Nuclear equations — AQA GCSE Combined Science
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Nuclear equations explained
A nuclear equation is a symbolic summary of a radioactive decay process.
Read the full explanation
It shows the starting nucleus on the left and the products on the right, each written with its chemical symbol, mass number as a superscript and atomic number as a subscript. For alpha decay, the nucleus loses an alpha particle, so the mass number decreases by 4 and the atomic number decreases by 2. For beta decay, a neutron changes into a proton and an electron, so the mass number stays the same while the atomic number increases by 1. For gamma emission, the nucleus loses energy without changing its mass or atomic number. In every valid nuclear equation, the total mass numbers and total atomic numbers must balance on both sides. For example, americium-241 decays by alpha emission to neptunium-237: ²⁴¹₉₅Am → ⁴₂He + ²³⁷₉₃Np. Checking 241 = 4 + 237 and 95 = 2 + 93 confirms the equation is balanced.
In a nuclear equation an alpha particle may be represented by the symbol:
An alpha particle is a helium nucleus, so in a nuclear equation it is represented by the symbol ⁴₂He or ⁴₂α. The superscript 4 is the mass number, showing that the alpha particle contains four nucleons: two protons and two neutrons. The subscript 2 is the atomic number, showing that it contains two protons. Because an alpha particle has a 2⁺ charge, it is sometimes written as ⁴₂He²⁺, but in nuclear equations the charge is not usually shown. When an alpha particle is emitted, the parent nucleus loses four units of mass number and two units of atomic number. For example, radium-226 decays to radon-222: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He. The symbol ⁴₂He is preferred in AQA GCSE Combined Science because it shows the helium nucleus clearly, while ⁴₂α is also accepted.
and a beta particle by the symbol:
A beta particle is a fast-moving electron emitted from a nucleus during beta decay. In nuclear equations, it is written with the symbol β or e, carrying a mass number of 0 and an atomic number of −1. The top number is 0 because an electron has negligible mass; the bottom number is −1 because it has a single negative charge. For example, carbon-14 decays to nitrogen-14 and a beta particle: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e (or ⁰₋₁β). The nucleon numbers balance (14 = 14 + 0) and the proton numbers balance (6 = 7 + (−1)). Writing the beta particle correctly as ⁰₋₁e or ⁰₋₁β is essential when balancing nuclear equations, because its 0 and −1 values explain why the mass number stays the same while the atomic number increases by 1.
The emission of the different types of nuclear radiation may cause a change in the mass and /or the charge of the nucleus. For example:
When a nucleus emits nuclear radiation, its mass number and atomic number can change. Alpha emission removes two protons and two neutrons, so the mass number decreases by 4 and the atomic number decreases by 2: for example, ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Beta emission converts a neutron into a proton and emits an electron, so the mass number stays the same but the atomic number increases by 1: for example, ¹⁴₆C → ¹⁴₇N + ⁰₋₁β. Gamma emission releases energy without changing either the mass number or the atomic number. Nuclear equations must balance in both mass number and atomic number, so the emitted particle's symbol explains exactly how the nucleus changes.
So alpha decay causes both the mass and charge of the nucleus to decrease.
An alpha particle is a helium nucleus: two protons and two neutrons, so it has mass number 4 and charge 2⁺. When an unstable nucleus emits an alpha particle, it loses those two protons and two neutrons, so its mass number falls by 4 and its proton number falls by 2. For example, uranium-238 decays to thorium-234: ²³⁸₉₂U → ⁴₂He + ²³⁴₉₀Th. The mass number decreases because nucleons leave the nucleus, and the charge decreases because two positive protons leave. The nucleus becomes a different element because its proton number changes. Alpha emission is common in very heavy nuclei and is stopped by a few centimetres of air or a sheet of paper.
So beta decay does not cause the mass of the nucleus to change but does cause the charge of the nucleus to increase.
In beta decay, a neutron in the nucleus changes into a proton and emits a beta particle, which is a fast-moving electron. The electron has negligible mass compared with nucleons, so the mass number stays the same. However, the nucleus gains one proton, so its proton number increases by 1 and its charge increases by 1 unit. For example, carbon-14 decays to nitrogen-14: ¹⁴₆C → ⁰₋₁e + ¹⁴₇N. The beta particle is written with mass number 0 and charge 1⁻. Because the proton number changes, the nucleus becomes a different element. Beta emission is common in nuclei with too many neutrons and is stopped by a few millimetres of aluminium.
Students should be able to use the names and symbols of common nuclei and particles to write balanced equations that show single alpha (α) and beta (β) decay. This is limited to balancing the atomic numbers and mass numbers. The identification of daughter elements from such decays is not required.
Nuclear equations represent changes in the nucleus during radioactive decay. You must use the standard symbols for common nuclei and particles, such as ²³⁸₉₂U for uranium-238, ⁴₂α for an alpha particle and ⁰₋₁β for a beta particle. In every balanced equation, the total mass number (top number) and the total atomic number (bottom number) must be the same on both sides. For alpha decay, the parent loses 4 from its mass number and 2 from its atomic number. For beta decay, the mass number is unchanged and the atomic number increases by 1. You are not required to name the daughter element; balancing the numbers is sufficient. For example, ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂α is balanced because 238 = 234 + 4 and 92 = 90 + 2.
The emission of a gamma ray does not cause the mass or the charge of the nucleus to change.
Gamma emission is a way for an unstable nucleus to lose surplus energy without altering what the nucleus is. A gamma ray is a high-energy electromagnetic wave, so it carries energy away but has no mass and no charge. Because the proton number and the nucleon number are untouched, the emitting nuclide keeps the same atomic number and mass number, and the nuclear equation balances with the same symbol on both sides, often written with a gamma term such as γ. For example, technetium-99m emits a gamma ray to become technetium-99: the mass number stays 99 and the atomic number stays 43. This contrasts with alpha emission, which lowers the mass number by 4 and the atomic number by 2, and beta emission, which leaves the mass number unchanged but raises the atomic number by 1.
Your focus
- Write a balanced nuclear equation for a given alpha or beta decay.
- Identify the daughter nuclide produced when a named parent nuclide undergoes alpha or beta decay.
- Check that mass numbers and atomic numbers are conserved on both sides of a nuclear equation.
Show all 24 objectives
- State the symbol used to represent an alpha particle in a nuclear equation.
- Explain the meaning of the mass number and atomic number in the symbol ⁴₂He or ⁴₂α.
- Use the alpha particle symbol correctly when writing a balanced nuclear equation for alpha decay.
- Write the symbol for a beta particle as ⁰₋₁e or ⁰₋₁β in a nuclear equation.
- Explain why the mass number of a beta particle is 0 and its atomic number is −1.
- Balance a nuclear equation for beta decay by conserving mass number and atomic number.
- Describe how alpha, beta and gamma emission each affect the mass number and atomic number of a nucleus.
- Write and balance nuclear equations for alpha and beta decay.
- Use conservation of mass number and atomic number to identify the products of a nuclear change.
- State that an alpha particle is a helium nucleus with mass number 4 and charge 2⁺.
- Explain why alpha decay decreases the mass number by 4 and the proton number by 2.
- Balance a nuclear equation for alpha decay using mass numbers and proton numbers.
- State that beta decay converts a neutron into a proton and an electron.
- Explain why beta decay leaves the mass number unchanged but increases the proton number by 1.
- Balance a nuclear equation for beta decay using mass numbers and proton numbers.
- Use standard symbols to represent common nuclei, alpha particles and beta particles in nuclear equations.
- Write balanced equations for single alpha and beta decay by conserving mass number and atomic number.
- Deduce the missing nucleus in a decay equation without needing to identify the daughter element by name.
- Describe gamma emission as the loss of energy from an excited nucleus without loss of particles.
- Write and balance nuclear equations for gamma emission, keeping mass number and atomic number unchanged.
- Distinguish gamma emission from alpha and beta emission in terms of changes to the nucleus.
Nuclear equations exam tips
Marking Points
- A nuclear equation represents a radioactive decay by showing the parent nucleus and the emitted particle or radiation together with the daughter nucleus.
- Each nuclide is written with its chemical symbol, a mass number as a superscript and an atomic number as a subscript.
- In alpha decay, the mass number decreases by 4 and the atomic number decreases by 2 because an alpha particle (⁴₂He or ⁴₂α) is emitted.
- In beta decay, the mass number is unchanged and the atomic number increases by 1 because a neutron changes into a proton and an emitted beta particle (⁰₋₁e or ⁰₋₁β).
- In gamma emission, the mass number and atomic number are unchanged because gamma radiation is electromagnetic energy released from the nucleus.
- A balanced nuclear equation has equal totals of mass number and equal totals of atomic number on both sides.
- An alpha particle is a helium nucleus and is represented by the symbol ⁴₂He or ⁴₂α.
- The superscript 4 is the mass number and shows that the alpha particle contains four nucleons.
- The subscript 2 is the atomic number and shows that the alpha particle contains two protons.
- An alpha particle has a 2⁺ charge because it contains two protons and two neutrons, but the charge is not usually shown in a nuclear equation.
- When an alpha particle is emitted, the parent nucleus loses four units of mass number and two units of atomic number.
- A beta particle is represented by the symbol β or e with a mass number of 0 written as a superscript and an atomic number of −1 written as a subscript, for example ⁰₋₁e or ⁰₋₁β.
- The mass number of 0 shows that the emitted electron has negligible mass compared with protons and neutrons, so the total nucleon number of the nucleus is unchanged by beta emission.
- The atomic number of −1 shows that the beta particle carries a single negative charge, which balances the increase of 1 in the nuclear charge when a neutron changes into a proton.
- In a balanced nuclear equation, the sum of the mass numbers on the left equals the sum on the right, and the sum of the atomic numbers on the left equals the sum on the right.
- For example, in ¹⁴₆C → ¹⁴₇N + ⁰₋₁e, the mass numbers give 14 = 14 + 0 and the atomic numbers give 6 = 7 + (−1).
- Alpha emission decreases the mass number by 4 and the atomic number by 2 because an alpha particle contains two protons and two neutrons.
- Beta emission leaves the mass number unchanged but increases the atomic number by 1 because a neutron changes into a proton and an electron.
- Gamma emission does not change the mass number or the atomic number because it is electromagnetic radiation carrying energy only.
- In every nuclear equation, the total mass number before the change equals the total mass number after, and the total atomic number before equals the total after.
- For example, in ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He, the mass numbers give 238 = 234 + 4 and the atomic numbers give 92 = 90 + 2.
- An alpha particle consists of 2 protons and 2 neutrons, so it has mass number 4 and charge 2⁺.
- Emitting an alpha particle removes 2 protons and 2 neutrons from the nucleus.
- The mass number of the nucleus decreases by 4 because 4 nucleons are lost.
- The proton number (atomic number) decreases by 2, so the nuclear charge decreases by 2 units.
- The nucleus changes into a different element because its proton number changes.
- In a nuclear equation, the total mass number and total proton number must balance on both sides.
- A beta particle is a fast-moving electron emitted from the nucleus.
- In beta decay, a neutron changes into a proton and an electron.
- The mass number does not change because a neutron is replaced by a proton, so the number of nucleons stays the same.
- The proton number increases by 1, so the nuclear charge increases by 1 unit.
- The beta particle has mass number 0 and charge 1⁻ in a nuclear equation.
- The nucleus becomes a different element because its proton number increases by 1.
- Use correct symbols for common nuclei, showing mass number as a superscript and atomic number as a subscript.
- Represent an alpha particle as ⁴₂α and a beta particle as ⁰₋₁β.
- Balance mass numbers so that the sum before decay equals the sum after decay.
- Balance atomic numbers so that the sum before decay equals the sum after decay.
- Write equations for single alpha decay by reducing the parent mass number by 4 and atomic number by 2.
- Write equations for single beta decay by keeping the mass number the same and increasing the atomic number by 1.
- Complete an equation by deducing the missing nucleus from the conservation of mass number and atomic number.
- States that a gamma ray is electromagnetic radiation with no mass and no electric charge.
- Explains that gamma emission changes only the energy of the nucleus, not its proton number or nucleon number.
- Applies the rule to a nuclear equation by keeping the same nuclide symbol on both sides, for example Tc-99m → Tc-99 + γ.
- Contrasts gamma emission with alpha emission, which reduces mass number by 4 and atomic number by 2, and beta emission, which raises atomic number by 1 while keeping mass number the same.
- Uses the terms proton number and nucleon number correctly when justifying why the nucleus is unchanged.
Examiner Tips
- 💡Write nuclear symbols clearly with the mass number directly above the atomic number so the examiner can see both values.
- 💡After writing any nuclear equation, spend a moment checking the mass-number and atomic-number totals on each side.
- 💡If a question gives the parent nuclide and the type of decay, work out the daughter nuclide by subtracting or adding the correct numbers before writing the full equation.
- 💡Use the correct symbol for an alpha particle, ⁴₂He or ⁴₂α, and for a beta particle, ⁰₋₁e or ⁰₋₁β, rather than writing words such as 'alpha' or 'beta' alone.
- 💡Learn the symbol ⁴₂He or ⁴₂α for an alpha particle and ⁰₋₁e or ⁰₋₁β for a beta particle so you can recognise them quickly.
- 💡When an equation includes an alpha particle, check that the mass numbers and atomic numbers balance on both sides.
- 💡If a question asks for the symbol of an alpha particle, write ⁴₂He or ⁴₂α rather than just the word 'alpha'.
- 💡Remember that the top number is the mass number and the bottom number is the atomic number; this helps you avoid swapping them.
- 💡When balancing a nuclear equation, write the mass numbers as a top row and the atomic numbers as a bottom row, then check each row separately.
- 💡Remember that beta decay leaves the mass number unchanged but increases the atomic number by 1, so the new element is one place to the right in the periodic table.
- 💡Practise writing the beta symbol with a superscript 0 and a subscript −1 (⁰₋₁e or ⁰₋₁β), and make sure the minus sign is clearly attached to the 1.
- 💡Use a two-row table for mass numbers and atomic numbers when balancing nuclear equations, and check each row separately.
- 💡Link the type of radiation to the change: alpha changes mass by 4 and charge by 2, beta changes charge by 1 only, gamma changes neither.
- 💡After balancing, identify the new element by using the atomic number and the periodic table, and check that the symbol matches the proton number.
- 💡Write the nuclear equation and check that mass numbers and proton numbers balance on both sides.
- 💡State clearly that the proton number decreases by 2, so the charge decreases by 2 units.
- 💡Use the term nucleon when explaining why mass number falls by 4.
- 💡Check that the mass number is the same on both sides of a beta decay equation.
- 💡Show the proton number increasing by 1 from reactant to product.
- 💡Remember that beta particles are electrons, so their charge is 1⁻ and their mass number is 0.
- 💡Draw a vertical line between the two sides of the equation and compare the top totals and bottom totals separately.
- 💡If a nucleus is missing, use the difference between the two sides to find its mass number and atomic number.
- 💡Write the alpha and beta symbols with their mass and atomic numbers so the balancing is visible.
- 💡Do not waste time identifying element names unless the question explicitly asks for them.
- 💡When asked to complete a nuclear equation, check that the total mass number and total atomic number are equal on both sides before writing the gamma symbol.
- 💡If a question asks why the nucleus is unchanged, refer explicitly to gamma having zero mass and zero charge rather than saying it is 'just energy'.
- 💡Use the metastable form, such as Tc-99m, when a nucleus emits gamma to reach a lower energy state, and explain that m indicates a higher-energy state of the same nuclide.
Common Mistakes
- Writing the mass number as a subscript and the atomic number as a superscript. Correction: the mass number is the superscript and the atomic number is the subscript, for example ²³⁸₉₂U.
- Forgetting to balance mass numbers and atomic numbers across the arrow. Correction: always check that the sum of mass numbers on the left equals the sum on the right, and do the same for atomic numbers.
- Treating beta decay as if the mass number decreases. Correction: in beta decay the mass number stays the same because a neutron becomes a proton, and the atomic number increases by 1.
- Omitting the emitted particle from the equation. Correction: include the alpha particle, beta particle or gamma radiation as a product so the equation represents the full decay.
- Writing the alpha particle as ²₄He or ²₄α, which swaps the mass number and atomic number. Correction: the mass number is the superscript 4 and the atomic number is the subscript 2, so write ⁴₂He or ⁴₂α.
- Using the symbol ⁰₋₁e for an alpha particle. Correction: ⁰₋₁e represents a beta particle, while an alpha particle is ⁴₂He or ⁴₂α.
- Thinking that an alpha particle has a 2⁻ charge. Correction: an alpha particle contains two protons and two neutrons, so it has a 2⁺ charge.
- Forgetting to include the alpha particle as a product in a decay equation. Correction: write the alpha particle on the right-hand side of the arrow together with the daughter nucleus.
- Writing the beta particle as ⁰₊₁e or ⁰₁β: the error is giving it a positive or zero charge; the correction is to use ⁰₋₁e or ⁰₋₁β because a beta particle is an electron with charge −1.
- Omitting the beta particle from the products of a nuclear equation: the error is an unbalanced equation; the correction is to include ⁰₋₁e so that both mass numbers and atomic numbers balance.
- Confusing beta emission with alpha emission and writing ⁴₂He instead: the error is using the wrong particle; the correction is to check whether the atomic number increases by 1 (beta) or decreases by 2 (alpha) and use the matching symbol.
- Thinking that beta emission changes the mass number: the error is assuming a particle is lost from the nucleus; the correction is that the mass number stays the same because a neutron is replaced by a proton and the emitted electron has negligible mass.
- Forgetting to change the atomic number after alpha emission: the error is leaving the proton number unchanged; the correction is to subtract 2 from the atomic number because two protons are lost.
- Treating gamma emission as if it changes the nucleus: the error is altering mass or atomic numbers; the correction is to leave both unchanged because gamma radiation carries away energy only.
- Thinking the mass number decreases by 2 rather than 4: correct this by counting both protons and neutrons in the alpha particle.
- Believing the charge stays the same because neutrons are also lost: correct this by noting only protons carry nuclear charge, and 2 protons are lost.
- Writing the alpha particle as ⁴₂He with the wrong charge or mass: correct this by remembering it is a helium nucleus, mass number 4 and charge 2⁺.
- Saying the mass number increases by 1: correct this by noting a neutron is replaced by a proton, so the total number of nucleons is unchanged.
- Thinking the charge decreases because an electron is emitted: correct this by tracking the proton number, which increases by 1.
- Writing the beta particle as ⁰₊₁e: correct this by using ⁰₋₁e, since the electron has charge 1⁻.
- Error: writing the mass number and atomic number the wrong way round on a symbol. Correction: mass number is the superscript and atomic number is the subscript.
- Error: balancing only the mass number and ignoring the atomic number. Correction: check both totals separately on each side of the equation.
- Error: giving the beta particle a mass number of 1. Correction: a beta particle has mass number 0 and atomic number −1.
- Error: trying to name the daughter element when the question only asks for a balanced equation. Correction: focus on the numbers; naming is not required.
- Thinking a gamma ray removes a particle from the nucleus; correct this by stressing that gamma is energy only, so no proton or neutron is lost.
- Writing a nuclear equation in which the mass number or atomic number changes after gamma emission; correct this by balancing both numbers and showing the same nuclide before and after.
- Confusing gamma emission with beta emission because both may follow a decay; correct this by noting that beta emission changes a neutron into a proton and so raises the atomic number, whereas gamma emission does not.