Nuclear equations — AQA GCSE Physics
Test yourself on Nuclear equations with AQA GCSE practice questions.
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Nuclear equations explained
A nuclear equation shows what a nucleus turns into when it decays.
Read the full explanation
The original nucleus goes on the left, and the new nucleus plus the emitted particle go on the right, joined by an arrow. Each nucleus is written with its mass number above and its atomic number below the chemical symbol, as in ²³⁸₉₂U. Two conservation rules govern the equation: the total mass number on the right equals the mass number on the left, and the total atomic number on the right equals the atomic number on the left, because nucleon number and charge are both conserved. Those two running totals are all you need to complete any equation the exam sets.
In a nuclear equation an alpha particle may be represented by the symbol: and a beta particle by the symbol: 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: So alpha decay causes both the mass and charge of the nucleus to decrease.
In an equation the alpha particle is written ⁴₂He, because it is two protons and two neutrons, and the beta particle is written ⁰₋₁e, because it is an electron with negligible mass and a charge of -1. In alpha decay the nucleus loses two protons and two neutrons, so its mass number falls by 4 and its atomic number falls by 2: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Both numbers decrease, which is what distinguishes alpha decay at a glance. Because the atomic number has changed, the daughter is a different element, sitting two places earlier in the periodic table. Check the equation by adding each column: 234 + 4 = 238 and 90 + 2 = 92.
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 inside the nucleus turns into a proton, and the electron created in the process is ejected as the beta particle. Count the nucleons: one neutron has gone but one proton has appeared, so the total is unchanged and the mass number stays the same. Count the charge: there is now one more proton, so the atomic number rises by one and the daughter is the next element along in the periodic table. For example ¹⁴₆C → ¹⁴₇N + ⁰₋₁e, where 14 = 14 + 0 and 7 + (-1) = 6. A rise of one in the proton number with no change in mass number is the signature that identifies a decay as beta.
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.
Work through a decay equation in a fixed order. Copy the original nucleus with both its numbers. Write the emitted particle in full, ⁴₂He for alpha or ⁰₋₁e for beta. Then use the two conservation rules to fill in the daughter nucleus. Alpha: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He, where 222 + 4 = 226 and 86 + 2 = 88. Beta: ²¹⁴₈₂Pb → ²¹⁴₈₃Bi + ⁰₋₁e, where 214 + 0 = 214 and 83 + (-1) = 82. The same method run backwards identifies the radiation emitted: if the atomic number rose by one and the mass number held still, the decay was beta. Single decay means one particle, so do not add a second.
This is limited to balancing the atomic numbers and mass numbers.
The examinable skill is arithmetic, not nuclear theory. You balance two totals and nothing else: the mass numbers across the equation and the atomic numbers across the equation. Neutrinos, binding energy, decay chains and the details of what holds a nucleus together are all outside this specification. Treat the emitted particle as a full member of the totals, with its own two numbers, ⁴₂He or ⁰₋₁e, and remember that the -1 on a beta particle has to be included when the atomic numbers are added. A gamma ray contributes zero to both totals, so it never changes the balance of an equation it appears in.
The emission of a gamma ray does not cause the mass or the charge of the nucleus to change.
A gamma ray is electromagnetic radiation, not a particle of matter. It has no mass and no charge, so when a nucleus emits one it loses no nucleons and no protons: the mass number stays the same and the atomic number stays the same, and the nucleus remains the same element. What changes is energy. The nucleus was left in an excited, higher-energy arrangement, usually just after emitting an alpha or a beta particle, and emitting the gamma ray carries that surplus energy away and leaves the nucleus more stable. In a balanced equation a gamma ray therefore contributes 0 to the mass number total and 0 to the atomic number total.
Your focus
- Write a nuclear equation with the original nucleus, the new nucleus and the emitted particle in the correct positions.
- State the two quantities that must balance on both sides of a nuclear equation.
- Check a given nuclear equation and say whether it balances, explaining any error.
Show all 18 objectives
- Write the nuclide symbols for an alpha particle and a beta particle.
- Complete an alpha decay equation by reducing the mass number by 4 and the atomic number by 2.
- Check that a completed alpha decay equation balances by adding each column.
- Complete a beta decay equation, keeping the mass number the same and raising the atomic number by one.
- Explain why the mass number does not change when a beta particle is emitted.
- Determine from a pair of nuclide symbols whether the decay between them was alpha or beta.
- Complete a nuclear equation for a single alpha decay, filling in both missing numbers.
- Complete a nuclear equation for a single beta decay and show that both columns balance.
- Determine the type of radiation emitted from the changes in mass number and atomic number, giving a reason.
- Complete the equation for a krypton nucleus decaying into a rubidium nucleus by beta emission by writing the missing mass number and atomic number.
- Include the emitted particle's mass number and atomic number correctly in the totals, including the -1 of a beta particle.
- Identify an error in a nuclear equation that does not balance and correct it.
- Determine, from a decay equation in which neither the mass number nor the atomic number changes, that a gamma ray was emitted, and give a reason.
- Explain why gamma emission leaves the element unchanged, referring to the properties of a gamma ray.
- Complete a nuclear equation that includes a gamma ray and show that both totals still balance.
Nuclear equations exam tips
Marking Points
- one mark for writing the original nucleus on the left and the new nucleus plus emitted particle on the right
- one mark for using the nuclide notation with mass number above the atomic number
- one mark for stating that the total mass number is the same on both sides
- one mark for stating that the total atomic number, and so the charge, is the same on both sides
- one mark for representing the alpha particle as ⁴₂He and the beta particle as ⁰₋₁e
- one mark for reducing the mass number of the nucleus by 4 in alpha decay
- one mark for reducing the atomic number of the nucleus by 2 in alpha decay
- one mark for a completed equation in which both the mass numbers and the atomic numbers balance
- one mark for stating that the mass number is unchanged in beta decay
- one mark for stating that the atomic number increases by one
- one mark for explaining that a neutron in the nucleus changes into a proton
- one mark for identifying a decay as beta because the proton number has gone up by one
- one mark for each correct missing mass number in the completed equation
- one mark for each correct missing atomic number in the completed equation
- one mark for writing the emitted particle with its own mass number and atomic number, ⁴₂He or ⁰₋₁e
- one mark for naming the type of decay from the way the numbers changed, for example beta because the proton number rose by one
- one mark for the total mass number on the right equalling the mass number on the left
- one mark for the total atomic number on the right equalling the atomic number on the left
- one mark for including the emitted particle's own numbers in both totals
- one mark for a completed equation with every missing value filled in
- one mark for stating that the mass number of the nucleus is unchanged
- one mark for stating that the atomic number, and so the charge, is unchanged
- one mark for explaining this because a gamma ray has no mass and no charge
- one mark for stating that the nucleus loses energy and becomes more stable
Examiner Tips
- 💡Write the two totals in the margin, one for mass numbers and one for atomic numbers, before filling any gaps.
- 💡Check both totals at the end; each is usually worth a separate mark.
- 💡Keep the arrow pointing from the original nucleus to the products, never the other way.
- 💡Memorise the two symbols exactly; a wrong subscript loses the balancing marks that follow.
- 💡Subtract 4 and 2 as a single habit for alpha, then check the columns add up.
- 💡Alpha decay is the only common decay in which both numbers fall, which makes it easy to spot.
- 💡Remember the mass number is unchanged because a neutron is replaced by a proton, both of relative mass 1.
- 💡Use the -1 on the beta particle when you check the atomic number column; it must be included in the total.
- 💡If a question asks which radiation was emitted, compare the two atomic numbers first.
- 💡Fill in the emitted particle first; the daughter nucleus then follows from subtraction.
- 💡Set the numbers out in two columns so the totals can be checked at a glance.
- 💡Give the reason as well as the name when identifying a decay type, since the reason usually carries the second mark.
- 💡Two totals, two checks; do them both before moving on.
- 💡Never change a number the question has already printed.
- 💡If a gamma ray appears, write 0 above and 0 below it so the totals stay clear.
- 💡Answer in two halves: both numbers unchanged, and why, which is no mass and no charge.
- 💡Mention that gamma emission still makes the nucleus more stable, since it loses energy.
- 💡In an equation, write 0 above and 0 below the gamma symbol so the balance is obvious.
Common Mistakes
- writing the emitted particle on the same side as the original nucleus
- swapping the positions of the mass number and the atomic number
- balancing the mass numbers and leaving the atomic numbers unbalanced
- adding state symbols as though it were a chemical equation
- writing ⁴₂He correctly but forgetting to subtract 4 and 2 from the original nucleus
- taking 2 off the mass number and 4 off the atomic number
- giving the beta particle a mass number of 1 instead of 0
- writing the charge on the beta particle as +1 rather than -1
- reducing the mass number by one because an electron has been emitted
- decreasing the atomic number instead of increasing it
- saying the emitted electron came from an electron shell outside the nucleus
- claiming the number of neutrons in the nucleus is unchanged
- leaving the emitted particle out of the equation altogether
- balancing the mass numbers and forgetting to balance the atomic numbers
- writing the word alpha in place of the symbol when the question asks for an equation
- showing both an alpha and a beta particle when the question specifies a single decay
- adding a neutrino or other particle that the specification does not require
- balancing the equation by altering the original nucleus instead of the products
- ignoring the -1 on a beta particle when adding the atomic numbers
- subtracting the atomic number from the mass number by mistake while checking
- reducing the mass number because energy has left the nucleus
- saying the nucleus becomes a different element after gamma emission
- describing a gamma ray as a particle emitted from the electron shells
- assuming a nucleus that emits gamma must also emit an alpha or beta particle in the same step