Cambridge IGCSE0625

Radioactivity

Physics 0625 Chapter Notes

What this chapter covers

Radioactivity - Detection of radioactivityRadioactivity - The three types of nuclear emissionRadioactivity - Radioactive decayRadioactivity - Half-lifeRadioactivity - Safety precautions
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In this chapter

  1. 1The Nuclear Atom and Isotopes
  2. 2Types of Nuclear Radiation
  3. 3Properties of Radiation
  4. 4Radioactive Decay and Half-Life
  5. 5Nuclear Equations and Background Radiation
  6. 6Uses and Dangers of Radioactivity

1. The Nuclear Atom and Isotopes

At the centre of every atom is a tiny, dense nucleus, which contains positively charged protons and neutral neutrons. These particles are collectively called nucleons. Negatively charged electrons orbit the nucleus. The atomic number (Z), or proton number, defines an element and is the number of protons in the nucleus. The mass number (A), or nucleon number, is the total number of protons and neutrons. The number of neutrons (N) can be found by N = A - Z. In a neutral atom, the number of electrons equals the number of protons.

A = Z + N (Mass Number = Atomic Number + Neutron Number)

Nuclide Notation: ^{A}_{Z}X

Key term

Isotopes: Atoms of the same element (same number of protons) but with different numbers of neutrons (different mass number).

Examiner insight

Examiners expect you to be able to quickly determine the number of each subatomic particle from standard nuclide notation.

Common pitfall

Confusing the mass number (A) with the atomic number (Z). Remember, A is always the larger number and is written at the top.

Worked example 13 marks

A neutral atom of uranium is represented by the symbol $^{235}_{92}U$. Determine the number of protons, neutrons, and electrons in this atom.

  1. 1

    Step 1: Identify the atomic number (Z) and mass number (A) from the notation $^{A}_{Z}X$. Here, A = 235 and Z = 92.

  2. 2

    Step 2: The number of protons is equal to the atomic number, Z. So, number of protons = 92.

  3. 3

    Step 3: The number of electrons in a neutral atom is equal to the number of protons. So, number of electrons = 92.

  4. 4

    Step 4: The number of neutrons (N) is the mass number (A) minus the atomic number (Z). N = A - Z = 235 - 92 = 143. So, number of neutrons = 143.

Recap

  • The nucleus contains protons (positive) and neutrons (neutral).
  • Electrons (negative) orbit the nucleus.
  • Atomic number (Z) is the number of protons.
  • Mass number (A) is the total number of protons and neutrons.
  • Isotopes are atoms with the same number of protons but different numbers of neutrons.
  • In nuclide notation $^{A}_{Z}X$, A is the mass number and Z is the atomic number.

Quick check

  1. How many neutrons are in a nucleus of carbon-14 ($^{14}_{6}C$)?1 mark
  2. State the charge of a proton, neutron, and electron in relative terms.2 marks

2. Types of Nuclear Radiation

Some atomic nuclei are unstable. To become more stable, they spontaneously and randomly break down, or 'decay', emitting energy and/or particles. This process is called radioactive decay, and the emitted particles/energy are called nuclear radiation. There are three main types: alpha particles (α), beta particles (β), and gamma rays (γ).

Key term

Radioactive Decay: The spontaneous and random process by which an unstable atomic nucleus loses energy by emitting radiation.

Fun fact

The process of beta decay involves a neutron in the nucleus turning into a proton and an electron. The proton stays in the nucleus, and the electron is ejected at high speed.

Worked example 14 marks

Complete the table below to compare the properties of alpha, beta, and gamma radiation.

  1. 1

    | Property | Alpha (α) | Beta (β) | Gamma (γ) |

  2. 2
  3. 3

    | Nature | Helium nucleus (2 protons, 2 neutrons) | High-energy electron | High-frequency electromagnetic wave |

  4. 4

    | Relative Mass | 4 | ~1/1840 | 0 |

  5. 5

    | Relative Charge | +2 | -1 | 0 |

Recap

  • Unstable nuclei undergo radioactive decay to become more stable.
  • Radioactive decay is a random and spontaneous process.
  • The three main types of radiation are alpha (α), beta (β), and gamma (γ).
  • An alpha particle is a helium nucleus ($^{4}_{2}He$).
  • A beta particle is a fast-moving electron ($^{0}_{-1}e$).
  • A gamma ray is a high-energy electromagnetic wave.

Quick check

  1. Which type of radiation has a negative charge?1 mark
  2. What is an alpha particle composed of?1 mark

3. Properties of Radiation

The three types of radiation interact with matter differently. Ionising power is the ability to knock electrons out of atoms, creating ions. Alpha particles are large and highly charged, making them strongly ionising. Beta particles are smaller and less charged, making them moderately ionising. Gamma rays have no charge or mass, so they are weakly ionising. Penetrating power is the ability to pass through materials. Alpha is stopped by paper or a few cm of air. Beta is stopped by a few mm of aluminium. Gamma is highly penetrating and requires thick lead or several metres of concrete to significantly reduce its intensity. In electric or magnetic fields, the charged particles (alpha and beta) are deflected, while neutral gamma rays are not.

Key term

Ionisation: The process by which an atom loses or gains an electron, resulting in a charged particle called an ion.

Examiner insight

For questions on deflection, examiners look for both the direction of deflection (based on charge) and the amount of deflection (based on mass/charge ratio). Beta particles are deflected more than alpha particles.

Fun fact

The ionising property of alpha particles is used in smoke detectors. The alpha particles ionise air, creating a small current. When smoke enters, it neutralises these ions, the current drops, and the alarm sounds.

Worked example 14 marks

A radioactive source emits a mixture of alpha, beta, and gamma radiation. The beam passes through an upward-pointing electric field between two charged plates. Describe the path of each type of radiation.

  1. 1

    Step 1: Alpha particles (α) are positively charged (+2). They will be attracted to the negative plate and repelled by the positive plate, so they will curve downwards.

  2. 2

    Step 2: Beta particles (β) are negatively charged (-1). They will be attracted to the positive plate and repelled by the negative plate, so they will curve upwards.

  3. 3

    Step 3: Because beta particles have a much smaller mass than alpha particles, they are deflected more easily and will follow a more curved path.

  4. 4

    Step 4: Gamma rays (γ) are uncharged. They will be unaffected by the electric field and pass straight through without deflection.

Recap

  • Ionising power: α > β > γ.
  • Penetrating power: γ > β > α.
  • Alpha radiation is stopped by paper.
  • Beta radiation is stopped by thin aluminium.
  • Gamma radiation is reduced by thick lead or concrete.
  • Alpha and beta particles are deflected by electric and magnetic fields; gamma rays are not.

Quick check

  1. Which type of radiation is the most penetrating?1 mark
  2. A student wants to block alpha radiation but allow beta to pass through. What material should they use?1 mark

4. Radioactive Decay and Half-Life

The activity of a radioactive sample is the rate at which its nuclei decay. It is measured in becquerels (Bq), where 1 Bq = 1 decay per second. The activity of a sample decreases over time because the number of unstable nuclei decreases. The half-life (t½) is a measure of how quickly a sample decays. It is the time taken for the number of undecayed nuclei in a sample (and therefore its activity) to fall to half of its original value. This is a constant value for a given isotope.

Activity after n half-lives = Initial Activity / 2ⁿ

Key term

Half-life: The time taken for the activity of a radioactive isotope, or the number of undecayed nuclei, to fall to half of its initial value.

Examiner insight

When asked to determine half-life from a graph, you must show your workings on the graph itself. Draw lines from the y-axis (e.g., from 100% to 50%) across to the curve and then down to the x-axis to read the time.

Common pitfall

When reading a decay graph, students often read the time value that corresponds to half the initial activity, instead of the time interval from t=0 to that point.

Worked example 13 marks

The activity of a sample of Technetium-99m is 800 kBq. Its half-life is 6 hours. What will its activity be after 24 hours?

  1. 1

    Step 1: Calculate the number of half-lives(n) that have passed. n = Total time / Half-life = 24 hours / 6 hours = 4 half-lives.

  2. 2

    Step 2: Calculate the final activity. After each half-life, the activity halves.

  3. 3

    After 1 half-life (6h): 800 / 2 = 400 kBq.

  4. 4

    After 2 half-lives (12h): 400 / 2 = 200 kBq.

  5. 5

    After 3 half-lives (18h): 200 / 2 = 100 kBq.

  6. 6

    After 4 half-lives (24h): 100 / 2 = 50 kBq.

  7. 7

    Alternatively, use the formula: Final Activity = 800 / 2⁴ = 800 / 16 = 50 kBq.

Worked example 23 marks

A decay curve for a radioactive source shows its initial count rate is 640 counts per minute. After 30 minutes, the count rate is 80 counts per minute. Determine the half-life of the source.

  1. 1

    Step 1: Determine how many times the count rate has halved. 640 -> 320 (1 half-life), 320 -> 160 (2 half-lives), 160 -> 80 (3 half-lives). So, 3 half-lives have passed.

  2. 2

    Step 2: The total time for these 3 half-lives is 30 minutes.

  3. 3

    Step 3: Calculate the time for one half-life. Half-life = Total time / Number of half-lives = 30 minutes / 3 = 10 minutes.

Recap

  • Activity is the rate of decay, measured in Becquerels (Bq).
  • Half-life is the time for activity to halve.
  • Radioactive decay is exponential; the activity never reaches zero but becomes very small.
  • Half-life can be determined from a decay curve by finding the time it takes for the count rate to drop to half its value.
  • A short half-life means a substance decays quickly and has a high initial activity.

Quick check

  1. An isotope has a half-life of 2 days. What fraction of the original sample will remain after 6 days?2 marks

5. Nuclear Equations and Background Radiation

Nuclear reactions, like radioactive decay, can be represented by balanced equations. In any nuclear equation, both the total mass number (A) and the total atomic number (Z) must be conserved (the same on both sides of the arrow). Background radiation is the low level of ionising radiation that is present all around us. Major sources include radon gas from rocks, cosmic rays from space, radiation in food and drink, and man-made sources like medical x-rays. When measuring the activity of a source, a detector will also pick up this background radiation. For an accurate measurement of the source's activity, the background count rate must first be measured and then subtracted from the total count rate.

Alpha Decay: ^{A}_{Z}X → ^{A-4}_{Z-2}Y + ^{4}_{2}α

Beta Decay: ^{A}_{Z}X → ^{A}_{Z+1}Y + ^{0}_{-1}β

Corrected Count Rate = Total Count Rate - Background Count Rate

Key term

Background Radiation: The ubiquitous ionising radiation that originates from natural and artificial sources in the environment.

Examiner insight

Marks for nuclear equations are given for the correct new mass number, the correct new atomic number, and the correct symbols for all particles.

Common pitfall

Forgetting to subtract background radiation when calculating the half-life from experimental data. Always use the corrected count rate.

Worked example 13 marks

Radium-226 ($^{226}_{88}Ra$) decays by emitting an alpha particle. Write a balanced nuclear equation for this decay and identify the element produced.

  1. 1

    Step 1: Write down the initial nucleus and the emitted alpha particle: $^{226}_{88}Ra → Y + ^{4}_{2}α$.

  2. 2

    Step 2: Conserve the mass number (A). 226 = A_Y + 4. So, the mass number of the daughter nucleus Y is A_Y = 226 - 4 = 222.

  3. 3

    Step 3: Conserve the atomic number (Z). 88 = Z_Y + 2. So, the atomic number of the daughter nucleus Y is Z_Y = 88 - 2 = 86.

  4. 4

    Step 4: The new nucleus is $^{222}_{86}Y$. Looking at the periodic table, the element with atomic number 86 is Radon (Rn).

  5. 5

    Step 5: Write the final balanced equation: $^{226}_{88}Ra → ^{222}_{86}Rn + ^{4}_{2}α$.

Worked example 22 marks

A Geiger counter records a count rate of 350 counts per minute near a radioactive source. When the source is removed, the count rate drops to 30 counts per minute. What is the corrected count rate from the source?

  1. 1

    Step 1: Identify the total count rate and the background count rate. Total count rate = 350 counts/min. Background count rate = 30 counts/min.

  2. 2

    Step 2: Use the formula: Corrected Count Rate = Total Count Rate - Background Count Rate.

  3. 3

    Step 3: Calculate the value: Corrected Count Rate = 350 - 30 = 320 counts per minute.

Recap

  • In nuclear equations, both mass number (top) and atomic number (bottom) are conserved.
  • Alpha decay reduces mass number by 4 and atomic number by 2.
  • Beta decay does not change the mass number but increases the atomic number by 1.
  • Background radiation comes from natural and artificial sources.
  • To find the true activity of a source, you must subtract the background count rate from your measurement.

Quick check

  1. Carbon-14 ($^{14}_{6}C$) undergoes beta decay. What is the nuclide symbol of the atom it becomes?2 marks
  2. State two natural sources of background radiation.2 marks

6. Uses and Dangers of Radioactivity

The properties of radioactive isotopes make them useful in medicine, industry, and research, but their ability to ionise atoms also makes them dangerous. The main danger is to living cells; ionisation can damage DNA, causing mutations that may lead to cancer, or it can kill cells outright. We protect ourselves by limiting exposure time, increasing distance from the source, and using shielding (e.g., lead aprons, concrete walls). It is crucial to distinguish between irradiation (being exposed to radiation from an outside source) and contamination (when a radioactive source gets onto or inside an object). An irradiated object does not become radioactive, but a contaminated one does.

Key term

Contamination: The unwanted presence of radioactive material on other materials, or within a person's body.

Examiner insight

When explaining the choice of an isotope for a particular use, you must link its specific properties (radiation type, half-life) to the requirements of the application.

Common pitfall

Confusing irradiation and contamination. A person who has had an X-ray has been irradiated but is not radioactive. A person who has swallowed a radioactive substance is contaminated and is radioactive.

Worked example 14 marks

Explain why a gamma-emitting isotope with a half-life of 6 hours is a suitable choice for use as a medical tracer to diagnose problems in a patient's body.

  1. 1

    Step 1: State the property related to its emission type. It is a gamma emitter. Gamma rays are highly penetrating, so they can pass out of the patient's body to be detected by an external scanner.

  2. 2

    Step 2: State a second advantage of its emission type. Gamma rays are weakly ionising, which minimises the damage to the patient's cells and tissues.

  3. 3

    Step 3: State the property related to its half-life. The half-life of 6 hours is short. This means it is long enough for the medical examination to be completed.

  4. 4

    Step 4: State a second advantage of its half-life. It is also short enough that the activity will decay to a safe level quickly after the procedure, minimising the long-term radiation dose to the patient.

Recap

  • Dangers of radiation stem from its ability to ionise cells, causing damage or death.
  • Safety precautions include minimising time, maximising distance, and using shielding.
  • Irradiation is exposure to radiation; contamination is contact with a radioactive source.
  • Alpha emitters are used in smoke detectors.
  • Beta emitters are used for controlling the thickness of paper or foil.
  • Gamma emitters are used for sterilising equipment and as medical tracers.

Quick check

  1. Why would an alpha emitter be unsuitable as a medical tracer to be injected into the body?2 marks
  2. State the three main ways to reduce your exposure to a radioactive source.3 marks

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. An atom of lead is represented by the nuclide symbol $^{208}_{82}Pb$. Another isotope of lead is lead-210. State the number of protons and neutrons in an atom of lead-210.2 marks
  2. Describe the nature of alpha, beta and gamma radiation in terms of their physical composition and relative charge.3 marks
  3. A beam of beta particles is directed into a uniform magnetic field that is pointing into the page. Describe the path of the beta particles within the field and explain your reasoning.3 marks
  4. The half-life of radioactive iodine-131 is 8 days. A hospital receives a sample with an activity of 1280 Bq. Calculate the activity of the sample after 32 days.3 marks
  5. A Geiger-Muller tube is used to measure the activity of a radioactive source. It gives a reading of 425 counts per minute. When the source is removed, the reading is 25 counts per minute. The source is measured again 60 hours later and gives a reading of 75 counts per minute. Calculate the half-life of the source.5 marks
  6. Uranium-238 ($^{238}_{92}U$) decays into Thorium (Th) by emitting an alpha particle. Thorium then decays into Protactinium (Pa) by emitting a beta particle. Write the two balanced nuclear equations for these decays.4 marks
  7. Explain why alpha radiation is highly ionising but has low penetrating power, whereas gamma radiation is weakly ionising but has high penetrating power.4 marks
  8. A factory uses a beta source and a detector to monitor the thickness of aluminium foil being produced. Explain how this system works.4 marks
  9. State two naturally occurring sources of background radiation and one artificial source.3 marks
  10. Distinguish between radioactive contamination and irradiation, giving an example of each.4 marks

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