Radioactive Decay

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Isotopes

Isotopes are nuclei with the same number of protons but different numbers of neutrons.
An isotope of an element has a fixed proton number (Z) but a different nucleon number (A).
Some isotopes are unstable due to an imbalance of neutrons and protons, causing them to decay and emit radiation.
Unstable isotopes can decay over timescales ranging from a few nanoseconds to 100,000 years.
Isotopic data refers to the relative amounts of different isotopes of an element in a substance.
The relative atomic mass of an element is calculated using the masses and abundances of its naturally occurring isotopes.
The percentage abundance of isotopes in a sample can be measured using a mass spectrometer.

Isotopes of hydrogen

Radioactive Decay

Radioactive decay is the spontaneous disintegration of a nucleus to form a more stable nucleus, emitting an α, β or gamma particle.
Radioactive decay is a random process: the exact time of decay of a nucleus cannot be predicted.
Each nucleus has a constant probability of decaying in a given time.
Radioactive decay is spontaneous: it cannot be influenced by environmental factors such as temperature, pressure or chemical conditions.
The random nature of decay is demonstrated by fluctuations in the count rate of a Geiger-Muller (GM) tube.
With large numbers of nuclei, the behaviour of the group can be statistically predicted.

Alpha decay

Background Radiation

Background radiation is the ionising radiation present in the environment.
Natural sources include radon gas from rocks and buildings, cosmic rays from space, carbon-14 in biological material, and radioactive material in food and drink.
In the UK, radon gas is the largest proportion of background radiation.
Artificial sources include nuclear medicine, nuclear waste, nuclear fallout and nuclear accidents.
Background radiation must be accounted for by measuring the count rate with no source present and subtracting it from readings with the source present.
The corrected count rate is the count rate of a source minus the background count rate.
Accuracy of count rate measurements can be improved by repeating readings and taking averages, and by taking readings over a long period of time.

Alpha, Beta & Gamma Particles

An α (α) particle is a high-energy helium nucleus containing 2 protons and 2 neutrons; it has mass 4u and charge +2e.
A β-minus (β⁻) particle is a high-energy electron with mass 0.0005u and charge −1e; it is emitted when a neutron turns into a proton.
A β-plus (β⁺) particle is a high-energy positron with mass 0.0005u and charge +1e; it is emitted when a proton turns into a neutron.
Gamma (γ) radiation is high-energy electromagnetic radiation emitted by nuclei losing excess energy; it has no charge and no mass.
α particles are highly ionising and have low penetrating power; they can be stopped by a sheet of paper.
β particles are moderately ionising and penetrating; they can be stopped by a few millimetres of aluminium foil.
Gamma radiation is weakly ionising and highly penetrating; its intensity can be reduced by several centimetres of lead or metres of concrete.
In electric and magnetic fields, α and β particles are deflected, while gamma radiation is not.

Penetrating power of alpha, beta and gamma radiation

Radioactive Decay Equations

α decay: nucleon number decreases by 4, proton number decreases by 2. General equation: ᴬ_Z X → ᴬ⁻⁴_Z−2 Y + ⁴₂α.
β-minus decay: nucleon number stays the same, proton number increases by 1. General equation: ᴬ_Z X → ᴬ_Z+1 Y + ⁰₋₁β + ν̄_e.
β-plus decay: nucleon number stays the same, proton number decreases by 1. General equation: ᴬ_Z X → ᴬ_Z−1 Y + ⁰₊₁β + ν_e.
Electron capture: a proton combines with an orbiting electron to form a neutron and a neutrino; proton number decreases by 1, nucleon number stays the same.
Gamma emission: proton number and nucleon number remain unchanged; it usually follows α or β decay.
An electron neutrino (ν_e) is produced during β⁺ decay; an electron antineutrino (ν̄_e) is produced during β⁻ decay.
Decay modes are determined by the type of instability: too many neutrons → β⁻; too many protons → β⁺ or electron capture; too many nucleons → α; too much energy → γ.

Beta decay

Activity & Half-Life

Activity is the number of nuclei that decay per unit time, measured in becquerels (Bq); 1 Bq = 1 decay per second.
Half-life is the time taken for half the undecayed nuclei to decay, or for the activity to fall to half its original value.
Different isotopes have different half-lives, ranging from fractions of a second to billions of years.
The proportion of an isotope remaining after n half-lives is (1/2)ⁿ.
After 1 half-life, 50% remains; after 2, 25%; after 3, 12.5%; after 4, 6.25%.
To find half-life from a graph, determine the time for the activity to halve from its initial value.
The half-life is constant for a particular isotope.

A half-life graph showing activity falling from A0 to A0/2 to A0/4

Applications of Radioactivity

When selecting a radioactive isotope for use, consider its penetrating power and half-life.
Carbon dating: carbon-14 has a half-life of about 5730 years; it is used to date samples between 500 and 60,000 years old.
Uranium-lead dating: uranium-238 decays to lead-206 with a half-life of 4.5 billion years; used to determine the age of rocks and the Earth.
Detecting leaks in underground pipes uses a gamma emitter (e.g. sodium-24) because gamma radiation can penetrate several metres of ground.
Controlling thickness of materials uses β radiation (e.g. for aluminium foil) because α would be absorbed and gamma would pass through undetected.
Smoke detectors contain americium-241, an α emitter; α particles ionise air, allowing a small current that is disrupted by smoke.
Sterilising equipment uses gamma radiation (e.g. cobalt-60) because it can penetrate sealed plastic bags.

Mass Defect & Nuclear Binding Energy

Mass defect is the difference between the mass of a nucleus and the sum of the masses of its individual nucleons.
Binding energy is the energy required to separate a nucleus into its constituent protons and neutrons.
Mass and energy are related by Einstein's equation: ΔE = Δmc².
The binding energy of a nucleus can be calculated using the mass defect: E = Δm c².
Binding energy per nucleon is the binding energy of a nucleus divided by the number of nucleons in the nucleus.
A higher binding energy per nucleon indicates a more stable nucleus.
The mass defect for helium-4 is about 5.04 × 10⁻²⁹ kg, giving a binding energy of about 28 MeV.

Binding Energy per Nucleon Curve

The binding energy per nucleon curve plots binding energy per nucleon against nucleon number.
The curve rises steeply for light nuclei, peaks around iron-56 (nucleon number ~56), and gradually decreases for heavier nuclei.
The peak represents the most stable nuclei, with a binding energy per nucleon of about 8.8 MeV.
Nuclei with lower binding energy per nucleon are less stable and can undergo fusion (light nuclei) or fission (heavy nuclei) to become more stable.
The graph helps explain why energy is released in nuclear fusion and fission.

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Practice questions

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1.Which of the following is the correct definition of isotopes?
Easy
- ANuclei that have the same number of protons but different numbers of neutrons
- BNuclei that have the same number of neutrons but different numbers of protons
- CNuclei that have the same number of protons and the same number of neutrons
- DNuclei that have the same mass number but different proton numbers
2.Which of the following statements about radioactive decay is correct?
Medium
- AIt is spontaneous and random.
- BIt is spontaneous but not random.
- CIt is random but can be influenced by temperature.
- DIt can be affected by chemical conditions.
3.Which of the following are natural sources of background radiation? (select all that apply)
Medium
- ARadon gas from rocks and buildings
- BCosmic rays from space
- CNuclear fallout from nuclear weapons
- DCarbon-14 in biological material
- ENuclear medicine
4.An α particle is a high-energy helium nucleus containing 2 protons and 2 neutrons.
Easy
True or false?
5.Match each type of radiation with its correct description.
Medium
- α particle
- β-minus particle
- Gamma radiation
- High-energy electron
- High-energy electromagnetic radiation
- High-energy helium nucleus
6.Which of the following correctly describes the charge and mass of an electron neutrino?
Easy
- ACharge zero, mass negligible
- BCharge +1e, mass 0.0005 u
- CCharge -1e, mass 0.0005 u
- DCharge zero, mass 1 u
7.A radioactive sample has a half-life of 10 days. What is the approximate percentage of the sample remaining after 25 days?
Medium
- A20%
- B19%
- C16%
- D15%
8.Which of the following is the correct definition of half-life?
Easy
- AThe time taken for half the undecayed nuclei to decay
- BThe time taken for all the nuclei to decay
- CThe time taken for the activity to double
- DThe time taken for the number of nuclei to halve in size

More questions

9.A neutral atom of uranium-234 has the symbol 92 234 U. How many protons, neutrons and electrons does it contain?
Medium
- A92 protons, 92 neutrons, 92 electrons
- B92 protons, 142 neutrons, 92 electrons
- C142 protons, 92 neutrons, 142 electrons
- D234 protons, 142 neutrons, 92 electrons
10.A sample of californium-239 has an activity of 4000 Bq. The half-life of californium-239 is 1 minute. What will the activity be after 4 minutes?
Medium
- A4000 Bq
- B1000 Bq
- C500 Bq
- D250 Bq
11.The average binding energy per nucleon of a neon-20 nucleus is 8.0 MeV. What is the total energy required to separate all the nucleons of one neon-20 nucleus?
Medium
- A0 MeV
- B8 MeV
- C160 MeV
- D800 MeV
12.The mass defect for a helium-4 nucleus is 5.04 × 10^–29 kg. What is the binding energy of helium-4 closest to? (c = 3.00 × 10⁸ m/s)
Medium
- A0.02 MeV
- B28 MeV
- C190 MeV
- D1225 MeV
13.The binding energy per nucleon of oxygen-16 is 7.98 MeV. Approximately how much energy is needed to completely separate the nucleons of this atom?
Medium
- A33.2 MeV
- B63.9 MeV
- C88.5 MeV
- D127.7 MeV
14.The rest mass of a boron-11 nucleus is m_B, the rest mass of a proton is m_P and the rest mass of a neutron is m_N. Which expression gives the binding energy of boron-11? (Boron-11 has 5 protons and 6 neutrons.)
Medium
- A(5m_P + 6m_N – m_B)c²
- B(5m_P + 6m_N + m_B)c²
- C(5m_P + 11m_N – m_B)c²
- D(6m_P + 5m_N – m_B)c²
15.Two identical nuclei, each of mass m, fuse to form a single heavier nucleus of mass M with no other products. Which statement is correct?
Hard
- Am = M
- B2m = M
- C2m is greater than M
- D2m is less than M
16.Which statement is the definition of binding energy per nucleon?
Medium
- AThe difference between an atom's mass and the sum of the masses of its nucleons
- BThe binding energy of a nucleus divided by the number of nucleons in the nucleus
- CThe energy required to break a nucleus into its constituent protons and neutrons
- DThe amount of kinetic energy required for fusion to occur
17.A radioactive source is known to emit β radiation. A Geiger-Muller tube is used to measure the count rate at increasing distances from the source. Which statement correctly describes the variation in count rate over these distances?
Medium
- AThe count rate remains constant because β radiation has infinite range
- BThe count rate decreases to zero immediately because β is absorbed by a few millimetres of air
- CThe count rate decreases gradually, falling to the background level after a range of around 20 cm to 3 m
- DThe count rate increases with distance because β is deflected by air molecules
18.A source is known to be radioactive but the type of radiation is unknown. A Geiger-Muller tube is placed close to the source and different materials are placed between the two. The background count rate is 15 counts per minute. The count rates recorded are: nothing 1064, paper 528, aluminium 524, thick lead 17. What types of radiation are being emitted?
Hard
- Aα, β and gamma
- Bα only
- Cβ and gamma
- Dα and gamma
19.Which of the following statements about the properties of α, β and gamma radiation are correct? (select all that apply)
Medium
- Aα particles are the most ionising type of radiation
- BGamma radiation is deflected by an electric field because it has no charge
- Cβ particles are deflected towards the positive plate in an electric field
- Dα particles have the greatest penetrating power
- EGamma radiation follows an inverse square law and has an infinite range in air
20.Which of the following are artificial sources of background radiation? (select all that apply)
Medium
- ARadon gas from rocks and buildings
- BNuclear medicine procedures such as X-rays and CT scans
- CCosmic rays from the Sun
- DNuclear fallout from nuclear weapons
- ECarbon-14 in biological material
21.Radioactive decay is a spontaneous process, meaning it cannot be influenced by environmental factors such as temperature, pressure or chemical conditions.
Easy
True or false?
22.In β-plus decay, a proton turns into a neutron, so the proton number decreases by 1 and the nucleon number stays the same.
Easy
True or false?
23.Match each type of radioactive decay with the correct change in the nucleus.
Medium
- α decay
- β-minus decay
- β-plus decay
- Gamma emission
- Proton number decreases by 2, nucleon number decreases by 4
- Proton number increases by 1, nucleon number stays the same
- Proton number decreases by 1, nucleon number stays the same
- Proton number and nucleon number both stay the same
24.Place the following types of radiation in order of increasing penetrating power, from least penetrating to most penetrating.
Medium
- α particles
- β particles
- Gamma radiation
25.Starting from a sample of pure uranium-238, arrange the following stages of its decay chain in the correct order.
Medium
- Uranium-238 decays by α emission to thorium-234
- Thorium-234 decays by β-minus emission to protactinium-234
- Protactinium-234 undergoes further decays ending with stable lead-206
26.An isotope of americium-241 (Z = 95, A = 241) undergoes α decay. Which row correctly gives the proton number and neutron number of the daughter nucleus?
Medium
- AProton number 93, neutron number 144
- BProton number 93, neutron number 146
- CProton number 97, neutron number 144
- DProton number 93, neutron number 142
27.A student measures the background count rate using a Geiger-Müller tube with no source present. The tube records 18 counts in 2 minutes. What is the background count rate in counts per second?
Medium
- A0.15 counts per second
- B0.30 counts per second
- C9.0 counts per second
- D0.075 counts per second
28.A detector is placed near a radioactive source. The count rate is measured with different absorbers placed between the source and the detector. The results are: no absorber 800 counts/min, paper 780 counts/min, 3 mm aluminium 400 counts/min, 10 mm lead 390 counts/min. The background count rate is 20 counts/min. Which types of radiation are emitted by the source?
Medium
- Aα, β and gamma
- Bβ and gamma only
- Cα and gamma only
- DGamma only
29.Which of the following would improve the accuracy of a measurement of the count rate from a radioactive source? (select all that apply)
Medium
- ARepeating the measurement several times and taking an average
- BTaking the reading over a longer period of time
- CMoving the source closer to the detector
- DSubtracting the background count rate from the measured count rate
- EUsing a thicker absorber between source and detector
30.In an experiment to determine the half-life of a radioactive isotope, a student measures the count rate every minute. Which of the following is the most important reason for measuring the background count rate before starting?
Medium
- ATo check that the Geiger-Müller tube is working
- BTo allow the background count rate to be subtracted from each reading
- CTo determine the type of radiation emitted by the source
- DTo calculate the activity of the source in becquerels
31.A radioactive source has a half-life of 8 days. A student measures its activity as 640 Bq. After 24 days, what is the activity of the source?
Hard
- A80 Bq
- B160 Bq
- C213 Bq
- D320 Bq
32.A radioactive isotope is used as a tracer in a medical scan. It emits gamma radiation and has a half-life of 6 hours. A patient is injected with a sample of activity 800 MBq. What will be the activity of the sample after 24 hours?
Medium
- A50 MBq
- B100 MBq
- C200 MBq
- D400 MBq
33.A sample of rock initially contains only uranium-238. Uranium-238 decays through a chain to stable lead-206 with a half-life of 4.5 billion years. In a rock sample, the ratio of lead-206 atoms to uranium-238 atoms is found to be 3:1. What is the approximate age of the rock?
Hard
- A4.5 billion years
- B9.0 billion years
- C13.5 billion years
- D18.0 billion years
34.A radioactive source emits β particles and is used to control the thickness of aluminium foil in a factory. Which of the following is the main reason why β radiation is chosen rather than α or gamma?
Medium
- Aα particles would be completely absorbed by the foil, and gamma rays would pass through with little absorption.
- Bβ particles are the most ionising, so they give the largest signal.
- Cβ particles have a very long half-life, so the source lasts longer.
- Dβ particles are not deflected by electric fields, so the measurement is simpler.
35.Which of the following best describes the term 'isotopic data'?
Easy
- AThe relative amounts of different isotopes of an element present within a substance
- BThe total number of nucleons in a nucleus
- CThe energy released when a nucleus decays
- DThe time taken for half of a radioactive sample to decay
36.A sample of oxygen contains three isotopes: oxygen-16 (abundance 99.76%), oxygen-17 (0.04%) and oxygen-18 (0.20%). What is the relative atomic mass of this sample to two decimal places?
Easy
- A16.00
- B16.04
- C17.00
- D16.20
37.Which of the following is the definition of background radiation?
Easy
- AThe ionising radiation present in the environment
- BThe radiation emitted by a radioactive source in a laboratory
- CThe radiation that remains after all shielding is removed
- DThe radiation produced only by nuclear power stations
38.In the UK, which source contributes the largest proportion of background radiation?
Easy
- ARadon gas from rocks and buildings
- BCosmic rays from space
- CNuclear waste and fallout
- DCarbon-14 in biological material
39.Which of the following is a natural source of background radiation?
Easy
- ACosmic rays from space
- BX-rays used in medical imaging
- CFallout from nuclear weapons testing
- DNuclear waste from power stations
40.Which of the following statements about α particles are correct? (select all that apply)
Medium
- AAn α particle is a high-energy helium nucleus containing 2 protons and 2 neutrons.
- BAn α particle has a charge of +2e.
- CAn α particle has a mass of 0.0005u.
- DAn α particle is the most ionising type of radiation.
- EAn α particle can be stopped by a single sheet of paper.
41.The half-life of carbon-14 is 5700 years. What percentage of the original carbon-14 remains after 11 400 years?
Medium
42.What is the name of the particle emitted during β-plus decay that has no charge and negligible mass?
Easy
43.Complete the sentence about the properties of α, β and gamma radiation.
Medium
The greater the ionising ability of a type of radiation, the ____ its penetrating power.
44.A pure sample of a radioactive nuclide decays to a stable daughter. What fraction of the original sample remains undecayed after 5 half-lives? Give your answer as a decimal.
Medium
45.A radioactive sample has a half-life of 3 years. After 15 years, what is the ratio of decayed nuclei to original nuclei? Give your answer as a decimal.
Medium
46.Complete the sentences about radioactive decay.
Easy
Radioactive decay is a ____ process because it cannot be influenced by environmental factors, and it is a ____ process because the exact time of decay of a nucleus cannot be predicted.
47.Complete the nuclear equation for β-minus decay.
Medium
In β-minus decay, a neutron turns into a proton and emits a ____ particle and an ____.
48.What is the name of the process in which an orbiting electron is taken in by the nucleus and combined with a proton to form a neutron and a neutrino?
Easy
49.A Geiger counter records 24 counts in 1 minute when no radioactive source is present. Calculate the background count rate in counts per second.
Easy
50.A Geiger counter records 285 counts in 1 minute when a radioactive source is present and 24 counts in 1 minute when no source is present. Calculate the corrected count rate of the source in counts per second.
Medium
51.Complete the sentence about the random nature of radioactive decay using the words provided.
Medium
The fluctuations in the count rate of a radioactive source measured with a Geiger-Muller tube provide evidence for the ____ of radioactive decay, meaning that the exact time of decay of a nucleus cannot be ____.
52.Complete the sentences about the properties of α, β and gamma radiation.
Medium
α radiation is the most ____ type of radiation and has the ____ penetrating power. Gamma radiation is the least ____ type of radiation and has the ____ penetrating power.
53.Explain why the count rate of a radioactive source measured with a Geiger-Müller tube fluctuates even when the source is constant.
Hard
54.Explain why the count rate of a radioactive source measured with a Geiger-Muller tube fluctuates even when the source is constant.
Hard
55.Explain why β radiation is used, rather than α or gamma radiation, to monitor and control the thickness of aluminium foil in a factory.
Hard
56.A student is investigating the penetrating power of α, β and gamma radiation using a Geiger-Müller tube and different absorbers. Describe how the student should carry out the experiment and how the results would show the relative penetrating powers of the three types of radiation.
Hard
57.The half-life of carbon-14 is 5700 years. What percentage of the original carbon-14 remains after 11 400 years?
Medium
- A25 %
- B31 %
- C28 %
- D22 %
58.A pure sample of a radioactive nuclide decays to a stable daughter. What fraction of the original sample remains undecayed after 5 half-lives? Give your answer as a decimal.
Medium
- A1.0313
- B-0.9688
- C0.03125
- D2.0313
59.A radioactive sample has a half-life of 3 years. After 15 years, what is the ratio of decayed nuclei to original nuclei? Give your answer as a decimal.
Medium
- A1.9688
- B-0.0313
- C2.9688
- D0.96875
60.A Geiger counter records 24 counts in 1 minute when no radioactive source is present. Calculate the background count rate in counts per second.
Easy
- A-0.6 counts per second
- B0.4 counts per second
- C1.4 counts per second
- D2.4 counts per second
61.A Geiger counter records 285 counts in 1 minute when a radioactive source is present and 24 counts in 1 minute when no source is present. Calculate the corrected count rate of the source in counts per second.
Medium
- A6.35 counts per second
- B3.35 counts per second
- C4.35 counts per second
- D5.35 counts per second

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