \to 1

: 95.0 nm

Balmer series (transitions to

n = 2

):

n = 3 \to 2

: 656.3 nm,

\quad n = 4 \to 2

: 486.1 nm,

\quad n = 5 \to 2

: 434.0 nm,

\quad n = 6 \to 2

: 410.2 nm

Use

\Delta E = \dfrac{hc}{\lambda}

, where

h = 6.63 \times 10^{-34}

J s and

c = 3.00 \times 10^{8}

m s

^{-1}

.

a

Calculate the energy of the photon emitted in the

n = 3 \to 2

transition. [2]

b

Using your answer to (a) and the data above, deduce the energy of the photon emitted in the

n = 3 \to 1

transition without using the 102.6 nm value directly, then compare your result with the value obtained from 102.6 nm. [3]

c

The Lyman series wavelengths decrease from 121.6 nm to 95.0 nm as the upper level rises from

n = 2

to

n = 5

, yet the decreases get smaller with each step. Analyse how both series together support the conclusion that energy level spacing decreases as

n

increases. [3]

Solutions

16QuestionRutherford’s nuclear modelAssessment Practice

8 marks~12 minCriterion B

A beam of alpha particles of fixed intensity and energy strikes gold foils of different thicknesses. The table below shows the number of alpha particles detected in each angular range.

Foil thickness 0.5 μm — particles detected: 0°–10°: 9500 | 10°–30°: 400 | 30°–60°: 80 | 60°–90°: 15 | 90°–180°: 5

Foil thickness 1.0 μm — particles detected: 0°–10°: 9200 | 10°–30°: 600 | 30°–60°: 150 | 60°–90°: 30 | 90°–180°: 20

Foil thickness 2.0 μm — particles detected: 0°–10°: 8800 | 10°–30°: 800 | 30°–60°: 300 | 60°–90°: 60 | 90°–180°: 40

a

Describe the trend in the number of alpha particles scattered at angles greater than 90° as foil thickness increases. [2]

b

Deduce the number of alpha particles scattered at angles greater than 90° for a foil of thickness 1.5 μm, showing your reasoning clearly. [3]

c

Analyse how Coulomb repulsion and the probability of close nuclear encounters together account for the trend identified in part (a). [3]

Solutions

17QuestionSubatomic particles: Proton (charge, mass, location) , Neutron (charge, mass, location), Electron (charge, mass, location)Assessment Practice

12 marks~18 minCriterion D

A hospital uses Technetium-99m (

^{99m}

Tc) for medical imaging.

^{99m}

Tc has a half-life of approximately 6 hours and emits gamma radiation. It is produced in nuclear reactors, administered to patients, and the resulting radioactive waste requires careful disposal. Gamma cameras detect the emitted radiation to produce images of internal organs.

a

Describe the properties of the three subatomic particles and explain how the nuclear properties of

^{99m}

Tc make it suitable for medical imaging. [3]

b

Explain the environmental risks arising from the production and disposal of

^{99m}

Tc, including how radioactive contamination can spread through an ecosystem. [4]

c

Evaluate whether the benefits of using

^{99m}

Tc in medical imaging justify the risks to patients and the environment, proposing measures to reduce those risks. [5]

Solutions

18QuestionHalf-life DefinitionAssessment Practice

5 marks~8 minCriterion B

A student monitors a radioactive source, recording count rate every 30 s.

Time (s)	0	30	60	90	120	150	180	210	240	270	300
Count rate (counts/s)	800	566	400	283	200	141	100	71	50	35	25

a

Calculate the half-life of this isotope, showing clearly which data values you used. [1]

b

Show that the count rate data is consistent with exponential decay by demonstrating the halving pattern across at least four successive half-life intervals. [2]

c

Evaluate whether the full dataset provides convincing evidence that the decay constant

\lambda

remains unchanged throughout the 300 s observation period. Use the relationship

N(t) = N_0\, e^{-\lambda t}

in your reasoning. [2]

Solutions

19QuestionApplications of radioactivity in Industry/ medicine / archaeology/biology/ meteorologyAssessment Practice

6 marks~9 minCriterion B

Archaeologists use the ratio of carbon-14 (parent) to nitrogen-14 (daughter) atoms in bone samples to estimate their age. The half-life of carbon-14 is 5730 years. Measurements from bone samples of known age are shown below.

Sample age (years)	0	5730	11 460	17 190
Parent-daughter ratio	1.00	0.50	0.25	0.125

a

Deduce the mathematical relationship between the parent-daughter ratio

R

and the number of half-lives

n

elapsed, using the data in the table to support your answer. [2]

b

Calculate the parent-daughter ratio for a bone sample that is 22 920 years old, and explain what this value tells an archaeologist about the remaining carbon-14 in the sample. [2]

c

A colleague claims that carbon-14 dating becomes unreliable beyond about 50 000 years because the parent-daughter ratio falls below a measurable threshold. Analyse this claim using the exponential decay model, and evaluate whether the data trend supports it. [2]

Solutions

20QuestionHalf-life Interpretation of decay graphsAssessment Practice

6 marks~9 minCriterion A

A researcher monitors the mass of a radioactive isotope sample at regular intervals. The results are recorded below.

Time (s)	0	10	20	30	40	50
Mass (g)	80	56	40	28	20	?

a

Deduce the half-life of this sample. Use the data to support your answer. [2]

b

Calculate the predicted mass at 50 s. Show your working clearly. [2]

c

A second sample of the same isotope has an initial mass of 160 g. Analyse whether the half-life of this second sample is different from the first. Justify your answer with reference to the nature of radioactive decay. [2]

Solutions

21QuestionSpontaneous and random nature of decayAssessment Practice

2 marks~3 minCriterion C

A Geiger counter is placed near a radioactive source. The counts recorded in six consecutive 10-second intervals are:

Interval 1: 12 counts
Interval 2: 8 counts
Interval 3: 15 counts
Interval 4: 11 counts
Interval 5: 9 counts
Interval 6: 14 counts

Explain how this data supports the conclusion that radioactive decay is a random process. [2]

Solutions

22QuestionFission and FusionAssessment Practice

3 marks~5 minCriterion C

The graph below shows binding energy per nucleon (MeV) against mass number

A

for stable nuclei. The curve rises steeply for light nuclei, peaks near iron-56 at approximately 8.8 MeV, then decreases gradually for heavy nuclei.

a

State what a higher binding energy per nucleon indicates about nuclear stability. [1]

b

Using the graph, explain why energy is released when two light nuclei undergo fusion. [1]

c

A student claims: "Fission and fusion both release energy, so the binding energy curve must be symmetric about its peak." Evaluate this claim. [1]

Solutions

23QuestionDefinition of radioactivityAssessment Practice

5 marks~8 minCriterion D

A student uses a cloud chamber to observe alpha decay from a radioactive source. The following observations are recorded:

1. All tracks are straight and approximately 4 cm long.
2. Tracks originate from a single point.
3. Tracks appear at irregular, unpredictable time intervals.
4. No tracks are curved or branched.

a

State what the consistent track length indicates about the energy of the emitted alpha particles. [1]

b

Explain how observations 1 and 4 together support the conclusion that alpha particles are emitted as discrete, massive, charged particles. [2]

c

Evaluate how well all four observations support the model of radioactive decay as a random and spontaneous process, identifying one limitation of this experimental evidence. [2]

Solutions

24QuestionDetection methods: Geiger-Müller counter, Photographic filmAssessment Practice

2 marks~3 minCriterion B

A student uses a Geiger–Müller (GM) counter to measure the count rate from a radioactive source at several distances. Background radiation has been subtracted.

Distance (cm)	10	20	30	40	50
Count rate (counts s $^{-1}$ )	400	100	44	25	16

a

Deduce the mathematical relationship between count rate and distance shown by these data. Support your answer with at least one numerical check. [1]

b

Using the relationship identified in (a), calculate the count rate expected at a distance of 60 cm. [1]

Solutions

25QuestionBackground radiation: Natural sources (cosmic, rocks), Artificial sourcesAssessment Practice

5 marks~8 minCriterion A

The average background radiation dose rate at different altitudes is given below.

Altitude (m)	0	3000	6000	10 000
Dose rate (µSv/h)	0.06	0.30	0.80	5.00

The annual public dose limit is 1 mSv (1000 µSv). An airline pilot flies 900 hours per year at 10 000 m and spends all remaining hours at sea level.

a

Calculate the annual radiation dose received by a worker who spends the entire year at sea level. [1]

b

Calculate the pilot's total annual radiation dose, accounting for both flight hours and ground hours. [2]

c

Analyse how altitude, atmospheric shielding, and total exposure time together explain why the pilot's annual dose exceeds the public limit, while the ground worker's dose does not. [2]

Solutions

26QuestionDetection methods: Geiger-Müller counter, Photographic filmAssessment Practice

8 marks~12 minCriterion D

A student uses a Geiger–Müller (GM) counter to measure the count rate from a beta-emitting point source at several distances. The background count rate is 20 counts per minute (cpm). The corrected count rates (background already subtracted) are:

Distance (cm)	10	20	30	40	50
Corrected count rate (cpm)	980	245	109	61	39

The inverse-square law states that count rate

I \propto \dfrac{1}{d^2}

, where

d

is the distance from the source.

a

Show that the expected corrected count rate at

d = 20

cm, using

d = 10

cm as the reference, is 245 cpm. [2]

b

Calculate the percentage difference between the measured and expected corrected count rates at

d = 30

cm and at

d = 50

cm. Use:

\text{Percentage difference} = \frac{|\text{measured} - \text{expected}|}{\text{expected}} \times 100\%

[2]

c

Evaluate whether the experimental data support the inverse-square law model for beta radiation. In your answer, use the percentage differences from (b), consider why background radiation was subtracted before comparison, and identify one experimental factor that could cause deviations from the inverse-square law at larger distances. [4]

Solutions

27QuestionPractical uses in Sterilization/ Medical imaging/ Industrial thickness controlAssessment Practice

6 marks~9 minCriterion C

A student investigates how lead absorbs gamma radiation. The background count rate is 15 counts per minute. After subtracting background, the corrected count rate

I

at each thickness

x

of lead is:

x

(mm): 0, 2, 4, 6, 8, 10

I

(counts/min): 480, 340, 240, 170, 120, 85

Gamma attenuation follows

I = I_0 e^{-\mu x}

, where

\mu

is the linear attenuation coefficient.

a

Calculate

\ln I

for each thickness and deduce whether the relationship between

\ln I

and

x

is linear. [1]

b

Using the data points at

x = 0

and

x = 10

mm, calculate the gradient of the

\ln I

vs

x

graph and hence determine

\mu

. [3]

c

A radiation protection engineer claims that 8 mm of lead is sufficient to reduce the count rate to less than 25% of

I_0

. Using your value of

\mu

, evaluate this claim. [2]

Solutions

28QuestionDeflection in electric and magnetic fieldsAssessment Practice

5 marks~8 minCriterion A

In an experiment, alpha, beta, and gamma radiation pass through a uniform electric field of strength

E = 2.0 \times 10^4 \, \text{N/C}

and a separate uniform magnetic field of strength

B = 0.50 \, \text{T}

.

Particle properties:

Alpha	charge $q = +2e$	mass $m = 6.64 \times 10^{-27}$ kg	speed $v = 1.5 \times 10^7$ m/s
Beta	charge $q = -e$	mass $m = 9.11 \times 10^{-31}$ kg	speed $v = 2.0 \times 10^8$ m/s

Gamma:

q = 0

a

Calculate the electric force

F_E

and magnetic force

F_B

acting on the alpha particle. [2]

b

Show that the beta particle experiences a greater force than the alpha particle in the magnetic field, and explain why this produces a larger deflection despite beta having a smaller charge. [2]

c

Evaluate which radiation type is deflected most in each field, justifying your answer using charge-to-mass ratios and the accelerations experienced by each particle. [1]

Solutions

29QuestionBackground radiation: Natural sources (cosmic, rocks), Artificial sourcesAssessment Practice

5 marks~8 minCriterion C

A student uses a Geiger counter to measure background radiation at three locations, recording counts per minute three times at each:

Location A (basement of a granite building)	22	25	19
Location B (ground floor of a concrete building)	15	17	14
Location C (high-altitude mountain laboratory)	28	31	26

a

Calculate the mean count rate for each location. [3]

b

A classmate claims that "background radiation is constant everywhere on Earth." Evaluate this claim using your calculated mean count rates, and discuss how differences in cosmic ray intensity and the radioactivity of geological materials may account for the pattern observed across the three locations. [2]

Solutions

30QuestionBinding energy (qualitative)Assessment Practice

6 marks~9 minCriterion C

The table below shows nuclear data for five light isotopes.

Isotope	H-1	H-2	H-3	He-3	He-4
Nucleon number	1	2	3	3	4
Total binding energy (MeV)	0	2.22	8.48	?	28.30
Binding energy per nucleon (MeV/nucleon)	0	1.11	2.83	?	7.08

a

Calculate the total binding energy of He-3, given that its binding energy per nucleon is

2.57 \text{ MeV/nucleon}

. [2]

b

Deduce which of H-3 and He-3 is more stable, using values from the table. [2]

c

Evaluate whether binding energy per nucleon is a reliable indicator of nuclear stability for the isotopes in this dataset, referring to at least two specific values in your answer. [2]

Solutions

31QuestionBinding energy (qualitative)Assessment Practice

6 marks~9 minCriterion D

A government must choose between a uranium-235 fission power plant and a coal-fired power plant to meet future energy demands.

Data: binding energy per nucleon of uranium-235 ≈ 7.6 MeV; average binding energy per nucleon of fission products ≈ 8.4 MeV; energy released per coal combustion reaction ≈ 4 eV per carbon atom.

a

Using the data above, calculate the energy released per fission event of uranium-235. [2]

b

Explain why nuclear fuel releases significantly more energy per kilogram than coal. [2]

c

Evaluate the ethical trade-offs a government must consider when choosing between these two energy sources, addressing intergenerational equity in your answer. [2]

Solutions

32QuestionRadioactive vs stable isotopesAssessment Practice

3 marks~5 minCriterion A

The graph below shows the number of neutrons (

N

) plotted against the number of protons (

Z

) for stable isotopes of elements from hydrogen to calcium (

Z = 1

to

20

). The dashed line shows

N = Z

for reference.

a

Describe the trend in the neutron-to-proton ratio (

N/Z

) for stable isotopes as

Z

increases from 1 to 20. [1]

b

Explain why light stable isotopes (

Z \leq 10

) cluster near

N/Z \approx 1

. [1]

c

Explain why heavier stable isotopes require progressively more neutrons than protons to remain stable. [1]

Solutions

33QuestionNeutron-to-proton ratioAssessment Practice

6 marks~9 minCriterion B

The graph of neutron number (

N

) versus proton number (

Z

) for all known stable isotopes displays the band of stability and the line

N = Z

.

Three isotopes lie within the band of stability:

Carbon-12	$Z = 6$	$N = 6$
Iron-56	$Z = 26$	$N = 30$
Lead-208	$Z = 82$	$N = 126$

a

Deduce the neutron-to-proton ratio (

N/Z

) for each of the three isotopes above. [3]

b

Interpret the difference in

N/Z

between Carbon-12 and Iron-56 in terms of nuclear stability. [1]

c

Analyse the trend in

N/Z

across the three isotopes and explain, using the concept of nuclear forces, why heavy stable nuclei require a greater proportion of neutrons than light stable nuclei. [2]

Solutions

34QuestionNotation of isotopes (e.g., ¹⁴C)Assessment Practice

12 marks~18 minCriterion D

Carbon-14 dating estimates the age of archaeological material by measuring the radioactive decay of

^{14}

C. Living organisms continuously exchange carbon with the atmosphere, maintaining a constant

^{14}

C/

^{12}

C ratio. After death,

^{14}

C decays with a half-life of approximately 5730 years, while

^{12}

C remains stable. Dating requires destroying a small sample, which raises serious concerns when applied to Indigenous burial sites, where ancestral remains are considered sacred.

a

Explain what the notation

^{14}

C communicates about the structure of this isotope and why this structure makes it suitable for dating. [2]

b

Discuss the ethical conflict that arises when

^{14}

C dating is applied to Indigenous burial sites, addressing both the scientific value of the technique and the cultural concerns of affected communities. [4]

c

Analyse how the limitations of

^{14}

C dating — including contamination, calibration uncertainty, and assumptions about past atmospheric

^{14}

C levels — affect the reliability of age determinations from burial sites. [4]

d

Evaluate whether the use of

^{14}

C dating on human remains from Indigenous burial sites can be justified. [2]

Solutions

35QuestionSafety principles: Time (reduce exposure time), Distance (increase distance), Shielding (lead, concrete)Assessment Practice

6 marks~9 minCriterion B

A radiation safety technician measures the count rate from a gamma source at several distances.

Distance (m)	0.5	1.0	1.5	2.0	3.0
Count rate (counts min $^{-1}$ )	1200	300	133	75	33

a

Construct a graph of count rate (y-axis) against distance (x-axis) and interpret the shape of the curve. [2]

b

Deduce whether the data follow an inverse-square law by calculating the product (count rate)

\times

(distance)

^{2}

for each data point. [2]

c

A radiation worker must not be exposed to more than 20 counts min

^{-1}

from this source. Analyse whether standing at 4.0 m provides a safe working distance, and justify your conclusion using the inverse-square law. [2]

Solutions

36QuestionSafety principles: Time (reduce exposure time), Distance (increase distance), Shielding (lead, concrete)Assessment Practice

6 marks~9 minCriterion D

A hospital is designing a radiology room and must choose between two wall-shielding options: 5 cm of lead (density

11.3\ \text{g cm}^{-3}

, atomic number

Z = 82

) or 20 cm of concrete (density

2.4\ \text{g cm}^{-3}

,

Z \approx 14

). Lead costs significantly more and adds greater structural load; concrete is cheaper but reduces usable floor space. Both options are claimed to provide equivalent radiation protection.

a

Explain why lead achieves equivalent radiation attenuation to concrete using a much thinner layer, referencing the physical properties of each material. [2]

b

Analyse the limitations of concrete shielding, considering both its physics-based performance and the practical consequences for hospital design. [2]

c

Evaluate which shielding option the hospital should choose, justifying your recommendation by weighing effectiveness, cost, space, and structural load. [2]

Solutions

37QuestionRisk vs benefit analysis in applicationsAssessment Practice

6 marks~9 minCriterion C

A radiation worker places increasing thicknesses of lead between a Cs-137 gamma source and a detector. The source emits 662 keV gamma rays. Initial intensity without shielding is 100 mSv/h.

Lead thickness (cm)	0	1	2	3	4	5
Intensity (mSv/h)	100.0	50.0	25.0	12.5	6.25	3.13

The published half-value layer (HVL) for Cs-137 gamma rays in lead is 0.65 cm.

a

Deduce the mathematical relationship between lead thickness and measured intensity. Use your relationship to predict the intensity at 7 cm. [2]

b

Show that the intensity predicted by the published HVL at 7 cm differs from your answer in (a). Explain one physical reason for this difference. [2]

c

A hospital physicist must choose between 7 cm of lead shielding (based on the experimental data) and 4.55 cm of lead (based on the published HVL), both claimed to reduce intensity to a similarly safe level. Evaluate which thickness the physicist should recommend, justifying your answer with reference to the two intensity values and the conditions under which each was obtained. [2]

Solutions

38QuestionSafety principles: Time (reduce exposure time), Distance (increase distance), Shielding (lead, concrete)Assessment Practice

3 marks~5 minCriterion B

A radiation worker monitors a gamma source. The background count rate has been subtracted from all readings.

Count rate (counts/s) at each distance:
0.5 m: 400 — 1.0 m: 100 — 1.5 m: 44 — 2.0 m: 25 — 2.5 m: 16 — 3.0 m: 11

a

State the relationship between intensity and distance described by the inverse square law. [1]

b

Use two values from the data to show that the count rate follows the inverse square law. [1]

c

Explain, using the inverse square law, why increasing distance from the gamma source reduces a worker's radiation exposure. [1]

Solutions

39QuestionRisk vs benefit analysis in applicationsAssessment Practice

3 marks~5 minCriterion C

The graph below shows the relationship between cumulative radiation dose (in millisieverts, mSv) and excess relative risk of developing cancer. The data follows the linear no-threshold (LNT) model.

a

Describe the trend shown in the graph. [1]

b

Explain what the graph indicates about the relationship between dose and cancer risk. [1]

c

Discuss why the LNT model implies there is no completely safe dose of radiation, and identify one limitation of applying this model to real-world radiation safety decisions. [1]

Solutions

40QuestionSafety principles: Time (reduce exposure time), Distance (increase distance), Shielding (lead, concrete)Assessment Practice

5 marks~8 minCriterion A

A student measures background-corrected count rates (CPM) at 20 cm from a Cs-137 gamma source using a Geiger counter.

No shielding: 4800 CPM

Lead thickness (cm)	2	5	10
Count rate (CPM)	2400	600	38

Concrete thickness (cm)	5	10	15	20
Count rate (CPM)	1200	300	75	19

The student claims both materials follow the exponential attenuation model:

I = I_0 \, e^{-\mu x}

where

I_0

is the initial count rate,

x

is thickness (cm), and

\mu

is the attenuation coefficient (cm

^{-1}

).

a

Calculate the percentage reduction in count rate produced by 5 cm of lead. [1]

b

Deduce the thickness of concrete that produces the same percentage reduction as 5 cm of lead. Show your working. [2]

c

Evaluate the validity of the exponential attenuation model for lead by calculating

\mu

from the 2 cm and 5 cm data, predicting the count rate at 10 cm, and comparing this prediction with the measured value. [2]

Solutions

Atomic Physics — Free MYP4 Physics Practice Questions