IB Physics SL E.3 Radioactive decay Questions

Practise IB Physics SL E.3 by modelling radioactive decay, activity, half-life, detectors and nuclear equations.

112 questions in this syllabus scope, with question parts counted together.

Exam points & syllabus

Exam points

Define isotopes using equal proton numbers and different neutron numbers; define half-life using undecayed nuclei or activity, not vague sample amount.
Determine whether a supplied decay sequence produces an isotope by tracking the total changes in A and Z separately.
Define binding energy as the energy needed for complete nuclear separation, or the energy released when free nucleons assemble into the nucleus.
Use nuclear mass defect Zmₚ+(A−Z)mₙ−M and E=Δmc²; distinguish a nuclear mass from an atomic mass that includes electrons.
Convert binding energy per nucleon to total binding energy using A, and divide by A only when the asked quantity is per nucleon.
For fission or fusion with conserved free-nucleon inventory, obtain released energy from total product binding energies minus total reactant binding energies.
Sketch the binding-energy-per-nucleon curve with a peak near iron/nickel and a gentle decline towards heavy nuclei, retaining the required axes and references.
Explain energy release by comparing binding energy per nucleon in the specified reactants and products, weighting by nucleon count in calculations.
For a full reaction mass-energy balance, include every incoming and outgoing particle, including neutrons and specified electrons or positrons.
Keep mass and energy units distinct: MeV/c² denotes mass, MeV denotes energy, and multiplying a rest energy by c² again is incorrect.
Distinguish a reaction’s energy from energy per unit fuel mass; compare the energy released by each complete reaction and its consumed fuel mass.
For an endothermic reaction, explain that the final rest energy exceeds the initial rest energy and incoming kinetic energy must supply the deficit.
Read an energy release from the supplied transition endpoints rather than inventing a rest-mass calculation or using an unrelated transition.
Compare short-range attractive strong forces between nucleons with long-range electrostatic repulsion between protons.
Distinguish random decay, whose individual nucleus and time are unpredictable, from spontaneous decay under ordinary external conditions.
Represent alpha emission with A=4 and Z=2, preserving total A and Z across the full decay equation.
For beta-minus decay, preserve A, increase daughter Z by one, and emit an electron and an antineutrino.
For beta-plus decay, preserve A, decrease daughter Z by one, and emit a positron and a neutrino.
Include a specified gamma photon without changing the balanced A and Z of the nuclear products.
Balance each stage of a supplied nuclear reaction and decay chain, retaining all emitted particles rather than mixing products between equations.
On an N-versus-Z chart, apply each decay vector and draw the complete forward path with arrows; derive N from A−Z where needed.
For equal-energy radiation, rank ionizing ability as gamma below beta below alpha, and pair alpha’s high ionization with low penetration.
Link alpha’s short range to the experimental geometry, such as a thin glass wall or an air gap that prevents detection.
Compare equal absorber thicknesses using corrected count rates, and justify radiation identification from the observed transmission.
In general radiation-property choices, gamma travels faster than beta in vacuum and is more penetrating but less ionizing.
Use integer halvings for parent nuclei, radioactive parent mass or activity, converting time units and using the interval between the specified times.
Distinguish a fraction lost from a fraction remaining; subtract remaining parent fraction from one to obtain the fraction decayed.
For initially pure parents producing stable daughters, use daughter count N₀−N and convert daughter-to-parent ratios before counting half-lives.
Work backwards by doubling the present parent amount for each elapsed half-life; compare samples using their individual remaining fractions.
For a decay graph, show a smooth curve through the required integer-halving points and distinguish the initial value from the half-life.
Read both crossing times for an allowed activity band and subtract them to obtain the usable duration.
Measure activity over time, plot a curve and average repeated half-life estimates when required; test analogues using constant half-life or equal-time ratios.
Subtract background before halving source counts and restore it when predicting an observed detector rate.
Read background from a long-time baseline or infer it by requiring successive net readings one half-life apart to differ by a factor of two.
Estimate half-life above the background baseline; halving the uncorrected total can give a longer, incorrect interval.
Treat a nonzero residual detector count as compatible with background, an instrument offset or a longer-lived radioactive component.
Distinguish source activity from shielding of the detector, and reject a fixed finite “whole-life” for every nucleus to disappear.

Covered syllabus points

E.3.1—Isotopes E.3.2—Binding energy and mass defect E.3.3—Binding energy curve E.3.4—Mass-energy equivalence E.3.5—Strong nuclear force E.3.6—Random radioactive decay E.3.7—Decay nuclear changes E.3.8—Decay equations E.3.9—Neutrinos and antineutrinos E.3.10—Radiation penetration and ionization E.3.11—Activity, count rate and half-life E.3.12—Half-life changes E.3.13—Background radiation

Exam points

Define a nuclide by the specified numbers of protons and neutrons in its nucleus, rather than by the element name alone.
Define isotopes as nuclei or atoms with the same proton number but different neutron numbers; include both similarities and differences.
For a decay sequence, track the total changes in A and Z before deciding whether the initial and final nuclei are isotopes.

[Maximum number: 1]

The isotope tritium (hydrogen-3) has a radioactive half-life of 12 days.

State what is meant by the term isotope.

Exam points

Define binding energy as the minimum energy to separate a nucleus completely into nucleons, or the energy released when those free nucleons assemble.
Define mass defect as the free-nucleon mass sum minus nuclear mass, counting Z protons and A−Z neutrons and excluding electrons for a nuclear mass.
Link a nucleus’s lower rest mass to energy released on formation through E=Δmc²; supplying separation energy restores the free-nucleon mass equivalent.
Convert between total binding energy and binding energy per nucleon using A, rather than proton number or the number of nuclei.
Use Δmc² and the joule-to-eV conversion to express a supplied mass defect as a binding energy in the requested units.
For alpha decay or fusion, multiply each binding energy per nucleon by its nucleus’s A before comparing product and reactant totals.
To infer a parent’s binding energy, subtract the released decay energy from the product binding-energy total before dividing by the parent A.
Find nuclear mass from Zmₚ+(A−Z)mₙ−BE/c², including the binding-energy correction and converting MeV and GeV consistently.
Explain unequal masses at the same A using emitted-particle rest mass and released energy, and state explicitly which named nucleus is heavier.
For energy-releasing fusion, distinguish lower total nuclear rest mass from higher total binding energy; use binding per nucleon to discuss tighter binding.
Explain the convenience of u, eV or MeV by the very small numerical sizes of nuclear masses and energies in SI units.

[Maximum number: 1]

This question is in two parts. Part 1 is about renewable energy. Part 2 is about nuclear energy and radioactivity.

A small coastal community decides to use a wind farm consisting of five identical wind turbines to generate part of its energy. At the proposed site, the average wind speed is $8.5 \mathrm{~m} \mathrm{~s}^{-1}$ and the density of air is $1.3 \mathrm{~kg} \mathrm{~m}^{-3}$ . The maximum power required from the wind farm is 0.75 MW . Each turbine has an efficiency of 30 %.

State what is meant by the binding energy of a nucleus.

Exam points

Sketch BE per nucleon rising to a maximum near the iron/nickel region and then declining more gently for heavy nuclei; use any supplied reference marker.
Identify the curve maximum as the region of greatest binding per nucleon and high nuclear stability, rather than a boundary below which decay cannot occur.
Use the graph explicitly to explain energy-releasing fission: a heavy nucleus splits into smaller products with higher binding energy per nucleon.
Distinguish per-nucleon from total binding energy when ordering fission nuclei or comparing ratios; the products’ total binding energy increases on release.
For fission or fusion, read each BE per nucleon, multiply by its nucleon count and subtract the total reactant binding from total product binding.
Convert a graph-based fusion release from MeV to joules and retain enough working to establish a rounded show-that target.
For complete breakup of one nucleus, multiply its graph-read binding energy per nucleon by A, not proton number Z.
Combine nuclear-number balance with the heavy-side curve when comparing fission-fragment BE per nucleon; track emitted neutrons before finding fragment A.
Explain the stated stability comparison using nuclear attraction, proton repulsion and the binding energy per nucleon of the named nuclei.

[Maximum number: 5]

This question is in two parts. Part 1 is about renewable energy. Part 2 is about nuclear energy and radioactivity.

(a)

On the axes, sketch a graph showing the variation of nucleon number with the binding energy per nucleon.

[ 2 ]

(b)

Explain, with reference to your graph, why energy is released during fission of U-235.

[ 3 ]

Exam points

Distinguish mass in MeV/c² from rest energy in MeV; once an energy equivalent is in eV, convert to joules without multiplying by c² again.
Convert a mass in u to MeV/c² using the stated mass-energy equivalent of u, while keeping the mass and energy units distinct.
Calculate released energy from the reactant rest-mass sum minus the product rest-mass sum, including all reaction coefficients and neutron terms.
Include charged leptons on the correct side of a nuclear mass balance: emitted electrons or positrons are products, while captured electrons are reactants.
For fusion with unchanged free-proton and neutron inventory, multiply each binding energy per nucleon by A before comparing total product and reactant binding.
Explain an endothermic reaction through greater product rest mass, with incident kinetic energy supplying the required increase.
Find combined final kinetic energy by subtracting a positive rest-energy increase from the initial kinetic energy, rather than adding it as a release.
In a show-that energy calculation, show the mass-difference substitution and units or retain enough significant figures to demonstrate the stated target.
Estimate specific fusion energy by counting reaction pairs or dividing the energy per reaction by the mass of one reacting pair, giving J/kg.
When comparing energy per unit fuel mass, divide the mass converted in each reaction by its reacting fuel mass before taking the ratio.
Distinguish conserved nucleon number from a changing sum of particle rest masses; connect released energy to the rest-mass decrease through ΔE=Δmc².

[Maximum number: 2]

Tritium may be produced by bombarding a nucleus of the isotope lithium-7 with a high-energy neutron. The reaction equation for this interaction is

{ }_{3}^{7} \mathrm{Li}+{ }_{0}^{1} \mathrm{n} \rightarrow{ }_{1}^{3} \mathrm{H}+{ }_{Z}^{4} \mathrm{X}+{ }_{0}^{1} \mathrm{n} .

Use the following data to show that the minimum energy that a neutron must have to initiate the reaction in (b)(i) is about 2.5 MeV .

\begin{array}{ll} \text { Rest mass of lithium-7 nucleus } & =7.0160 \mathrm{u} \\ \text { Rest mass of tritium nucleus } & =3.0161 \mathrm{u} \\ \text { Rest mass of X nucleus } & =4.0026 \mathrm{u} \end{array}

(mass difference $=) 7.0160-[3.0161+4.0026]=(-) 2.7 \times 10^{-3} \mathrm{u}$ ;
( energy required $=)(-) 2.7 \times 10^{-3} \times 931.5$ or 2.5151 MeV ;
( $\approx 2.5 \mathrm{MeV}$ )

Marking guidance:

Allow unit conversions via mass and $m c^{2}$ .

Exam points

Recognize nuclear attraction as short-range at nucleon separations; avoid treating it as attractive or repulsive at every distance.
Identify the proton as subject to both nuclear attraction and Coulomb interaction, distinguishing nuclear participation from electric charge.
Explain stable nuclear cohesion through short-range attraction between nucleons overcoming proton–proton electromagnetic repulsion at nuclear distances.

[Maximum number: 2]

The neutron number N and the proton number Z are not equal for the nuclide ${ }_{81}^{205} \mathrm{Tl}$ . Explain, with reference to the forces acting within the nucleus, the reason for this.

Exam points

Explain random decay by saying that the particular nucleus that decays, or the time of its decay, cannot be predicted.
Distinguish spontaneous decay from randomness: ordinary temperature or pressure changes do not control the decay in the course model.
Recognize that a sample’s activity can follow an exponential trend while the individual decay events remain unpredictable.

[Maximum number: 2]

Radioactive decay is said to be "random" and "spontaneous". Outline what is meant by each of these terms.

Random:
Spontaneous:

Exam points

Identify alpha emission from a fall of four in A and two in Z, even when a gamma photon is also listed among the emissions.
Recognize that beta decay preserves nucleon number while changing proton number, neutron number and nuclear charge.
Add every nuclear-number change in a decay sequence before testing for an isotope: one alpha and two beta-minus emissions restore Z but reduce A.
On an N-versus-Z chart, use alpha steps (ΔZ,ΔN)=(-2,-2) and beta-minus steps (+1,-1), drawing the complete sequence with forward arrows.
For a supplied capture-and-decay sequence, separate neutron capture’s A increase from the Z increases caused by subsequent beta-minus emissions.

[Maximum number: 3]

Thallium-205 $\left({ }_{81}^{205} \mathrm{Tl}\right)$ can also form from successive alpha ( $\alpha$ ) and beta-minus ( $\beta^{-}$ ) decays of an unstable nuclide. The decays follow the sequence $\alpha \beta^{-} \beta^{-} \alpha$ . The diagram shows the position of $\frac{205}{81} \mathrm{Tl}$ on a chart of neutron number against proton number.

Draw four arrows to show the sequence of changes to N and Z that occur as the ${ }_{81}^{205} \mathrm{Tl}$ forms from the unstable nuclide.

any $\alpha$ change correct

any $\beta$ change correct

diagram fully correct

Award [2 max] for a correct diagram without arrows drawn.

For MP1 accept a (-2, -2) line with direction indicated, drawn at any position in the graph.

For MP2 accept a (1, -1) line with direction indicated, drawn at any position in the graph.

Award [1] max for a correct diagram with all arrows in the opposite direction

Exam points

Balance nucleon number A and proton number Z separately on both sides of a nuclear decay equation.
Write alpha emission as a helium nucleus with A=4 and Z=2; reduce the daughter’s A by four and Z by two.
For beta-minus decay, preserve A, increase daughter Z by one, and include an electron and an antineutrino.
For beta-plus decay, preserve A, decrease daughter Z by one, and include a positron and a neutrino.
Distinguish the neutrino in beta-plus decay from the antineutrino in beta-minus decay; a charge-balanced equation can still have the wrong particle.
Complete every requested entry: some schemes award a single mark only when both nuclear numbers, or Z and the antineutrino, are correct.
Include a specified gamma photon with A=0 and Z=0 alongside alpha emission without changing the daughter’s balanced nuclear numbers.
In successive decays, apply each change to A and Z before calculating the final neutron number N=A−Z.
Label a requested proton number explicitly rather than giving an unexplained nuclide symbol.

[Maximum number: 2]

A nucleus of tritium decays to a nucleus of helium-3. Identify the particles X and Y in the nuclear reaction equation for this decay.

{ }_{1}^{3} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+\mathrm{X}+\mathrm{Y}

X:
Y:

$\beta^{-}$ or ${ }_{-1}^{0} \mathrm{e}$ or $\mathrm{e}^{-}$ or electron or beta particle;
$\bar{v}$ or ${ }_{0}^{0} \bar{v}$ or antineutrino;

Marking guidance:

Allow answers in either order.

Exam points

Identify the antineutrino as the additional particle in a beta-minus equation that already shows the daughter nucleus and electron.

[Maximum number: 1]

This question is in two parts. Part 1 is about kinematics and gravitation. Part 2 is about radioactivity.
Part 1 Kinematics and gravitation
A ball is released near the surface of the Moon at time t=0. The point of release is on a straight line between the centre of Earth and the centre of the Moon. The graph below shows the variation with time t of the displacement s of the ball from the point of release.

The nuclear equation for the decay of calcium-47 into scandium-47 $\left({ }_{21}^{47} \mathrm{Sc}\right)$ is given by

{ }_{20}^{47} \mathrm{Ca} \rightarrow{ }_{21}^{47} \mathrm{Sc}+{ }_{-1}^{0} \mathrm{e}+\mathrm{X}

Identify X .

(electron) anti-neutrino $/ \bar{v}$ ;

Exam points

For equal-energy radiation, rank ionizing ability in increasing order as gamma, beta, alpha.
Pair alpha radiation’s high ionizing ability with its low penetrating ability.
Explain a very thin glass wall by alpha particles’ low penetration: a thinner wall makes passage through the glass more likely.
Keep an alpha detector close enough for the particles’ short range in air; a 20 cm gap can absorb the particles before detection.
Compare absorbers at the same thickness: a lower background-corrected count rate indicates stronger absorption in the stated experiment.
Support radiation identification with penetration evidence: counts surviving lead indicate gamma, while detected particles crossing foil are not alpha.
Qualify any beta inference from absorber results; the scheme accepts alternatives with a justified thin-metal argument rather than a unique beta verdict.
In a combined gamma–beta comparison, gamma is faster in vacuum and more penetrating, while beta has greater ionizing ability.

[Maximum number: 4]

An experiment is carried out to determine the count rate, corrected for background radiation, when different thicknesses of copper are placed between a radioactive source and a detector. The graph shows the variation of corrected count rate with copper thickness.

Further results were obtained in this experiment with copper and lead absorbers.

Comment on the radiation detected from this radioactive source.

Exam points

Define half-life as the time for the activity, or the number of undecayed parent nuclei, to fall to half its initial value.
For an integer number of half-lives, halve the activity or remaining parent population at each step; convert time units first.
Distinguish remaining parents from accumulated stable daughters: with no initial daughters, daughter count equals initial parents minus remaining parents.
Convert a daughter-to-parent ratio into the parent fraction before counting half-lives; retain an extra figure in a show-that calculation.
Subtract background before halving a source count rate, then add it back if the requested result is the observed detector rate.
For a decay curve with a nonzero background, halve the excess above background rather than the total plotted count rate.
Read half-life as the time interval for activity to halve, using the plotted scale and suitable repeated readings.
Draw a smooth decay curve through the initial activity and successive integer-halving points at equal time intervals.
Measure activity over time, plot the decay curve and average at least three graphical half-life estimates when the method asks for this detail.
Find a permitted activity interval by reading both boundary times and subtracting them; use the full stated tolerance band.
Test a decay model using a constant half-life or constant ratios over equal time intervals, using the graph line rather than individual scattered points.
Distinguish source activity from detector shielding: reducing the amount of radioactive material lowers initial activity.
Reject a finite “whole-life” for complete disappearance; select a decay curve that approaches zero rather than reaching it at a fixed time.

[Maximum number: 3]

(a)

The isotope tritium (hydrogen-3) has a radioactive half-life of 12 days.

[ 1 ]

(i)

Define radioactive half-life.

[ 1 ]

(b)

A sample of tritium has an activity of $8.0 \times 10^{4} \mathrm{~Bq}$ at time t=0. The half-life of tritium is 12 days.

[ 2 ]

(i)

Using the axes below, construct a graph to show how the activity of the sample varies with time from t=0 to t=48 days.

[ 2 ]

Exam points

Identify how many complete half-lives fit the elapsed time, using consistent units, then halve the remaining parent amount at each step.
Distinguish a decrease by a fraction from the fraction remaining: a loss of seven-eighths leaves one-eighth, equal to three half-lives.
When asked for the fraction or percentage decayed, subtract the remaining fraction from one before converting to a percentage.
Work backwards by doubling the present parent amount for each elapsed half-life to recover an earlier amount.
Use the interval between the two stated times rather than automatically counting half-lives from time zero.
Infer elapsed time from a power-of-two activity decrease, or divide elapsed time by the integer number of halvings to find half-life.
Subtract background from the initial observed count, apply the halvings to the source count, then restore background to predict the observation.
For two equally populated samples, find each remaining fraction from their ratio before comparing their half-lives.
Sketch a smooth decay curve through N₀/2, N₀/4 and N₀/8 at one, two and three half-lives, with the required time range shown.
When sketching a different isotope, change the initial activity and half-life independently rather than scaling only one axis.
Apply integer halving to a validated decay analogue using its measured half-life; support a stopping-time prediction with the specified graph method.

[Maximum number: 2]

This question is in two parts. Part 1 is about renewable energy. Part 2 is about nuclear energy and radioactivity.

U-235 $\left({ }_{92}^{235} \mathrm{U}\right)$ can undergo alpha decay to form an isotope of thorium (Th).

A sample of rock contains a mass of 5.6 mg of U-235 at the present day.

The half-life of U-235 is $7.0 \times 10^{8}$ years. Calculate the initial mass of the U-235 if the rock sample was formed $2.1 \times 10^{9}$ years ago.

Exam points

Subtract the background count rate from every measured reading to obtain the source’s net count rate.
When predicting a measured count after decay, halve only the source contribution, then add the unchanged background back.
Read a constant background count rate from the long-time baseline of an observed decay curve, using the graph’s units.
Infer an unknown background from two readings one half-life apart by setting the second net count equal to half the first net count.
Suggest background radiation as a cause of a nonzero baseline, while recognizing accepted alternatives such as a detector offset or long-lived component.

[Maximum number: 1]

Outline how the count rate was corrected for background radiation.

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