E.3 Radioactive decay
Practice exam-style IB Physics questions for Radioactive decay, aligned with the syllabus and grouped by topic.
Question 1
Atoms of two isotopes of the same element have the same
A.
number of protons but different numbers of neutrons.
B.
chemical properties only if both are radioactive.
C.
number of neutrons but different numbers of protons.
D.
nucleon number and different proton numbers.
Question 2
A nucleus emits an alpha particle. The changes in proton number and nucleon number are
A.
proton number increases by 1; nucleon number is unchanged.
B.
proton number decreases by 4; nucleon number decreases by 2.
C.
proton number is unchanged; nucleon number is unchanged.
D.
proton number decreases by 2; nucleon number decreases by 4.
Question 3
The missing particle in the decay equation
A.
\({}^{0}_{-1}\beta^-\)
B.
\({}^{0}_{+1}\beta^+\)
C.
\(\gamma\)
D.
\({}^{4}_{2}\alpha\)
Question 4
The SI unit of activity is
A.
becquerel, equal to one decay per second.
B.
gray, equal to one joule per kilogram.
C.
sievert, equal to one count per second.
D.
electronvolt, equal to one nuclear transition per second.
Question 5
Discrete gamma-ray energies emitted by a nucleus provide evidence for
A.
continuous nuclear binding energies.
B.
discrete nuclear energy levels.
C.
ionization of atomic electrons only.
D.
the absence of recoil of the daughter nucleus.
Question 6
A neutral atom has nuclide notation ({}^{35}_{17} ext{Cl}).
State the number of protons in the nucleus.
[1]
Determine the number of neutrons in the nucleus.
[1]
State what must be different in another isotope of chlorine.
[1]
Question 7
Complete the nuclear equation for beta-plus decay.
[{}^{22}{11} ext{Na}\rightarrow{}^{A}{Z} ext{Ne}+{}^{0}_{+1}\beta^+ +
u]
Determine (A).
[1]
Determine (Z).
[1]
State the type of additional neutral particle emitted.
[1]
Question 8
A radiation source is to monitor the thickness of aluminium sheet during manufacture. The most suitable emission is
A.
gamma, because it is completely absorbed by aluminium.
B.
neutrino, because it is weakly ionizing.
C.
alpha, because it is stopped by very thin materials.
D.
beta, because its absorption changes appreciably with sheet thickness.
Question 9
A sample has an initial corrected count rate of (640, ext{s}^{-1}). Its half-life is 12 min. The corrected count rate after 36 min is
A.
\(160\, ext{s}^{-1}\)
B.
\(213\, ext{s}^{-1}\)
C.
\(320\, ext{s}^{-1}\)
D.
\(80\, ext{s}^{-1}\)
Question 10
The existence of stable nuclei containing more than one proton requires a force that is
A.
short range, attractive and stronger than electrostatic repulsion at nuclear separations.
B.
long range, attractive and weaker than gravity.
C.
short range, repulsive and acting only between electrons.
D.
long range, neutral and independent of nucleon separation.
Question 11
A neutron-rich nuclide above the zone of stability is most likely to move toward stability by
A.
beta-minus decay.
B.
gamma emission only.
C.
beta-plus decay.
D.
electron capture followed by gamma emission only.
Question 12
A continuous beta-particle energy spectrum is evidence that
A.
gamma photons are always emitted with beta particles.
B.
the daughter nucleus has no recoil momentum.
C.
beta particles are emitted from atomic electron shells.
D.
energy is shared with an additional particle emitted in the decay.
Question 13
The approximate constancy of binding energy per nucleon for nuclei with (A>60) is evidence that the strong nuclear force
A.
is weaker than electrostatic repulsion at all nuclear separations.
B.
acts mainly between near-neighbour nucleons.
C.
acts only on protons and not on neutrons.
D.
acts equally between all nucleons in the universe.
Question 14
For a nucleus ({}^{7}_{3} ext{Li}), take (m_p=1.0073,u), (m_n=1.0087,u) and the nuclear mass as (7.0144,u).
State the number of neutrons in the nucleus.
[1]
Calculate the mass defect in (u).
[1]
State what this mass defect represents physically.
[1]
Question 15
A sealed source is to be used as a tracer to find a leak in an underground water pipe.
State one reason why an alpha emitter would be unsuitable.
[1]
State one reason why a gamma emitter may be suitable.
[1]
Outline one half-life requirement for the isotope used.
[1]
Question 16
A detector records an observed count rate of (92, ext{s}^{-1}) when a source is present. The background count rate is (18, ext{s}^{-1}).
Calculate the corrected count rate.
[1]
The corrected count rate falls by two half-lives. Calculate the new observed count rate, assuming the background is unchanged.
[1]
Question 17
A radioactive source is heated, then cooled, while its count rate is monitored with a fixed detector arrangement.
State what is meant by radioactive decay being random.
[1]
State what is meant by radioactive decay being spontaneous.
[1]
Explain why heating the source is not expected to change its half-life.
[1]
Question 18
A student measures the count rate from a radioactive source. Background count rate has been measured separately.
Determine the corrected count rate at the start of the experiment.
[1]
Use the graph to determine the half-life of the source.
[1]
Explain why the estimate from later readings is less reliable.
[1]
Question 19
The activity of a medical isotope is measured at equal time intervals.
| Time / h | Activity / MBq |
|---|---|
| 0 | 96.0 |
| 2 | 67.9 |
| 4 | 48.0 |
| 6 | 33.9 |
| 8 | 24.0 |
| 10 | 17.0 |
| 12 | 12.0 |
Determine the number of half-lives that have elapsed by the final measurement.
[1]
Determine the half-life of the isotope.
[1]
Calculate the activity expected after one further half-life.
[1]
Suggest why this isotope may be unsuitable if the scan is delayed for many half-lives.
[1]
Question 20
The total mass of the products of a nuclear reaction is less than the total mass of the reactants by (0.012,u). The energy released is approximately
A.
\(7.8\, ext{MeV}\)
B.
\(11\, ext{MeV}\)
C.
\(0.012\, ext{MeV}\)
D.
\(9.3 imes10^{2}\, ext{MeV}\)
Question 21
A radionuclide has decay constant (2.0 imes10^{-4}, ext{s}^{-1}). Its half-life is approximately
A.
\(3.5 imes10^{3}\, ext{s}\)
B.
\(5.0 imes10^{3}\, ext{s}\)
C.
\(1.0 imes10^{4}\, ext{s}\)
D.
\(1.4 imes10^{-4}\, ext{s}\)
Question 22
A sample contains (4.0 imes10^{12}) undecayed nuclei and has decay constant (3.0 imes10^{-6}, ext{s}^{-1}). Its activity is
A.
\(7.5 imes10^{-19}\, ext{Bq}\)
B.
\(4.0 imes10^{12}\, ext{Bq}\)
C.
\(1.2 imes10^{7}\, ext{Bq}\)
D.
\(1.3 imes10^{18}\, ext{Bq}\)
Question 23
The statement that the decay constant is the probability of decay per unit time is most accurate when
A.
the sample contains only one undecayed nucleus.
B.
the time interval is small enough that \(\lambda\Delta t\ll1\).
C.
the time interval is equal to exactly one half-life.
D.
background radiation has been subtracted.
Question 24
A graph of (\ln R) against time (t) for the corrected count rate of a radioactive source is a straight line with gradient (-0.018, ext{min}^{-1}). The decay constant is
A.
\(-0.018\, ext{min}^{-1}\)
B.
\(56\, ext{min}\)
C.
\(0.018\, ext{min}^{-1}\)
D.
\(0.693\, ext{min}^{-1}\)
Question 25
In a nuclear reaction the mass of the reactants exceeds the mass of the products by (3.2 imes10^{-29}, ext{kg}).
State whether energy is released or absorbed.
[1]
Calculate the energy transferred in joules using (c=3.00 imes10^8, ext{m s}^{-1}).
[1]
State one possible form in which the energy may appear.
[1]
Question 26
The binding energy per nucleon of ({}^{56} ext{Fe}) is greater than that of ({}^{235} ext{U}).
State what is meant by binding energy per nucleon.
[1]
Explain why a larger binding energy per nucleon indicates greater nuclear stability.
[1]
Suggest why very heavy nuclei may release energy by changing into lighter nuclei.
[1]
Question 27
A sample initially contains (8.0 imes10^{15}) undecayed nuclei. Its decay constant is (1.5 imes10^{-5}, ext{s}^{-1}).
Write the radioactive decay law for (N).
[1]
Calculate the number of undecayed nuclei after (2.0 imes10^4, ext{s}).
[1]
State why the exponential law is needed rather than repeated halving in this calculation.
[1]
Question 28
Beta-minus particles from a particular nuclear transition are detected with a continuous range of kinetic energies.
State the additional particle emitted in beta-minus decay.
[1]
Explain why a continuous beta spectrum supports the existence of this particle.
[1]
Question 29
On a neutron number against proton number plot, stable nuclides with large proton number lie above the line (N=Z).
State what this implies about the neutron-to-proton ratio of heavy stable nuclides.
[1]
Explain why extra neutrons help stability in heavy nuclei.
[1]
Question 30
Alpha-particle scattering from some nuclei deviates from the prediction of a purely electrostatic model at very small separations.
State the interaction responsible for the deviation.
[1]
Outline why the deviation occurs only at very small separations.
[1]
State what this provides evidence for.
[1]
Question 31
A nucleus emits gamma photons with energies of (0.41, ext{MeV}) and (0.96, ext{MeV}), with no photons detected at intermediate energies.
State what the word discrete means in this context.
[1]
Explain what these gamma-ray energies show about the nucleus.
[1]
Question 32
A detector is placed behind absorbers of different materials. A source emits one unknown type of ionizing radiation.
| Absorber | Thickness / mm | Count rate / min^-1 |
|---|---|---|
| None | 0 | 840 |
| Paper | 0.10 | 28 |
| Aluminium | 1.0 | 24 |
| Lead | 10 | 22 |
Identify the type of radiation most consistent with the absorption data.
[1]
State one observation from the data that supports your identification.
[1]
Explain why the other two common radiation types are less consistent with the data.
[1]
Question 33
The graph shows the variation of binding energy per nucleon with nucleon number.
Identify the region of greatest stability on the graph.
[1]
State whether energy can be released when two very light nuclei combine to form a heavier nucleus closer to the peak.
[1]
Explain your answer to
[1]
in terms of binding energy.
[1]
Suggest why alpha particles are commonly emitted by very heavy nuclei.
[1]
Question 34
A student records background counts and source-plus-background counts using the same detector.
| Interval | Condition | Time / s | Total counts | Count rate / s⁻¹ |
|---|---|---|---|---|
| B1 | Background | 60 | 18 | 0.30 |
| B2 | Background | 60 | 22 | 0.37 |
| B3 | Background | 60 | 20 | 0.33 |
| B4 | Background | 60 | 16 | 0.27 |
| B5 | Background | 60 | 24 | 0.40 |
| S1 | Source + background | 60 | 431 | 7.18 |
| S2 | Source + background | 60 | 450 | 7.50 |
| S3 | Source + background | 60 | 428 | 7.13 |
| S4 | Source + background | 60 | 444 | 7.40 |
Calculate the mean background count rate.
[1]
Determine the corrected count rate for the source for one stated interval.
[1]
Evaluate one change to the method that would reduce the percentage uncertainty in the background count rate.
[1]
Question 35
The figure shows neutron number against proton number for several unstable nuclides near the zone of stability.
Identify one nuclide that is neutron-rich relative to the zone of stability.
[1]
Predict the most likely beta decay mode for this nuclide.
[1]
Explain how this decay moves the nuclide toward the zone of stability.
[1]
Question 36
A radionuclide used in imaging has initial activity (A_0=4.8 imes10^8, ext{Bq}) and decay constant (\lambda=3.2 imes10^{-5}, ext{s}^{-1}).
Calculate the initial number of undecayed nuclei.
[1]
Calculate the activity after (1.0 imes10^4, ext{s}).
[1]
Question 37
A straight-line graph of (\ln(R_{ ext{corrected}})) against time has gradient (-0.024, ext{h}^{-1}).
State the decay constant in ( ext{h}^{-1}).
[1]
Calculate the half-life in hours.
[1]
State one advantage of using a logarithmic graph rather than reading a single halving interval.
[1]
Question 38
A particular nucleus has decay constant (6.0 imes10^{-4}, ext{s}^{-1}).
Estimate the probability that it decays in the next (2.0, ext{s}).
[1]
State the condition for using this estimate.
[1]
Calculate the exact probability of decay in (2.0, ext{s}) using the exponential law.
[1]
Question 39
The corrected count rate of a radioactive source is processed to produce a graph of (\ln R) against time.
Determine the decay constant from the graph.
[1]
Calculate the half-life.
[1]
Explain why the graph should be linear if the source contains a single radionuclide.
[1]
Question 40
A gamma-ray spectrum from a radioactive daughter nucleus is shown.
State the evidence that the spectrum is discrete.
[1]
Determine the energy difference between two nuclear levels associated with one labelled gamma line.
[1]
Explain how the spectrum supports the model of nuclear energy levels.
[1]
Distinguish the origin of these photons from X-ray photons.
[1]
Question 41
High-energy electrons are scattered by a nucleus. The first diffraction minimum is observed in the angular distribution.
Determine the angle of the first minimum from the graph.
[1]
Use ( heta\approx\lambda/b) to estimate the nuclear diameter (b).
[1]
Explain why electron scattering can be used to investigate nuclear size.
[1]
Question 42
A hospital must choose a radionuclide for diagnostic imaging. Two possible isotopes emit ionizing radiation with similar activity when administered.
Outline the desirable properties of the radiation and half-life for a diagnostic imaging isotope.
[1]
Evaluate the choice between an alpha emitter, a beta emitter and a gamma emitter for this application, including dose and detectability.
[1]
Question 43
Stable nuclei exist despite containing positively charged protons close together.
Describe the roles of the electric force and the strong nuclear force in a nucleus.
[1]
Explain why heavy stable nuclei tend to contain neutrons as well as protons, and why the strong nuclear force does not affect everyday objects at large distances.
[1]
Question 44
Radioactive nuclei can emit alpha, beta-minus, beta-plus or gamma radiation.
Complete the changes in (A) and (Z) for alpha and gamma emission.
[1]
Compare and contrast beta-minus and beta-plus decay, including nuclear changes, emitted particles and conservation in nuclear equations.
[1]
Question 45
The kinetic energy spectrum of beta-minus particles from one radionuclide is shown.
Describe the shape of the beta spectrum.
[1]
State the particle emitted with the beta-minus particle.
[1]
Explain why a two-product decay would not produce the observed spectrum.
[1]
Evaluate how the spectrum supports conservation laws.
[1]
Question 46
A student investigates the half-life of a beta-emitting source using a Geiger–Müller tube and counter.
Describe how the background count rate should be measured and used.
[1]
Discuss how the student should determine the half-life and reduce uncertainty in the result.
[1]
Question 47
Historically, the beta-particle energy spectrum appeared to challenge conservation laws.
Describe the key difference between alpha-particle spectra and beta-particle spectra from nuclear decay.
[1]
Evaluate how the neutrino hypothesis resolves the beta-spectrum problem and how it differs from simply abandoning conservation of energy and momentum.
[1]
Question 48
The binding energy per nucleon rises steeply for light nuclei, reaches a maximum near (A\approx60), and is approximately constant for larger nuclei.
State two features of the binding-energy-per-nucleon curve above (A\approx60).
[1]
Explain how these features provide evidence for the short range and saturation of the strong nuclear force.
[1]
Question 49
Several observations provide evidence for the strong nuclear force and for nuclear structure.
Outline how alpha-particle scattering can show that a purely electrostatic model is incomplete.
[1]
Discuss how electron scattering and nuclear spectra provide additional evidence about nuclei, including nuclear size and discrete energy levels.
[1]
Question 50
A sample used for dating contains a radioactive isotope with decay constant (\lambda). The present activity is much smaller than the activity expected for a living sample of the same mass.
Derive the relationship between half-life and decay constant.
[1]
Evaluate how activity measurements can be used to determine the age of the sample, including assumptions and limitations.
[1]
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