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Topic 5.2 · Unit 5

Radioactivity

Background radiation, the three types of nuclear emission, how unstable nuclei decay, half-life and its uses, and how to work safely with radioactive sources.

In this topic

  1. 5.2.1Detection of radioactivity
  2. 5.2.2The three types of nuclear emission
  3. 5.2.3Radioactive decay
  4. 5.2.4Half-life
  5. 5.2.5Safety precautions

Key points

5.2.1 Detection of radioactivity

  • Ionising radiation is radiation that can remove electrons from atoms, turning them into ions.
  • Background radiation is the ionising radiation that is around us all the time. It is always there, even when no radioactive source is nearby.
  • The main sources of background radiation are:
    • radon gas in the air
    • rocks and buildings
    • food and drink
    • cosmic rays (radiation from space).
  • Ionising radiation is measured with a detector connected to a counter. Example: a Geiger–Müller tube connected to a counter.
  • The count rate is the number of counts in each second or each minute. Its unit is counts/s or counts/minute.
  • To find the count rate from a source alone, measure the background count rate with the source removed. Then subtract it from the measured count rate. The answer is the corrected count rate. Extended

5.2.2 The three types of nuclear emission

  • Radiation is emitted from a nucleus spontaneously (nothing causes it and nothing can change it) and randomly (in a random direction, at a random time).
  • An α-particle (alpha particle) is a helium nucleus: 2 protons and 2 neutrons. Its relative charge is +2.
  • A β-particle (beta particle) is a fast-moving electron emitted from the nucleus. Its relative charge is −1.
  • γ-radiation (gamma radiation) is an electromagnetic wave. It has no charge and no mass.
  • Ionising effect: α is the most strongly ionising, β is in the middle, γ is the least ionising.
  • Penetrating ability: α is the least penetrating, β is in the middle, γ is the most penetrating.
Emission What it is Relative charge Ionising effect Stopped by
α helium nucleus (2 protons + 2 neutrons) +2 strong a sheet of paper, or a few cm of air
β fast electron from the nucleus −1 medium a few mm of aluminium
γ electromagnetic wave 0 weak reduced by thick lead or concrete
  • In an electric field, α-particles are deflected towards the negative plate. β-particles are deflected towards the positive plate. γ-radiation is not deflected. Extended
  • In a magnetic field, α-particles and β-particles are deflected in opposite directions, because they have opposite charges. γ-radiation is not deflected. Extended
  • In both kinds of field, β-particles are deflected more than α-particles, because a β-particle has a much smaller mass. Extended
  • To find the direction of the force in a magnetic field, use the relative directions of force, field and current (see 4.5). A β-particle is negative, so the current is in the opposite direction to its motion. Extended
  • α-particles have a large charge (+2). This charge pulls strongly on the electrons in the atoms they pass. So an α-particle ionises many atoms in a short distance. Extended
  • Each ionisation takes some of the α-particle’s kinetic energy. So it loses all its kinetic energy quickly and has a short range. Extended
  • β-particles have a smaller charge (−1), so they pull less strongly on electrons. They ionise fewer atoms over the same distance. So they lose their kinetic energy more slowly and travel further than α-particles. Extended
  • γ-radiation has no charge, so it ionises very few atoms along its path. It loses its energy very slowly, so it travels furthest through materials. Extended

5.2.3 Radioactive decay

  • Radioactive decay is a change in an unstable nucleus. The nucleus emits an α-particle or a β-particle, and/or γ-radiation.
  • Radioactive decay is spontaneous and random. We cannot predict when a particular nucleus will decay.
  • In α-decay or β-decay, the number of protons changes. So the nucleus becomes a nucleus of a different element.
  • An isotope may be radioactive because its nucleus has too many neutrons, or because its nucleus is too heavy, or both. Extended
  • Decay makes the nucleus more stable. Extended
  • α-decay: the nucleus loses 2 protons and 2 neutrons. A goes down by 4 and Z goes down by 2. The nucleus becomes lighter. Extended
  • β-decay: inside the nucleus, a neutron changes into a proton and an electron. The electron is emitted as the β-particle. Extended
  • In nuclide notation: 10n → 11p + 0−1e Extended
  • So in β-decay, Z goes up by 1 and A stays the same. There is one fewer neutron, so the number of excess neutrons is reduced. Extended
  • γ-emission: the nucleus gives out energy as γ-radiation. A and Z do not change, so the element does not change. Extended
  • Example of α-decay: 24195Am → 23793Np + 42He Extended
  • Example of β-decay: 146C → 147N + 0−1e Extended
  • In every decay equation, the top numbers (A) balance and the bottom numbers (Z) balance. Extended

5.2.4 Half-life

  • The half-life of an isotope is the time it takes for half of its nuclei in a sample to decay. This time is the same for every sample of that isotope, whatever its size.
  • After one half-life, half of the nuclei are left. After two half-lives, one quarter are left. After three half-lives, one eighth are left.
  • The count rate due to the source also halves in each half-life. This is the count rate after the background count rate has been subtracted.
  • In Core questions, the data you are given do not include background radiation.
  • To find the half-life from a table or a decay curve, find the time for the count rate due to the source to fall to half of any starting value.
  • If the background radiation has not been subtracted, subtract it from every reading first. Then find the time for the corrected count rate to halve. Extended
  • The type of radiation and the half-life decide which isotope is used for a job. Extended
  • Smoke alarms use an α-source. The α-particles ionise the air, so a small current flows. Smoke absorbs the α-particles, the current falls and the alarm sounds. α is used because it is strongly ionising and is easily absorbed by smoke. It is also absorbed by a few cm of air and by the case, so it does not get out of the alarm. The source has a long half-life, so it lasts for many years. Extended
  • Irradiating food uses γ-radiation to kill bacteria. γ is used because it passes through the packaging and right through the food, so it reaches all the bacteria. The source has a long half-life, so it does not need to be replaced often. Extended
  • Sterilising equipment (for example, medical instruments) uses γ-rays to kill bacteria. γ is used because it can pass through the sealed packaging, so the equipment is sterilised after it is packed and stays sterile. The source has a long half-life, so it can be used for many years before it needs to be replaced. Extended
  • Measuring and controlling thickness: a source is placed on one side of a sheet and a detector on the other. If the sheet gets thicker, more radiation is absorbed and the count rate falls. A machine then adjusts the thickness. Extended
  • For paper or thin sheets, β is used. α would be completely stopped by the sheet. γ would pass through almost unchanged, so the count rate would hardly change. For thick metal sheets, γ is used. The source has a long half-life, so a change in count rate is caused by a change in thickness, not by decay. Extended
  • Diagnosis of cancer: a γ-emitter is injected into the body or swallowed. γ is used because it passes out of the body to a detector outside. The isotope has a short half-life, so it does not stay radioactive in the body for long. The half-life is still long enough for the scan to be done. Extended
  • Treatment of cancer: beams of γ-rays are aimed at the tumour to kill the cancer cells. γ is used because it is very penetrating, so it passes through the body tissue to reach a tumour deep inside. The source is outside the body and has a long half-life, so it stays useful for a long time without being replaced. Extended

5.2.5 Safety precautions

  • Ionising radiation can damage living cells. It can cause cell death, mutations (changes in the genetic material, DNA) and cancer.
  • Safe ways to move, use and store radioactive sources:
    • Store sources in lead-lined boxes, locked away, with a warning label.
    • Move sources in shielded containers.
    • Handle sources with long tongs, never with your hands.
    • Point the source away from people.
    • Use the source for the shortest possible time, then put it back.
  • All safety precautions work in three ways. Extended
    • Reduce the exposure time: less time near the source means less radiation is absorbed.
    • Increase the distance between the source and living tissue: the radiation spreads out and is partly absorbed by air, so less reaches you.
    • Use shielding: lead, concrete or other materials absorb the radiation before it reaches you.

Model

No model for this topic yet.

Equations

  • Corrected count rateExtended

    corrected count rate = measured count rate − background count rate

    count rates in counts/s or counts/minute

  • Amount left after n half-lives

    amount left = starting amount ÷ 2n

    amount = number of undecayed nuclei, or the count rate due to the source; n = number of half-lives that have passed

  • Alpha decayExtended

    AZX → A−4Z−2Y + 42He

    A = nucleon number, Z = proton number; X = parent nucleus, Y = new nucleus; 42He = α-particle

  • Beta decayExtended

    AZX → AZ+1Y + 0−1e

    A = nucleon number, Z = proton number; X = parent nucleus, Y = new nucleus; 0−1e = β-particle

  • Gamma emissionExtended

    AZX → AZX + 00γ

    A = nucleon number, Z = proton number; γ = gamma radiation

Corrected count rate Extended

A source is tested. The background count rate is 30 counts/minute. The table shows the measured count rate. Find the half-life.

Time / days 0 2 4 6 8
Measured count rate / counts/minute 830 596 430 313 230
  • Subtract the background from every reading: corrected count rates are 800, 566, 400, 283, 200 counts/minute.
  • Start at 800 counts/minute. Half of 800 is 400 counts/minute.
  • The corrected count rate is 400 counts/minute at 4 days.
  • Check: from 4 days to 8 days it falls from 400 to 200, which is half again.
  • Half-life = 4 days

Amount left after n half-lives

The count rate due to a source is 1600 counts/minute. The half-life is 3.0 hours. Find the count rate after 12 hours.

  • Given: starting count rate = 1600 counts/minute, half-life = 3.0 h, time = 12 h
  • Number of half-lives: n = 12 ÷ 3.0 = 4
  • Count rate = 1600 ÷ 24 = 1600 ÷ 16
  • Count rate = 100 counts/minute
  • Check by halving: 1600 → 800 → 400 → 200 → 100.

Alpha decay Extended

Nucleus 22688X emits an α-particle. Write the decay equation.

  • A: 226 − 4 = 222
  • Z: 88 − 2 = 86
  • 22688X → 22286Y + 42He
  • Check: top 226 = 222 + 4; bottom 88 = 86 + 2.

Beta decay Extended

Nucleus 9038X emits a β-particle. Write the decay equation.

  • A stays the same: 90
  • Z: 38 + 1 = 39
  • 9038X → 9039Y + 0−1e
  • Check: top 90 = 90 + 0; bottom 38 = 39 + (−1).

Gamma emission Extended

Nucleus 6028X emits γ-radiation. What happens to A and Z?

  • γ-radiation has no mass and no charge, so A and Z do not change.
  • 6028X → 6028X + 00γ
  • The nucleus is the same element. It has lost energy.

Common mistakes

  • Students write that radioactive decay can be sped up by heating the source. / The mark scheme wants: decay is spontaneous and random; nothing outside the nucleus changes it.
  • Students write that half-life is “half the time it takes for the source to decay”. / The mark scheme wants: the time for half of the nuclei in a sample of the isotope to decay.
  • Students find the half-life from count rates that still include background. / The mark scheme wants the background subtracted first, then the time for the corrected count rate to halve. Extended
  • Students write that a β-particle is an electron from the outer shell of the atom. / The mark scheme wants: a fast electron emitted from the nucleus.
  • Students write that γ-radiation is stopped by lead. / The mark scheme wants: γ is reduced (partly absorbed) by thick lead or concrete.
  • Students write that α is the most dangerous because it is the most penetrating. / The mark scheme wants: α is the most ionising but the least penetrating.

Exam tips

  • State the nature of each emission in a few words: α = helium nucleus, β = fast electron from the nucleus, γ = electromagnetic wave.
  • Describe deflection with direction words: “α and β are deflected in opposite directions; β is deflected more; γ is not deflected.” Extended
  • Explain ionising effect using both ideas named in the question, for example charge and kinetic energy. Each idea is usually worth a mark. Extended
  • Calculate half-life: show the halving and the time read from the graph or table. On a graph, draw lines on the curve to show where you read the values.
  • If the data include background radiation, show the corrected values first. Extended
  • Suggest a suitable isotope: give the type of radiation and the half-life, and say why each one fits the job. Extended
  • A typical 1-mark answer: “Background radiation is the ionising radiation that is always present around us.”
  • A typical 2-mark answer to “Describe how a source is stored safely”: “Keep it in a lead-lined box (1), locked away with a warning label (1).”
  • A typical 2-mark answer to “Why is γ used to sterilise equipment?”: “γ is very penetrating, so it passes through the packaging (1). It kills the bacteria on the equipment (1).” Extended
  • A typical 3-mark answer to “Explain these safety precautions”: “Handle the source with long tongs to increase the distance (1). Use it for as short a time as possible to reduce the exposure time (1). Store it in a lead-lined box, which absorbs the radiation (1).” Extended