E.3 Radioactive decay

Two nuclides are isotopes of the same element.

Which quantities must be the same for both?

Which statement about a change in a nucleus during radioactive decay is correct?

A nucleus contains several protons packed within a distance of about 10⁻¹⁵ m.

Why does the nucleus not fly apart?

A stationary nucleus of mass M decays into a nucleus of mass m₁ and an alpha particle of mass m₂.

What is the energy released in the decay? (c is the speed of light.)

A sealed sample contains only nuclei of a radioactive isotope X at time t = 0. X decays directly into a stable nuclide Y.

Which graph shows how the number N of nuclei of Y in the sample varies with time t?

In a cloud chamber, alpha particles leave short, thick, straight tracks of droplets, while beta particles leave longer, thinner tracks. The droplets form on ions that the particles produce in the air.

Which statement explains why the alpha-particle tracks are thicker?

The binding energy of a lithium-7 nucleus is 39.2 MeV.

What is the mass defect of this nucleus? (1 MeV = 1.60 × 10⁻¹³ J)

Uranium-235 and uranium-238 are isotopes. To make reactor fuel, the fraction of uranium-235 is increased in gas centrifuges, which separate molecules of a uranium gas compound by their mass, because the two isotopes cannot be separated by chemical reactions.

Which statement explains why the two isotopes behave identically in chemical reactions but differ in mass?

Background radiation comes from both natural and artificial sources.

Which row gives one natural source and one artificial source of background radiation?

A helium-4 nucleus contains two protons and two neutrons.

Which row describes the electrostatic force and the strong nuclear force between the two neutrons?

A marble made of uranium glass is placed in front of a Geiger–Müller tube, and 4500 counts are recorded in 10.0 minutes. With the marble removed, 600 counts are recorded in 20.0 minutes.

What is the count rate due to the marble?

Cobalt-60 decays by β⁻ emission to a nickel-60 nucleus in an excited state. The nickel-60 nucleus then emits two gamma-ray photons, of energies 1.17 MeV and 1.33 MeV, as it reaches its ground state.

What is the decrease in the mass of the nickel-60 nucleus as it emits the two photons? (1 u = 931.5 MeV c⁻²)

A household smoke detector contains a small sample of americium-241. During cooking, the detector warms from 20 °C to 60 °C. What happens to the half-life of the americium-241?

Iodine-123 and iodine-131 are both used in thyroid medicine. The thyroid absorbs both of them in the same way. What is the reason for this?

A Geiger counter is held over a granite kitchen worktop. The counts recorded in three successive one-minute intervals are 112, 98 and 105. What is the best explanation for the variation?

A food-irradiation plant uses a cobalt-60 source. Which change would increase the activity of the source?

Which statement about the strong nuclear force is correct?

For a typical person living in a region of granite bedrock, which is most likely to be the largest single source of their annual background radiation dose?

Two protons are held at a centre-to-centre separation of first 1.0 fm and then 4.0 fm. Which row gives the direction of the net force between them at each separation?

Separation 1.0 fm / Separation 4.0 fm

A domestic smoke detector contains a small source of americium-241, an alpha emitter. The alpha particles ionize the air between two plates so that a small current flows. Smoke entering the chamber reduces this current and triggers the alarm.
Which property of alpha radiation makes it suitable for this use?

A factory makes thin cardboard. A radioactive source sits on one side of the moving sheet and a detector on the other. The count rate is used to keep the thickness constant over many years of production.
Which source is most suitable?

In positron emission tomography (PET), carbon-11 atoms can replace carbon-12 atoms in a glucose molecule. The body then processes the molecule normally.
This is possible because carbon-11 and carbon-12 have the same

Bananas contain a small amount of potassium-40. Most potassium-40 nuclei decay by beta-minus (β⁻) decay. Which particles are emitted from the nucleus in this decay?

Which observation first suggested that an undetected particle is emitted in beta decay?

Nuclear masses are often quoted in units based on the electronvolt. Which of these is a unit of mass?

A hospital prepares a dose of technetium-99m (half-life 6.0 h) with an activity of 800 MBq at 08:00. What is the activity of the dose at 02:00 the following morning?

A uranium-235 nucleus undergoes fission into two medium-mass nuclei and some neutrons, and energy is released. Which statement explains the release of energy?

Two sealed sources P and Q contain the same radioactive isotope. Source P contains twice the mass of the isotope that source Q contains. Which comparison of P with Q is correct?

A household smoke detector contains a small source of americium-241, which emits alpha particles across a short air gap between two metal plates. Why is an alpha emitter chosen for this device?

Single-use surgical gloves are sealed in thick plastic packs and packed in cardboard boxes. The gloves are then sterilized by exposing the closed boxes to radiation. Which radiation is most suitable, and why?

Which observation about beta-minus decay led physicists to propose that a third, almost undetectable particle (the antineutrino) is also emitted?

Carbon-11 (¹¹₆C), used in medical imaging, decays by β⁺ emission.

Which equation represents this decay?

A factory makes paper in a continuous sheet about 0.1 mm thick. A radioactive source is placed on one side of the sheet and a detector on the other; the count rate is used to control the thickness of the sheet.

Which row gives the most suitable radiation and the reason for choosing it?

A radioactive tracer is injected into a patient so that the flow of blood through an organ can be followed by a detector outside the body. The measurement takes about one hour.

Which row describes the most suitable tracer?

The graph shows the variation of binding energy per nucleon with nucleon number.

Which statement is correct?

A nucleus ^A_ZX emits one alpha particle and then two β⁻ particles.

Which row gives the nucleon number and the proton number of the final nucleus?

A nucleus ^A_ZX has mass M. The mass of a proton is m_p and the mass of a neutron is m_n.

What is the binding energy per nucleon of this nucleus? (c is the speed of light.)

Two radioactive sources X and Y have the same activity at time t = 0. The half-life of X is 5.0 days and the half-life of Y is 10.0 days.

What is (activity of Y)/(activity of X) at t = 20 days?

Sample P is a pure radioactive isotope. Sample Q is the same isotope but has twice the mass of P.

Which row gives the ratios for Q compared with P?

The mass of a helium-4 nucleus is about 0.75 % less than the total mass of two free protons and two free neutrons.

Which statement explains this?

Fluorine-18, ¹⁸₉F, is used in medical imaging. It decays by β⁺ emission.

The chart shows neutron number N against proton number Z. Each arrow starts at fluorine-18. Which arrow represents the β⁺ decay of fluorine-18?

A sealed capsule contains 2.0 g of pure polonium-210, which decays by alpha emission to stable lead-206 with a half-life of 138 days. The alpha particles are stopped inside the capsule.

Which row gives the mass of polonium-210 in the capsule and the total mass of its contents 276 days later?

Copper-64, ⁶⁴₂₉Cu, is used in medical imaging. A nucleus of copper-64 can decay either to zinc-64, ⁶⁴₃₀Zn, or to nickel-64, ⁶⁴₂₈Ni.

Which row identifies the decay that produces each nucleus?

Uranium-238, ²³⁸₉₂U, decays through a series of alpha and β⁻ decays to stable lead-206, ²⁰⁶₈₂Pb. No other types of decay occur in the series.

How many antineutrinos are emitted in the series, for each uranium-238 nucleus that becomes lead-206?

A small gamma source emits one photon in each decay, equally in all directions. A detector with a window of area a faces the source at a distance d, where a is much smaller than d². Every photon that reaches the window is counted. Absorption in the air and the background are negligible.

The count rate is R. What is the activity of the source?

The binding energy of a carbon-12 nucleus is 92.2 MeV. The binding energy of a carbon-13 nucleus is 97.1 MeV.

What is the minimum energy needed to remove one neutron from a carbon-13 nucleus?

The binding energy per nucleon of stable nuclei is between about 7.5 MeV and 8.8 MeV for all but the lightest nuclei.

Which graph shows how the total binding energy E of a stable nucleus varies with its nucleon number A?

A technetium-99m nucleus has a half-life of 6.0 h. A single nucleus has already remained undecayed for 12 h. What is the probability that it decays during the next 6.0 h?

A nuclide of iron has proton number 26 and nucleon number 56. Which of the following nuclides is an isotope of this iron nuclide?

A space probe is powered by plutonium-238, which has a half-life of 88 years. Its thermal power is proportional to the activity of the plutonium. What fraction of the original thermal power remains after 264 years?

Carbon-14 in a sample of ancient wood decays by β⁻ emission to form nitrogen-14. Which row describes the change from the carbon-14 nucleus to the nitrogen-14 nucleus?

A hospital technician measures a sample containing a radioactive tracer. The measured count rate is 3.0 counts s⁻¹, and this includes a background count rate of 0.50 counts s⁻¹. What measured count rate is expected after two half-lives of the tracer?

Stable heavy nuclei, such as lead-208, contain significantly more neutrons than protons. What is the best explanation?

Long-haul airline pilots receive a larger annual dose of background radiation than people who work at ground level. Which statement explains this?

A student encloses a Geiger–Müller tube in a thick lead box, with no source present. The count rate falls but does not become zero. What is the most likely reason?

Radon-222 (²²²₈₆Rn), a major source of background radiation, decays by α emission. The product then decays by a second α emission, followed by a β⁻ emission. What is the nuclide produced after these three decays?

Nucleus X has a binding energy per nucleon of 8.8 MeV. Nucleus Y has a binding energy per nucleon of 7.6 MeV.
Which statement must be correct?

The mass defect of a helium-4 nucleus is 0.0304 u. Take 1 u = 931.5 MeV c⁻².
What is the binding energy per nucleon of helium-4?

A hospital needs a radioactive tracer to study blood flow through a patient's lungs. The radiation will be detected by a camera outside the body. The isotopes available are:
P: alpha emitter, half-life 6 hours
Q: gamma emitter, half-life 6 hours
R: gamma emitter, half-life 30 years
S: beta emitter, half-life 8 days
Which isotope is most suitable?

Radioisotope power sources on deep-space probes use heat from alpha decay. Plutonium-238 (half-life 88 years) is used rather than plutonium-239 (half-life 24 000 years). Both release a similar energy per decay.
Why is plutonium-238 preferred?

Radium-226 decays by alpha emission to radon-222, and energy is released.
Which statement is correct?

The mass defect of an oxygen-16 nucleus is 0.137 u. Take 1 u = 1.66 × 10⁻²⁷ kg and c = 3.00 × 10⁸ m s⁻¹.
What is the binding energy of the nucleus?

Fluorine-18, ¹⁸₉F, is used in PET medical scanners. It decays by beta-plus (β⁺) decay. What is the daughter nucleus?

Nuclear fusion in the Sun converts about 4.0×10⁹ kg of mass into energy every second. What is the approximate power output of the Sun?
(c = 3.0×10⁸ m s⁻¹)

Which statement about a stable nucleus is correct?

Self-luminous exit signs contain tritium, which decays by β⁻ decay to helium-3. The energy released in each decay is 18.6 keV. Which statement about the emitted electrons is correct?

In the thorium decay series, lead-212 (²¹²₈₂Pb) undergoes two successive β⁻ decays. What is the nuclide produced after the second decay?

A mobile phone battery stores an extra 40 kJ of chemical energy when it is fully charged. Which statement about the mass of the battery is correct?
(c = 3.0×10⁸ m s⁻¹)

A deep-space probe is powered by plutonium-238, which has a half-life of 88 years. Assume that the electrical power output is proportional to the activity of the plutonium. The probe can operate only while the output is at least 25% of its initial value. What is the maximum operating time?

A detector placed near a radioactive source records 260 counts per minute. The background count rate is 20 counts per minute. Two hours later the detector records 80 counts per minute. What is the half-life of the source?

Which statement about the nuclear binding energy of a stable nucleus is correct?

In a proposed fusion reactor, two deuterium nuclei (\(^2_1\)H) fuse to form a helium-4 nucleus. The binding energy per nucleon is 1.1 MeV for \(^2_1\)H and 7.1 MeV for \(^4_2\)He. What is the energy released in one fusion event?

A nucleus X undergoes one alpha decay. The daughter then undergoes two successive beta-minus decays. Which describes the final nucleus compared with X?

Fluorine-18 (proton number 9) is used as a tracer in positron emission tomography (PET) scans. It decays by β⁺ emission. Which statement about this decay is correct?

Technetium-99m, used in medical imaging, is an excited state of technetium-99. It decays to the ground state of technetium-99 by emitting a gamma photon. Which statement about this change is correct?

During maintenance work on a space station, an astronaut accidentally inhales dust containing an alpha-emitting nuclide. Why is the source more hazardous inside the body than the same source held a short distance outside it?

Carbon-11 (6 protons, 5 neutrons) is produced in a hospital cyclotron. The stable isotopes of carbon are carbon-12 and carbon-13. By which process is carbon-11 most likely to decay?

A detector placed near a radioactive source records a count rate C. With the source removed, the background count rate is B.

What count rate does the detector record, with the source in the same place, after three half-lives of the source?

Radioactive decay is described as a random and spontaneous process.

Which statement describes what is meant by spontaneous?

When a rock solidified it contained atoms of a radioactive isotope X but none of Y, the stable nuclide into which X decays directly. The age of the rock is now three half-lives of X.

What is now (number of Y atoms)/(number of X atoms)?

Iodine-131 has a half-life of 8.0 days. One particular nucleus in a sample of iodine-131 has not decayed after 16 days.

What is the probability that this nucleus decays during the next 8.0 days?

An alpha particle and a β⁻ particle have the same initial kinetic energy. Each is brought to rest in air. The average energy needed to produce one ion pair in air is the same for both particles.

Which row compares the alpha particle with the β⁻ particle?

A radioactive sample is placed near a detector. The graph shows how the count rate C recorded by the detector varies with time t. The values of C include a background count rate of 40 min⁻¹.

What is the half-life of the radioactive sample?

A detector in a research lab contains exactly 4 undecayed nuclei of the same radioactive isotope. What is the probability that exactly 2 nuclei are still undecayed after one half-life?

A radioactive sample gives an initial measured count rate of 165 counts min⁻¹. The background count rate is 5 counts min⁻¹. After how many half-lives will the measured count rate be twice the background count rate?

Polonium-210 decays by alpha emission to lead-206. The binding energies per nucleon are:
polonium-210: 7.834 MeV
lead-206: 7.875 MeV
helium-4: 7.074 MeV
What is the energy released in one decay?

A nucleus at rest undergoes β⁻ decay inside a particle detector. The tracks of the emitted electron and the recoiling daughter nucleus are both recorded. Which observation provides evidence that a third, undetected particle is also emitted?

The binding energy per nucleon is about 8.8 MeV for \(^{56}\)Fe and about 7.6 MeV for \(^{238}\)U. Which statement is correct?

Narrow beams of alpha particles, beta-minus particles and gamma radiation enter the same region of uniform magnetic field, all moving at right angles to the field. Each alpha particle has a kinetic energy of about 5 MeV and each beta particle about 1 MeV. Which describes the paths in the field?

Neptunium-237 (Z = 93) decays through a chain of alpha and beta-minus decays to the stable nuclide bismuth-209 (Z = 83). How many alpha decays and beta-minus decays occur in the chain?

In a hospital radiopharmacy, the activity A of a vial of a radioactive tracer is measured in a dose calibrator every 2.0 h. The label naming the isotope has been lost. The manufacturer states that each reading of the calibrator has an uncertainty of ±3 %. The readings are shown in the graph with their error bars.

The table gives the half-lives of five isotopes used in hospitals, taken from a nuclear data library.

A class models radioactive decay with small cubes, each with one face painted red. The cubes are shaken and thrown; every cube that lands red face up is said to have "decayed" and is removed, and the rest are counted and thrown again. Five groups each start with 500 cubes. The table gives, after selected throws, the mean number of cubes remaining and its uncertainty (half the range of the five groups' results). The graph shows these data, except for throw 4.

For this model the expected half-life is 3.8 throws.

Two students test the hypothesis that the background count rate is higher in room A, which has granite walls, than in room B, which has brick walls. A GM tube and counter, with no source nearby, are used to record ten separate one-minute counts in each room.

For room B the result is (22.5 ± 6.0) counts per minute. The uncertainty in a single count N is ±√N.

Students launch a weather balloon carrying a Geiger–Müller (GM) counter and a data logger. The logger records the number of counts in each one-minute interval and the altitude h of the balloon. No radioactive source is carried. The table and the graph show selected readings; the uncertainty in a number of counts N is ±√N.

After a leak from a nuclear power station, iodine-131 was deposited on the grass of a dairy farm. A food laboratory measured the activity A of iodine-131 per litre of the farm's milk every two days. Each measurement has an uncertainty of ±5 %. Time t is measured from the first sample.

The graph shows the data, with error bars. Milk may be sold only when A is less than 500 Bq L⁻¹.

A student investigates the decay of barium-137m. A solution containing barium-137m is washed out of a sealed caesium-137 generator and a few drops are placed in a dish just below the window of a Geiger–Müller (GM) tube connected to a data-logger. Starting at time t = 0, the logger records the number of counts N in a 10.0 s interval that begins every 60 s. Before preparing the solution, the student recorded 111 counts in 300 s with no source present.

The corrected count rate C is the count rate due to the barium-137m alone. The uncertainty in a number of counts N is ±√N. The graph shows C against t, with error bars, for all but two of the readings.

A student is asked to find which types of radiation are emitted by an unlabelled sealed source. The source is placed 2.0 cm from the window of a GM tube, and the number of counts in 100 s is recorded with different absorbers between the source and the tube. The source–tube distance is not changed.

The uncertainty in a number of counts N is ±√N.

A student uses an online database of atomic masses M to investigate how the binding energy per nucleon varies with nucleon number A. For each nuclide the mass defect is calculated from

Δm = Zm_H + (A − Z)m_n − M

where m_H = 1.007825 u is the mass of a hydrogen-1 atom and m_n = 1.008665 u is the mass of a neutron. (1 u = 931.5 MeV c⁻²) The graph shows the results for ten of the nuclides.

A factory monitors the thickness of aluminium foil with a gauge. A krypton-85 beta source is placed on one side of the foil and a detector on the other. The gauge is calibrated by recording the counts N in 10.0 s for standard foils whose thicknesses are known precisely. The background is negligible. The uncertainty in a number of counts N is ±√N.

The graph shows the count rate R against thickness, with error bars.