Radioactive decay

1. Overview

Radioactive decay is the process by which an unstable nucleus releases radiation to become more stable. This fundamental process explains how certain elements change into others over time and is the basis for understanding nuclear energy, medical imaging, and carbon dating.

Key Definitions

• Radioactive Decay: The process in which an unstable atomic nucleus loses energy by emitting radiation.
• Spontaneous: A process that is not affected by external factors (such as temperature, pressure, or chemical environment).
• Random: It is impossible to predict exactly which individual nucleus will decay next, or exactly when a specific nucleus will decay.
• Nuclide: A distinct kind of atom or nucleus characterized by its specific number of protons and neutrons.
• Isotope: Atoms of the same element with the same number of protons but different numbers of neutrons.

Core Content

The Nature of Decay

Unstable nuclei do not stay unstable forever. To reach a stable state, they undergo a change called radioactive decay. During this process, the nucleus emits one or more types of radiation:

• Alpha ($\alpha$) particles: Helium nuclei ($2$ protons, $2$ neutrons).
• Beta ($\beta$) particles: High-speed electrons.
• Gamma ($\gamma$) radiation: High-frequency electromagnetic waves.

Random and Spontaneous Process

• Spontaneous: You cannot "speed up" or "slow down" decay by heating a sample or changing the pressure.
• Random: While we can predict how many nuclei in a large sample will decay over time, we cannot point to one specific nucleus and say when it will explode.

Changing Elements

When a nucleus emits an alpha or beta particle, the number of protons in the nucleus changes. Because the atomic number defines the element, the nucleus changes into a different element.

• Alpha decay: The nucleus loses 2 protons; it "moves back" two places in the Periodic Table.
• Beta decay: The nucleus gains 1 proton; it "moves forward" one place in the Periodic Table.
• Gamma emission: This is just energy being released; the element stays the same.

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Extended Content (Extended Curriculum Only)

Why are some isotopes radioactive?

Isotopes are usually unstable (and therefore radioactive) for two main reasons:

1. Too many neutrons: The ratio of neutrons to protons is too high, making the nucleus "unbalanced."
2. Too heavy: The nucleus is simply too large for the strong nuclear force to hold it together (usually elements with an atomic number greater than 82).

Effects of Decay on the Nucleus

The goal of decay is to increase the stability of the nucleus.

• Alpha ($\alpha$) decay: Reduces the mass of the nucleus significantly. Both the number of protons and neutrons decrease.
• Beta ($\beta$) decay: Reduces the number of excess neutrons. A neutron in the nucleus actually transforms into a proton and an electron. The proton stays in the nucleus, and the electron is shot out as a $\beta$-particle.
  • Equation of change: $\text{neutron} \rightarrow \text{proton} + \text{electron}$
• Gamma ($\gamma$) emission: Occurs when a nucleus has "surplus" energy after alpha or beta decay. It releases this energy as a wave to reach its lowest energy state.

Decay Equations using Nuclide Notation

In these equations, the total mass number (top) and atomic number (bottom) must be equal on both sides.

1. Alpha Decay Example: $$^{238}{92}\text{U} \rightarrow ^{234}{90}\text{Th} + ^4_2\alpha$$ (Note: Mass decreases by 4, Atomic number decreases by 2)

2. Beta Decay Example: $$^{14}{6}\text{C} \rightarrow ^{14}{7}\text{N} + ^0_{-1}\beta$$ (Note: Mass stays the same, Atomic number increases by 1)

3. Gamma Decay Example: $$^{60}{27}\text{Co} \rightarrow ^{60}{27}\text{Co} + \gamma$$ (Note: No change to mass or atomic number)

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Key Equations

• Nuclide Notation: $^A_Z X$
  • $A$ = Nucleon number (mass)
  • $Z$ = Proton number (atomic number)
  • $X$ = Chemical symbol
• Alpha Particle: $^4_2\alpha$ or $^4_2\text{He}$
• Beta Particle: $^0_{-1}\beta$ or $^0_{-1}e$

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Common Mistakes to Avoid

• ❌ Wrong: Thinking that the probability of a single nucleus decaying decreases over time.
• ✅ Right: The total activity of the sample decreases, but the probability for any individual nucleus to decay remains constant.
• ❌ Wrong: Decreasing the mass number during Beta decay.
• ✅ Right: In Beta decay, a neutron turns into a proton. The total number of nucleons (mass) stays the same, but the atomic number increases by 1.
• ❌ Wrong: Thinking that shielding (like lead) stops the decay process.
• ✅ Right: Lead shields the environment from the radiation, but the internal decay inside the source continues at its own natural rate.
• ❌ Wrong: Thinking an alpha particle is just a "proton."
• ✅ Right: An alpha particle is a helium nucleus (2 protons AND 2 neutrons).

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Exam Tips

1. Conservation Check: When completing decay equations, always check that the numbers on the top (left vs right) and the numbers on the bottom (left vs right) add up to the same total.
2. Terminology: Use the words "spontaneous" and "random" specifically when asked to describe the nature of radioactive decay; examiners look for these exact keywords.
3. Identify the Particle: If the atomic number increases by 1 but the mass stays the same, it is always Beta decay. If the mass drops by 4 and the atomic number drops by 2, it is always Alpha decay.

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Exam-Style Questions

Practice these original exam-style questions to test your understanding. Each question mirrors the style, structure, and mark allocation of real Cambridge 0625 Theory papers.

Exam-Style Question 1 — Short Answer [5 marks]

Question:

(a) Define radioactive decay. [2]

(b) State two characteristics of radioactive decay. [2]

(c) Give one reason why some isotopes of an element are radioactive. [1]

Worked Solution:

(a)

1. Radioactive decay is the process where an unstable nucleus emits particles or energy. [definition]

How to earn full marks:

• Must mention an unstable nucleus to earn the first mark.
• Must mention emission of particles or energy to earn the second mark (alpha, beta, gamma are all acceptable).

(b)

1. Radioactive decay is spontaneous. [characteristic 1]

2. Radioactive decay is random. [characteristic 2]

How to earn full marks:

• "Spontaneous" means the decay is not influenced by external factors.
• "Random" means that it is impossible to predict which nucleus will decay or when.

(c)

1. Some isotopes are radioactive because the nucleus has too many neutrons. [reason]

How to earn full marks:

• Acceptable answers include "too many neutrons" or "nucleus is too heavy".

Common Pitfall: Students often confuse the terms "spontaneous" and "random." Remember that "spontaneous" means the decay isn't triggered by external factors, while "random" means you can't predict which specific nucleus will decay next.

Exam-Style Question 2 — Short Answer [6 marks]

Question:

A sample of Polonium-210 ($^{210}_{84}Po$) undergoes alpha decay.

(a) State what is meant by alpha decay. [2]

(b) Complete the nuclear equation for this decay. [4]

$^{210}{84}Po \rightarrow \space ^{\boxed{\text{ }}}{\boxed{\text{ }}}X \space + \space ^{\boxed{\text{ }}}_{\boxed{\text{ }}}He$

Worked Solution:

(a)

1. Alpha decay is the process where an unstable nucleus emits an alpha particle. [definition]

2. An alpha particle is a helium nucleus. [definition]

How to earn full marks:

• Must mention emission of an alpha particle.
• Must mention that the alpha particle is a helium nucleus (2 protons, 2 neutrons).

(b)

1. The alpha particle is a helium nucleus, so it is $^{4}_{2}He$ [alpha particle symbol]

2. The mass number of the Polonium decreases by 4, so the new nucleus has a mass number of 206. [mass number calculation]

3. The atomic number of the Polonium decreases by 2, so the new nucleus has an atomic number of 82. [atomic number calculation]

4. The element with atomic number 82 is Lead, so the new nucleus is Lead-206 ($^{206}_{82}Pb$) [identification of new element]

$^{210}{84}Po \rightarrow \space ^{\boxed{206}}{\boxed{82}}Pb \space + \space ^{\boxed{4}}_{\boxed{2}}He$

How to earn full marks:

• 1 mark for the correct mass number of the new element (206).
• 1 mark for the correct atomic number of the new element (82).
• 1 mark for the correct mass number of the alpha particle (4).
• 1 mark for the correct atomic number of the alpha particle (2).

Common Pitfall: When writing nuclear equations, make sure that both the mass numbers and atomic numbers balance on both sides of the equation. A common mistake is forgetting to subtract from the parent nucleus when an alpha or beta particle is emitted.

Exam-Style Question 3 — Extended Response [8 marks]

Question:

Strontium-90 ($^{90}_{38}Sr$) is a radioactive isotope that decays by beta emission.

(a) Describe what happens to the nucleus during beta decay. [3]

(b) Complete the nuclear equation for the beta decay of Strontium-90. [3]

$^{90}{38}Sr \rightarrow \space ^{\boxed{\text{ }}}{\boxed{\text{ }}}Y \space + \space ^{\boxed{\text{ }}}_{\boxed{\text{ }}}e \space + \space \overline{v}$

(c) A student suggests that a magnetic field can be used to distinguish between alpha, beta, and gamma radiation. Describe how a magnetic field can be used to separate beta and gamma radiation and predict the path of each type of radiation in the field. [2]

Worked Solution:

(a)

1. During beta decay, a neutron in the nucleus changes into a proton and an electron. [neutron decay]

2. The electron is emitted from the nucleus as a beta particle. [electron emission]

3. The nucleus now has one more proton and one less neutron, increasing the atomic number by 1, but the mass number stays the same. [change in nucleus]

How to earn full marks:

• Must mention that a neutron changes into a proton and an electron.
• Must mention that the electron is emitted as a beta particle.
• Must mention the change in atomic number (increase by 1) and mass number (no change).

(b)

1. The Strontium-90 decays to Yttrium-90. Therefore the mass number of the yttrium is 90. [mass number calculation]

2. The atomic number increases by 1. Therefore the atomic number of the yttrium is 39. [atomic number calculation]

3. The beta particle is an electron, so it is $_{-1}^{0}e$ [beta particle symbol]

$^{90}{38}Sr \rightarrow \space ^{\boxed{90}}{\boxed{39}}Y \space + \space ^{\boxed{0}}_{\boxed{-1}}e \space + \space \overline{v}$

How to earn full marks:

• 1 mark for the correct mass number of the Yttrium (90).
• 1 mark for the correct atomic number of the Yttrium (39).
• 1 mark for the correct beta particle symbol $_{-1}^{0}e$.

(c)

1. Beta particles are charged, so they will be deflected by a magnetic field. [charge and magnetic field]

2. Gamma rays are not charged, so they will not be deflected by a magnetic field. [gamma and magnetic field]

How to earn full marks:

• 1 mark for stating that beta particles are deflected.
• 1 mark for stating that gamma rays are not deflected.

Common Pitfall: Remember that beta particles have a negative charge, so they will be deflected in the opposite direction to alpha particles in a magnetic field. Gamma rays, being uncharged, will not be deflected at all.

Exam-Style Question 4 — Extended Response [9 marks]

Question:

A laboratory technician is investigating the decay of a newly discovered radioactive isotope, Element Z. She measures the count rate of a sample of Element Z over a period of time. Background radiation is present.

(a) State what is meant by background radiation and give two sources. [3]

(b) The technician records the following data. The background count rate is 15 counts/minute.

Time (minutes)	Measured Count Rate (counts/minute)	Corrected Count Rate (counts/minute)
0	615	600
20	375	360
40	231	216
60	153	138
80	105	90

Explain how the corrected count rate is calculated and use the data to estimate the half-life of Element Z. [4]

(c) Suggest two safety precautions that the technician should take when handling radioactive materials. [2]

Worked Solution:

(a)

1. Background radiation is the radiation that is present all around us. [definition of background radiation]

2. Two sources of background radiation are cosmic rays and rocks in the ground. [source 1]

3. Another source of background radiation is radon gas in the air. [source 2]

How to earn full marks:

• Must mention that background radiation is present all around us.
• Must give two valid sources of background radiation (e.g., cosmic rays, rocks in the ground, radon gas, medical sources, nuclear weapons testing).

(b)

1. The corrected count rate is calculated by subtracting the background count rate from the measured count rate. [calculation explanation]

2. At time 0, the corrected count rate is 600 counts/minute. After one half-life, the count rate will be half of this, 300 counts/minute. [initial count rate]

3. Looking at the table, 300 counts/minute occurs roughly between 20 minutes and 40 minutes. Interpolating, the half-life is approximately 33 minutes. [first half-life estimate]

4. After two half-lives, the count rate will be half of 300, which is 150 counts/minute. This corresponds to roughly 60 minutes + 6 minutes = 66 minutes in the data. Therefore, the half-life is approximately 33 minutes. [second half-life estimate]

$\boxed{Half-life = 33 \space minutes}$

How to earn full marks:

• Must explain that the background count rate is subtracted from the measured count rate.
• Must identify that the initial corrected count rate is 600 counts/minute.
• Must show working by using the table to estimate the time for the count rate to halve.
• Must state the final answer with the correct unit (minutes). (Acceptable range 32-34 minutes).

(c)

1. The technician should wear protective clothing, such as a lab coat and gloves. [precaution 1]

2. The technician should use tongs to handle the radioactive material. [precaution 2]

How to earn full marks:

• Must suggest two valid safety precautions (e.g., wear protective clothing, use tongs to handle the material, store the material in a lead-lined container, limit the time spent near the material, use a radiation monitor).

Common Pitfall: When calculating half-life from count rate data, always remember to subtract the background count rate first to get the corrected count rate. Forgetting this step will lead to an incorrect half-life calculation.