Nuclear equations and decay products

What you'll learn

This revision guide covers nuclear equations and decay products as required by the AQA GCSE Physics specification. You'll learn how to write and balance nuclear equations for alpha, beta and gamma decay, understand what happens to the nucleus during each type of radioactive decay, and be able to predict the products formed. This topic is essential for Paper 2 and frequently appears in 4-6 mark questions.

Key terms and definitions

Alpha particle (α) — a helium nucleus consisting of 2 protons and 2 neutrons, represented as ⁴₂He or ⁴₂α

Beta particle (β) — a high-speed electron emitted from the nucleus when a neutron converts to a proton, represented as ⁰₋₁e or ⁰₋₁β

Gamma ray (γ) — electromagnetic radiation emitted from an unstable nucleus, with no mass or charge

Mass number (A) — the total number of protons and neutrons in a nucleus, written as the superscript in nuclear notation

Atomic number (Z) — the number of protons in a nucleus, written as the subscript in nuclear notation, which determines the element

Isotope — atoms of the same element with the same number of protons but different numbers of neutrons

Nuclear equation — a symbolic representation of a radioactive decay process showing the parent nucleus, decay product(s) and radiation emitted

Decay product — the new nucleus formed after radioactive decay has occurred

Core concepts

Nuclear notation and structure

All nuclei are represented using standard notation: ᴬ𝚉X, where:

• X is the chemical symbol of the element
• A is the mass number (top number)
• Z is the atomic number (bottom number)

For example, uranium-238 is written as ²³⁸₉₂U, showing:

• 92 protons (atomic number)
• 238 total nucleons (protons + neutrons)
• Therefore 238 - 92 = 146 neutrons

The number of neutrons can always be calculated by subtracting the atomic number from the mass number (N = A - Z).

When writing nuclear equations, both the mass numbers and atomic numbers must balance on both sides of the equation. This conservation principle is fundamental to all nuclear processes.

Alpha decay

Alpha decay occurs when an unstable nucleus emits an alpha particle. The alpha particle carries away 2 protons and 2 neutrons.

Effects on the parent nucleus:

• Mass number decreases by 4
• Atomic number decreases by 2
• The element changes to one that is 2 places lower in the periodic table

General equation for alpha decay: ᴬ𝚉X → ᴬ⁻⁴𝚉₋₂Y + ⁴₂α

The alpha particle can be written as ⁴₂He or ⁴₂α (both are acceptable in exams).

Example: Radium-226 undergoes alpha decay to form radon: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂α

Check the equation balances:

• Mass numbers: 226 = 222 + 4 ✓
• Atomic numbers: 88 = 86 + 2 ✓

Alpha decay typically occurs in very heavy nuclei (with atomic numbers greater than 82) that have too many nucleons to be stable.

Beta-minus decay

Beta-minus decay (usually just called beta decay at GCSE) occurs when a neutron in the nucleus converts into a proton, releasing a beta particle (electron) and an antineutrino (the antineutrino is beyond GCSE scope but may be mentioned).

Effects on the parent nucleus:

• Mass number stays the same (neutron converted to proton, total nucleons unchanged)
• Atomic number increases by 1
• The element changes to one that is 1 place higher in the periodic table

General equation for beta decay: ᴬ𝚉X → ᴬ𝚉₊₁Y + ⁰₋₁β

The beta particle is represented as ⁰₋₁e or ⁰₋₁β.

Example: Carbon-14 undergoes beta decay to form nitrogen: ¹⁴₆C → ¹⁴₇N + ⁰₋₁β

Check the equation balances:

• Mass numbers: 14 = 14 + 0 ✓
• Atomic numbers: 6 = 7 + (-1) ✓

Beta decay occurs in nuclei that have too many neutrons relative to protons. By converting a neutron to a proton, the nucleus moves toward a more stable neutron-to-proton ratio.

Gamma emission

Gamma emission occurs when an excited nucleus releases energy in the form of electromagnetic radiation. Gamma rays have no mass and no charge.

Effects on the nucleus:

• Mass number stays the same
• Atomic number stays the same
• The element remains unchanged
• The nucleus moves from an excited state to a lower energy state

General representation: ᴬ𝚉X* → ᴬ𝚉X + γ

The asterisk (*) indicates an excited nuclear state.

Gamma emission often accompanies alpha or beta decay. After emitting an alpha or beta particle, the daughter nucleus is often left in an excited state and subsequently emits gamma radiation to lose excess energy.

Example combined decay: Cobalt-60 undergoes beta decay to nickel-60, which then emits gamma radiation: ⁶⁰₂₇Co → ⁶⁰₂₈Ni + ⁰₋₁β (followed by) ⁶⁰₂₈Ni* → ⁶⁰₂₈Ni + γ

Since gamma emission doesn't change the composition of the nucleus, it's sometimes omitted from simplified nuclear equations at GCSE level.

Balancing nuclear equations

To balance any nuclear equation, follow these rules:

1. The sum of mass numbers on the left must equal the sum on the right
2. The sum of atomic numbers on the left must equal the sum on the right

When you're asked to complete a nuclear equation:

Step 1: Write down what you know, using the notation ᴬ𝚉X for unknown nuclei

Step 2: Calculate the missing mass number by ensuring mass numbers balance

Step 3: Calculate the missing atomic number by ensuring atomic numbers balance

Step 4: Use the periodic table to identify the element from its atomic number

Step 5: Check your answer by verifying both numbers balance

This systematic approach works for all decay types and prevents common errors.

Decay chains and stability

Some radioactive isotopes undergo multiple decay events before reaching a stable nucleus. This is called a decay chain or decay series.

Example: Uranium-238 decay chain (simplified)

• ²³⁸₉₂U undergoes alpha decay → ²³⁴₉₀Th
• ²³⁴₉₀Th undergoes beta decay → ²³⁴₉₁Pa
• ²³⁴₉₁Pa undergoes beta decay → ²³⁴₉₂U
• This continues through multiple steps until stable ²⁰⁶₈₂Pb is formed

Each step in the chain can be represented by a nuclear equation. At GCSE, you need to be able to write equations for individual steps, not necessarily remember entire decay chains.

Nuclei decay because they are unstable. Factors affecting stability include:

• Very large nuclei (Z > 82) are always unstable
• Nuclei with significantly unequal numbers of protons and neutrons tend to be unstable
• Certain "magic numbers" of nucleons create extra stability (beyond GCSE scope in detail)

Worked examples

Example 1: Completing an alpha decay equation

Question: Polonium-214 undergoes alpha decay. Complete the nuclear equation:

²¹⁴₈₄Po → ____ + ⁴₂α

Solution:

Step 1: Set up the equation with unknowns ²¹⁴₈₄Po → ᴬ𝚉X + ⁴₂α

Step 2: Calculate mass number A Left side: 214 Right side: A + 4 Therefore: 214 = A + 4, so A = 210

Step 3: Calculate atomic number Z Left side: 84 Right side: Z + 2 Therefore: 84 = Z + 2, so Z = 82

Step 4: Identify element with Z = 82 Using the periodic table: Z = 82 is lead (Pb)

Step 5: Write complete answer ²¹⁴₈₄Po → ²¹⁰₈₂Pb + ⁴₂α

Mark scheme: [1 mark for correct mass number, 1 mark for correct atomic number OR element symbol]

Example 2: Identifying decay type from equation

Question: The equation below represents a radioactive decay:

⁹⁰₃₈Sr → ⁹⁰₃₉Y + ⁰₋₁β

(a) State the type of radioactive decay shown. [1 mark] (b) Explain what happens inside the nucleus during this decay. [2 marks]

Solution:

(a) Beta decay (or beta-minus decay) [1]

(b) Explanation:

• A neutron in the strontium nucleus changes into a proton [1]
• An electron (beta particle) is emitted from the nucleus [1]

Mark scheme notes: For part (b), accept "neutron converts to proton" or equivalent. The answer must refer to changes inside the nucleus, not just emission of beta particle.

Example 3: Multi-step decay problem

Question: Radium-226 (²²⁶₈₈Ra) decays by alpha emission to form radon. The radon then decays by alpha emission.

(a) Write a nuclear equation for the first decay. [2 marks] (b) Write a nuclear equation for the second decay. [2 marks] (c) Calculate the total change in mass number after both decays. [1 mark]

Solution:

(a) ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂α [2] (Mass number and atomic number both correct for 2 marks; 1 mark if only one correct)

(b) ²²²₈₆Rn → ²¹⁸₈₄Po + ⁴₂α [2] (Element must be identified as polonium from Z = 84)

(c) Total decrease = 4 + 4 = 8 [1] (Alternative method: 226 - 218 = 8)

Common mistakes and how to avoid them

• Confusing mass number and atomic number positions — Remember: mass number is always on TOP (like "mass is massive, so it's bigger and goes higher"), atomic number on bottom. Write ᴬ𝚉X, not 𝚉ᴬX.

• Getting the charge on beta particles wrong — Beta particles are electrons with charge -1, so they're written as ⁰₋₁β or ⁰₋₁e. Don't write ⁰₊₁β (that would be a positron, not tested at GCSE) or ⁰₁β (missing the negative sign).

• Thinking the element stays the same in alpha or beta decay — Alpha decay: element moves 2 places LEFT in periodic table. Beta decay: element moves 1 place RIGHT. Only gamma emission leaves the element unchanged.

• Forgetting to check both mass AND atomic numbers balance — Always verify your answer by checking totals on both sides. If either doesn't balance, you've made an error.

• Writing gamma radiation as ¹₀γ or ⁰₁γ — Gamma rays have no mass and no charge, so there are no numbers needed: just write γ. If you must write it in full form, use ⁰₀γ.

• Confusing the decay product with the radiation emitted — The decay product is the new nucleus formed (e.g., radon from radium), while the radiation is what's emitted (alpha, beta or gamma). Questions may ask for either or both.

Exam technique for "Nuclear equations and decay products"

• "Complete the equation" questions — Show your working by writing the calculation for mass number and atomic number separately. This can earn method marks even if your final answer is wrong. Always use the periodic table to check which element corresponds to your calculated atomic number.

• Command words matter — "State" means give a brief answer without explanation (e.g., "alpha decay"). "Describe" requires you to say what happens (e.g., "the nucleus emits an alpha particle consisting of 2 protons and 2 neutrons"). "Explain" needs reasoning (e.g., "alpha decay occurs because the nucleus is too large to be stable").

• Mark allocation guides detail required — A 1-mark question needs one clear point. A 2-mark question typically needs two distinct points or one point with development. For nuclear equations, 2 marks usually means 1 for mass number, 1 for atomic number.

• Use correct nuclear notation throughout — Even if the question uses simple notation, gain credit by using full nuclear notation (ᴬ𝚉X) in your answer. Make your numbers clearly distinguishable — write them large enough and in the correct positions.

Quick revision summary

Nuclear equations represent radioactive decay using standard notation (ᴬ𝚉X). Alpha decay decreases mass number by 4 and atomic number by 2, emitting ⁴₂α. Beta decay keeps mass number constant but increases atomic number by 1, emitting ⁰₋₁β when a neutron converts to a proton. Gamma emission (γ) releases energy without changing mass or atomic numbers. Always ensure both mass numbers and atomic numbers balance on each side of the equation. Use the periodic table to identify elements from their atomic numbers.