Cambridge IGCSE0972

Radioactivity

Physics 0972 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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1. Atomic Structure 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. Orbiting the nucleus are negatively charged electrons. An atom is electrically neutral because the number of protons equals the number of electrons. The identity of an element is determined solely by its proton number (Z), also called the atomic number. The mass number (A), or nucleon number, is the total count of protons and neutrons in the nucleus. Different versions of the same element, called isotopes, exist. Isotopes have the same number of protons but different numbers of neutrons. For example, Carbon-12 and Carbon-14 are isotopes of carbon. Both have 6 protons, but Carbon-12 has 6 neutrons (A=12) while Carbon-14 has 8 neutrons (A=14). We represent a specific nucleus, or nuclide, with the notation A_Z_X, where X is the element symbol.

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

Key term

Isotopes: Atoms of the same element that have the same number of protons but a different number of neutrons.

Common pitfall

Confusing mass number with atomic number. Remember, the atomic number (proton number) is always the smaller one and defines the element.

Worked example 13 marks

A nucleus of Uranium is represented by the symbol ²³⁵₉₂U. State the number of protons, neutrons, and electrons in a neutral atom of this isotope.

  1. 1

    Step 1: Identify the mass number (A) and atomic number (Z) from the symbol. 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: In a neutral atom, the number of electrons 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 minus the atomic number (N = A - Z). So, number of neutrons = 235 - 92 = 143.

Recap

  • The nucleus contains protons (positive) and neutrons (neutral).
  • Atomic number (Z) is the number of protons and defines the element.
  • Mass number (A) is the total number of protons and neutrons.
  • Isotopes of an element have the same Z but different numbers of neutrons.
  • In a neutral atom, the number of electrons equals the number of protons.

Quick check

  1. How many neutrons are in a nucleus of ¹⁴₆C?1 mark

2. The Three Types of Radiation

Some isotopes have unstable nuclei. To become more stable, they spontaneously break down, or 'decay', emitting energy and/or particles. This process is called radioactive decay, and the emissions are called nuclear radiation. There are three main types: Alpha (α), Beta (β), and Gamma (γ). An alpha particle is a helium nucleus, consisting of 2 protons and 2 neutrons. A beta particle is a high-energy electron that is created and ejected from the nucleus when a neutron changes into a proton. Gamma radiation is not a particle; it is a high-energy electromagnetic wave, often emitted alongside alpha or beta particles as the nucleus settles into a more stable energy state.

Key term

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

Examiner insight

Examiners look for precise definitions. For example, state a beta particle is a 'high-energy electron emitted from the nucleus', not just 'an electron'.

Worked example 12 marks

A radioactive source emits radiation that is deflected by a magnetic field towards the positive plate in an electric field. What type of radiation is it and why?

  1. 1

    Step 1: Identify the effect of the electric field. The radiation is deflected towards the positive plate.

  2. 2

    Step 2: Recall the charges of particles. Opposite charges attract. Therefore, the radiation must be negatively charged to be attracted to a positive plate.

  3. 3

    Step 3: Identify the type of radiation with this charge. Of the three main types, only beta particles have a negative charge (-1). Alpha particles are positive (+2) and gamma rays are neutral (0).

  4. 4

    Step 4: Conclude the radiation type. The radiation consists of beta particles.

Recap

  • Alpha particles (α) are helium nuclei (2 protons, 2 neutrons) with a +2 charge.
  • Beta particles (β) are high-energy electrons with a -1 charge, emitted from the nucleus.
  • Gamma rays (γ) are high-energy electromagnetic waves with no mass and no charge.
  • Radioactive decay is a random and spontaneous process.
  • Beta decay occurs when a neutron turns into a proton and an electron within the nucleus.

Quick check

  1. What is the composition and relative charge of an alpha particle?2 marks

3. Properties and Detection of Radiation

The three types of radiation interact with matter differently, giving them distinct properties. Penetrating power describes how far radiation can travel through a material. Alpha is the least penetrating (stopped by paper or a few cm of air). Beta is more penetrating (stopped by a few mm of aluminium). Gamma is the most penetrating (requiring thick lead or concrete to significantly reduce it). Ionising power is the ability to knock electrons out of atoms, creating ions. This is how radiation damages living cells. Alpha is the most ionising, and gamma is the least. These two properties are inversely related: highly ionising alpha particles interact strongly with matter, lose their energy quickly, and therefore do not penetrate far. Because of their charge, alpha and beta particles are deflected in electric and magnetic fields (in opposite directions), while neutral gamma rays are not. Radiation is detected using devices like a Geiger-Müller (GM) tube, which works by detecting the ionisation the radiation causes in a gas.

Key term

Ionisation: The process where radiation has enough energy to remove an electron from an atom or molecule, creating a charged ion.

Common pitfall

Confusing penetrating power with ionising power. Remember that the radiation that is easiest to stop (alpha) is the most dangerous if it gets inside the body because it is the most ionising.

Worked example 13 marks

A scientist has a radioactive source that emits a mixture of alpha, beta, and gamma radiation. She places a sheet of aluminium foil 3 mm thick in front of the detector. Which type(s) of radiation will be detected?

  1. 1

    Step 1: Consider the penetrating power of alpha radiation. Alpha is stopped by paper or a few cm of air, so it will definitely be stopped by 3 mm of aluminium.

  2. 2

    Step 2: Consider the penetrating power of beta radiation. Beta is stopped by a few mm of aluminium. The 3 mm foil is thick enough to stop most, if not all, of the beta particles.

  3. 3

    Step 3: Consider the penetrating power of gamma radiation. Gamma is highly penetrating and requires thick lead or concrete to be stopped. It will easily pass through 3 mm of aluminium.

  4. 4

    Step 4: Conclude which radiation reaches the detector. Only the gamma radiation will pass through the aluminium foil and be detected.

Recap

  • Alpha: Least penetrating, most ionising, stopped by paper.
  • Beta: Medium penetration, medium ionisation, stopped by aluminium.
  • Gamma: Most penetrating, least ionising, reduced by thick lead.
  • Alpha and Beta are deflected by electric/magnetic fields; Gamma is not.
  • Ionising power and penetrating power are inversely related.

Quick check

  1. Which type of radiation would cause the most damage to a cell if the source was inside the body? Explain why.2 marks

4. Activity 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 equals one decay per second. While the decay of any single nucleus is random, the overall rate of decay for a large sample is predictable. The activity of a sample decreases over time as the number of undecayed nuclei decreases. The time it takes for the activity of a sample to fall to half its initial value is called the half-life (t½). This is a constant for a given radioisotope. For example, if a sample has an activity of 800 Bq and a half-life of 10 days, its activity will be 400 Bq after 10 days, 200 Bq after 20 days, and 100 Bq after 30 days.

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

Key term

Half-life: The time taken for the number of undecayed nuclei in a sample to halve, or the time taken for the activity of a sample to fall to half its original value.

Examiner insight

When finding half-life from a graph, you must show your working on the graph itself by drawing lines from the half-activity value to the curve and down to the time axis. Marks are often awarded for these construction lines.

Worked example 13 marks

The half-life of Technetium-99m is 6 hours. A sample has an initial activity of 1200 Bq. What will its activity be after 24 hours?

  1. 1

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

  2. 2

    Step 2: Use the formula or work step-by-step. After 1 half-life (6h): 1200 / 2 = 600 Bq.

  3. 3

    Step 3: After 2 half-lives (12h): 600 / 2 = 300 Bq.

  4. 4

    Step 4: After 3 half-lives (18h): 300 / 2 = 150 Bq.

  5. 5

    Step 5: After 4 half-lives (24h): 150 / 2 = 75 Bq. The final activity is 75 Bq.

Worked example 22 marks

The activity of a radioactive sample is measured over time, yielding the data below. Use the graph to determine the half-life of the sample. Initial activity is 1600 units.

  1. 1

    Step 1: Find half of the initial activity. Half of 1600 is 800 units.

  2. 2

    Step 2: On the graph of activity vs. time, draw a horizontal line from 800 units on the y-axis across to the decay curve.

  3. 3

    Step 3: From the point where the line meets the curve, draw a vertical line straight down to the x-axis (time axis).

  4. 4

    Step 4: Read the value on the x-axis. This value is the half-life. (Based on the provided exam context graph, this would be approximately 8 days).

Recap

  • Activity is the rate of decay, measured in Becquerels (Bq).
  • 1 Bq = 1 decay per second.
  • Half-life is the time for activity to halve.
  • Radioactive decay is an exponential process.
  • Half-life is constant for a specific radioisotope.

Quick check

  1. A radioactive isotope has a half-life of 20 minutes. What fraction of the original nuclei will remain undecayed after 1 hour?2 marks

5. Nuclear Decay Equations

Nuclear equations are used to represent the changes that occur in a nucleus during radioactive decay. Like chemical equations, they must be balanced. This means the total mass number (A) and the total atomic number (Z) must be the same on both sides of the equation. In alpha decay, an alpha particle (a helium nucleus, ⁴₂He) is emitted. This causes the mass number (A) of the parent nucleus to decrease by 4 and the atomic number (Z) to decrease by 2. In beta decay, a beta particle (an electron, ⁰₋₁e) is emitted. This happens when a neutron turns into a proton. Therefore, the mass number (A) remains unchanged, but the atomic number (Z) increases by 1, forming a new element.

Alpha Decay: ᴬ_Z_X → ᴬ⁻⁴_Z⁻²_Y + ⁴₂He

Beta Decay: ᴬ_Z_X → ᴬ_Z⁺¹_Y + ⁰₋₁e

Key term

Nuclide: A distinct kind of atom or nucleus characterized by a specific number of protons and neutrons.

Common pitfall

Forgetting that the proton number increases in beta decay. Students often incorrectly subtract one, thinking of the electron's -1 charge.

Worked example 13 marks

Radium-226 (²²⁶₈₈Ra) decays by emitting an alpha particle. Write a balanced nuclear equation for this decay and identify the daughter nucleus.

  1. 1

    Step 1: Write down the parent nuclide and the emitted particle. Parent is ²²⁶₈₈Ra, particle is an alpha particle (⁴₂He).

  2. 2

    Step 2: Determine the new mass number (A) of the daughter nucleus. New A = 226 - 4 = 222.

  3. 3

    Step 3: Determine the new atomic number (Z) of the daughter nucleus. New Z = 88 - 2 = 86.

  4. 4

    Step 4: Identify the new element from its atomic number. The element with Z=86 is Radon (Rn).

  5. 5

    Step 5: Write the full balanced equation: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He.

Worked example 23 marks

Carbon-14 (¹⁴₆C) is a beta emitter. Write the nuclear equation for the decay of Carbon-14.

  1. 1

    Step 1: Write down the parent nuclide and the emitted particle. Parent is ¹⁴₆C, particle is a beta particle (⁰₋₁e).

  2. 2

    Step 2: Determine the new mass number (A). In beta decay, A is unchanged. New A = 14.

  3. 3

    Step 3: Determine the new atomic number (Z). In beta decay, Z increases by 1. New Z = 6 + 1 = 7.

  4. 4

    Step 4: Identify the new element from its atomic number. The element with Z=7 is Nitrogen (N).

  5. 5

    Step 5: Write the full balanced equation: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e.

Recap

  • Nuclear equations must balance for both mass number (A) and atomic number (Z).
  • In alpha decay, A decreases by 4 and Z decreases by 2.
  • In beta decay, A is constant and Z increases by 1.
  • A change in Z means the element has changed into a different element.
  • An alpha particle is ⁴₂He and a beta particle is ⁰₋₁e.

Quick check

  1. A nucleus undergoes beta decay. What happens to its mass number and its atomic number?2 marks

6. Background Radiation, Safety, and Uses

We are constantly exposed to low levels of ionising radiation from our surroundings. This is called background radiation. Natural sources are the biggest contributors and include: cosmic rays from space, radioactive rocks and soil (like granite), radon gas released from the ground, and radioactive elements in food and drink (like potassium-40 in bananas). Artificial sources include medical X-rays and treatments, and fallout from nuclear weapons testing or accidents. High doses of radiation are dangerous because ionisation can damage or kill living cells, or cause mutations in DNA that can lead to cancer. To work safely with radioactive sources, three principles are used: limit exposure time, increase distance from the source, and use shielding (e.g., lead aprons). Despite the dangers, radioisotopes have many beneficial uses. These include medical tracers (e.g., Technetium-99m to study blood flow), cancer therapy (radiotherapy), smoke detectors (Americium-241), and industrial thickness gauging.

Key term

Background Radiation: The low-level ionising radiation that is present all the time in the environment from a variety of natural and artificial sources.

Examiner insight

When explaining the choice of an isotope for a specific use, candidates must link the properties of the radiation (half-life, penetration, ionisation) to the requirements of the task.

Fun fact

The granite used for the countertops in some kitchens is slightly radioactive and contributes a tiny amount to the home's background radiation level.

Worked example 14 marks

Technetium-99m is a gamma emitter with a half-life of 6 hours. Explain why it is a suitable radioisotope for use as a medical tracer to diagnose problems in the body.

  1. 1

    Step 1: Consider the type of radiation. It is a gamma emitter. Gamma rays are highly penetrating, so they can easily pass out of the patient's body to be detected by a camera outside.

  2. 2

    Step 2: Consider the ionising power. Gamma rays are weakly ionising, which minimises the damage to the patient's cells and tissues.

  3. 3

    Step 3: Consider the half-life. The half-life of 6 hours is short enough that the activity will decay to a safe level quickly (within a day or two), minimising the long-term dose to the patient.

  4. 4

    Step 4: Consider the half-life in relation to the procedure. The half-life is also long enough for the medical examination to be carried out before the activity becomes too low to detect.

Recap

  • Background radiation is always present in the environment.
  • Natural sources include cosmic rays, rocks, and radon gas.
  • Radiation can be hazardous, causing cell damage or cancer.
  • Safety precautions involve limiting time, increasing distance, and using shielding.
  • Radioisotopes are chosen for uses based on their half-life and radiation type.

Quick check

  1. State two naturally occurring sources of background radiation.2 marks
  2. Give one reason why an alpha emitter would be unsuitable as a medical tracer to be injected into the blood.1 mark

End-of-chapter exercise

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

  1. Define the term 'half-life' of a radioactive isotope.2 marks
  2. State two properties of an alpha particle.2 marks
  3. A radioactive source has an initial activity of 640 Bq and a half-life of 15 days. Calculate its activity after 60 days.3 marks
  4. Complete the following nuclear equation for the beta decay of Thorium-234: ²³⁴₉₀Th → ... + ⁰₋₁e2 marks
  5. Explain why gamma rays are not deflected by a magnetic field, whereas beta particles are.3 marks
  6. The activity of a radioactive sample falls from 800 counts per minute to 50 counts per minute in 80 hours. Calculate the half-life of the sample.4 marks
  7. Americium-241 is used in smoke detectors. It is an alpha emitter with a very long half-life. Explain why these properties make it suitable for this use.4 marks
  8. A student measures the count rate from a radioactive source as 340 counts per minute. After placing the detector 1 metre away from the source, she measures a constant background radiation of 20 counts per minute. The half-life of the source is 30 minutes. Calculate the true count rate from the source after 1.5 hours.4 marks
  9. Compare the relative penetrating powers and relative ionising abilities of alpha particles, beta particles, and gamma rays.3 marks
  10. State one natural source and one artificial (man-made) source of background radiation.2 marks

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