OCR GCSE Physics A: Nuclear structure, isotopes and decay equations (J249)

This guide teaches the structure of the nucleus, isotopes and decay equations for OCR GCSE Physics A (Gateway Science, J249), using the specification Version 5.0 (July 2026). It covers learning outcomes P6.1a to P6.1g of topic P6.1 Radioactive emissions. No statement in this group is printed in bold in the specification, so each is open to both Foundation and Higher Tier candidates. The other outcomes in P6.1 (ionisation and changes in electron energy levels, half-life and the penetrating power of each emission) are taught on separate pages and are not repeated here.

Related pages: revision notes and practice questions. Course links: OCR GCSE Physics hub, printable checklist and free 10-minute diagnostics. For the atom itself, see atomic model, atomic size and density.

What this unit covers

Outcome	What you must be able to do	Tier
P6.1a	Recall that nuclei contain protons and neutrons, and that each element’s nucleus has a characteristic positive charge	Both
P6.1b	Recall that atoms of the same element can differ in nuclear mass because they have different numbers of neutrons	Both
P6.1c	Use the conventional nuclear representation to relate the differences between isotopes (identities, charges and masses)	Both
P6.1d	Recall that some nuclei are unstable and may emit alpha particles, beta particles or neutrons, and electromagnetic radiation as gamma rays	Both
P6.1e	Relate each emission to possible changes in the mass or the charge of the nucleus, or both	Both
P6.1f	Use names and symbols of common nuclei and particles to write balanced equations for decay	Both
P6.1g	Balance equations for alpha, beta or gamma emission in terms of the masses and charges involved	Both

P6.1a The nucleus: protons and neutrons

An atom has a tiny central nucleus made of protons and neutrons. Electrons are arranged around it. Protons and neutrons are the two particles in the nucleus, so together they are called nucleons.

Particle	Location	Charge (relative)	Mass (relative)
Proton	In the nucleus	+1	1
Neutron	In the nucleus	0	1
Electron	Outside the nucleus	-1	about 1/1800, so negligible

Neutrons have no charge, so the charge of a nucleus comes only from its protons. Every nucleus is therefore positive. The number of protons is the atomic number, Z. It is characteristic of the element: every nucleus with 6 protons is carbon, every nucleus with 8 protons is oxygen, and no other element has these numbers. The total number of protons and neutrons is the mass number, A. Because electrons have negligible mass, the mass number is the relative mass of the atom.

neutrons = mass number - atomic number, or N = A - Z

In an uncharged atom the electron count matches the proton count, so there are also Z electrons.

Worked example 1. An atom of aluminium has mass number 27 and atomic number 13. Find its protons, neutrons, electrons and the charge on its nucleus.

• Protons = Z = 13.
• Neutrons = 27 - 13 = 14.
• The atom is neutral, so electrons = 13.
• Each proton is +1 and neutrons add nothing, so the nucleus has relative charge +13.

Worked example 2. A nucleus has relative charge +16 and relative mass 33. Which element is it, and how many neutrons does it have?

• Relative charge +16 means 16 protons. The periodic table gives sulfur for Z = 16.
• Neutrons = 33 - 16 = 17.

P6.1b Isotopes

Isotopes are versions of one element whose nuclei hold different numbers of neutrons. Each has the same count of protons, so the atomic number and the nuclear charge match. Their mass numbers differ, so their nuclear masses differ.

Oxygen has isotopes with mass numbers 16, 17 and 18. All have 8 protons.

Isotope	Protons	Neutrons	Mass number
Oxygen-16	8	8	16
Oxygen-17	8	9	17
Oxygen-18	8	10	18

The name of an isotope is the element and its mass number, such as oxygen-17.

Worked example 3. Which of these nuclei are isotopes of each other? Carbon-12 (6 protons, 6 neutrons), carbon-14 (6, 8), nitrogen-14 (7, 7), oxygen-16 (8, 8), oxygen-17 (8, 9).

• Isotopes need the same number of protons. Carbon-12 and carbon-14 both have 6, and oxygen-16 and oxygen-17 both have 8.
• Carbon-14 and nitrogen-14 have the same mass number of 14, but 6 and 7 protons. They are different elements, so they are not isotopes.

P6.1c Nuclear notation

The conventional way to write a nucleus puts the mass number at the top left and the atomic number at the bottom left of the chemical symbol. In this guide the layout reads like ²⁴₁₂Mg, which is magnesium with A = 24 and Z = 12. Top number first, bottom number second.

Isotopes of one element share the symbol and the bottom number, and only the top number changes:

Nucleus	Protons	Neutrons	Relative charge	Relative mass
²⁴₁₂Mg	12	12	+12	24
²⁵₁₂Mg	12	13	+12	25
²⁶₁₂Mg	12	14	+12	26

The identities are the same element, the charges are equal, and the masses differ by one unit for each extra neutron. That is exactly the comparison P6.1c asks for.

Worked example 4. Write the symbol for a nucleus with 20 protons and 22 neutrons, then read the symbol ²⁰⁹₈₃Bi.

• A = 20 + 22 = 42 and Z = 20. The element with Z = 20 is calcium, so the symbol is ⁴²₂₀Ca.
• For ²⁰⁹₈₃Bi, protons = 83 and neutrons = 209 - 83 = 126. The nuclear charge is +83.

Particles use the same pattern, with the bottom number as the charge and the top number as the mass:

Particle	Symbol	Top number	Bottom number
Proton	¹₁p	1	+1
Neutron	¹₀n	1	0
Alpha particle	⁴₂He (also written α)	4	+2
Beta particle	⁰₋₁e (also written β)	0	-1
Gamma ray	γ	0	0

P6.1d Unstable nuclei and what they emit

Some nuclei are unstable. An unstable nucleus can change by emitting radiation, and this is radioactive decay. Four emissions are in the specification.

• Alpha particle (α): two protons and two neutrons, the same as a helium nucleus, ⁴₂He.
• Beta particle (β): a fast-moving electron that comes from the nucleus, ⁰₋₁e. It is not one of the atom’s orbiting electrons. Inside the nucleus a neutron changes into a proton and the electron is emitted.
• Neutron (n): a single neutron leaves the nucleus, ¹₀n.
• Gamma ray (γ): electromagnetic radiation. It has no mass and no charge.

Decay is random: you cannot say when a particular nucleus will decay. Being irradiated by a source does not make an object radioactive.

P6.1e How each emission changes the nucleus

Use the rule that mass number tracks the protons plus neutrons that remain, and atomic number tracks the protons.

Emission	Change in mass number A	Change in atomic number Z	New nucleus
Alpha	down by 4	down by 2	Different element
Beta	no change	up by 1	Different element
Neutron	down by 1	no change	Same element, different isotope
Gamma	no change	no change	Same nucleus, less energy

Why beta raises Z by 1: a neutron becomes a proton, so the nucleus gains one positive charge while the total of protons plus neutrons stays the same. Why gamma changes neither: it carries away energy only.

P6.1f and P6.1g Balanced decay equations

A decay equation has the parent nucleus on the left and the products on the right, joined by an arrow. It is balanced when both of these hold:

1. The top numbers (mass numbers) on the left equal the sum of the top numbers on the right.
2. The bottom numbers (charges) on the left equal the sum of the bottom numbers on the right.

Worked example 5 (alpha). Radium-224 (Z = 88) emits an alpha particle. Write the equation.

• Mass number: 224 - 4 = 220. Atomic number: 88 - 2 = 86. Z = 86 is radon.
• ²²⁴₈₈Ra → ²²⁰₈₆Rn + ⁴₂He
• Check: 220 + 4 = 224 and 86 + 2 = 88.

Worked example 6 (beta). Sodium-24 (Z = 11) emits a beta particle.

• Mass number stays at 24. Atomic number: 11 - (-1) = 12. Z = 12 is magnesium.
• ²⁴₁₁Na → ²⁴₁₂Mg + ⁰₋₁e
• Check: 24 + 0 = 24 and 12 + (-1) = 11.

Worked example 7 (gamma). The magnesium-24 nucleus formed above is left with extra energy, so it is excited. It gets rid of the energy by emitting a gamma ray.

• ²⁴₁₂Mg (excited) → ²⁴₁₂Mg + γ
• Both numbers are unchanged, and gamma has 0 and 0.

Worked example 8 (neutron). Helium-5 (Z = 2) emits a neutron.

• Mass number: 5 - 1 = 4. Atomic number stays at 2.
• ⁵₂He → ⁴₂He + ¹₀n
• The product is still helium, now helium-4.

Worked example 9 (finding unknowns). Bismuth-212 (Z = 83) emits a beta particle, and the product then emits an alpha particle to become lead-208 (Z = 82). Find both missing nuclei.

• Beta step: ²¹²₈₃Bi → ?₈₄Po + ⁰₋₁e. The top number is 212, and the bottom is 83 + 1 = 84, which is polonium. The nucleus is ²¹²₈₄Po.
• Alpha step: ²¹²₈₄Po → ²⁰⁸₈₂Pb + ⁴₂He. Check: 208 + 4 = 212 and 82 + 2 = 84.

Common errors

• Writing the mass number as the number of neutrons. Neutrons = A - Z.
• Saying isotopes have a different number of protons or electrons. Protons stay the same.
• Calling carbon-14 and nitrogen-14 isotopes because the mass numbers match.
• Giving a beta particle a mass number of 1. It is 0, and its charge is -1.
• Forgetting that subtracting a negative charge raises Z: 11 - (-1) = 12.
• Changing A in gamma emission, or saying gamma changes the element.
• Balancing only the top numbers and leaving the charges unchecked.
• Writing that the electron in beta decay came from the electron shells.

Next: condense this with the revision notes, then test yourself with the practice questions and the diagnostics.

Official syllabus

OCR GCSE (9-1) Gateway Science Physics A (J249), Version 5.0 (July 2026), for first assessment in 2018, published by OCR. This guide covers learning outcomes P6.1a to P6.1g.