understand and use the notation A Z X for the representation of nuclides

Notation \$^{A}_{Z}\text{X}\$ for Nuclides – Cambridge International AS & A Level Physics (9702)

1. Where this topic sits in the syllabus

Syllabus SectionRelevant Sub‑topics
AS 1‑11 (Atoms, nuclei and radiation)

11.1 Atoms, nuclei and radiation – nuclide notation, isotopic notation, decay modes, conservation of \$A\$ and \$Z\$ (this note).

11.2 Radioactivity – later: γ‑radiation, positron emission, electron capture, fission, fusion, lepton‑number conservation.

A 23.1 (Nuclear physics – mass‑defect & binding energy)Link‑on box below introduces the connection.
Other AS & A‑level units (kinematics, dynamics, waves, electricity, …)Will be used later – see the course road‑map hand‑out.

2. Learning Objectives

  • Read, write and interpret the nuclide notation \$^{A}_{Z}\text{X}\$.

  • Distinguish between nuclide notation \$^{A}_{Z}\text{X}\$ and isotopic notation \$^{A}\text{X}\$.

  • Identify the number of protons (\$Z\$), neutrons (\$N\$) and nucleons (\$A\$) for any given nuclide.

  • Write and balance nuclear‑reaction equations, explicitly conserving both \$A\$ (mass number) and \$Z\$ (atomic number).

  • Recognise the three basic decay modes (α, β⁻, β⁺) and electron capture (EC), and state their effect on \$A\$ and \$Z\$.

  • Connect nuclide notation to the upcoming topic of mass‑defect and binding energy.

3. What the symbols mean

  • \$\text{X}\$ – chemical symbol of the element (C, U, He …).

  • \$Z\$ – atomic number = number of protons.

  • \$A\$ – mass number = total number of nucleons (protons + neutrons).

  • \$N\$ – number of neutrons, given by \$N = A - Z\$.

Isotopic vs. Nuclide notation

• Isotopic notation – \$^{A}\text{X}\$ (mass number only). Used when the atomic number is obvious from the element symbol.

• Nuclide notation – \$^{A}_{Z}\text{X}\$ (both \$A\$ and \$Z\$). Required for any question involving nuclear reactions or when several isotopes of the same element appear together.

4. Reading & writing the notation

  1. Identify the element and write its symbol \$\text{X}\$.

  2. Find the atomic number \$Z\$ from the periodic table.

  3. Determine the mass number \$A\$ (given, or by adding protons + neutrons).

  4. Place \$A\$ as a superscript and \$Z\$ as a subscript to the left of \$\text{X}\$: \$^{A}_{Z}\text{X}\$.

  5. When you later write a nuclear equation, always check that the total \$A\$ and the total \$Z\$ are the same on both sides (the syllabus wording).

Example: A carbon nucleus with 6 protons and 8 neutrons has \$Z=6\$, \$A=14\$:

\$^{14}_{6}\text{C}\$

Neutrons \$N = 14 - 6 = 8\$.

5. Decay modes – effect on \$A\$ and \$Z\$

Decay typeParticle emittedCharge (subscript)Δ\$A\$Δ\$Z\$
α‑decay\$^{4}{2}\text{He}\$ (or \$^{4}{2}\alpha\$)+2–4–2
β⁻‑decay\$^{0}_{-1}e\$ (electron)–10+1
β⁺‑decay\$^{0}_{+1}e\$ (positron)+10–1
Electron capture (EC)\$^{0}_{0}e\$ (inner‑shell electron captured)00–1
γ‑radiation\$^{0}_{0}\gamma\$000

γ‑radiation carries no charge and does not change \$A\$ or \$Z\$ – it will be treated in Unit 11.2.

6. Common pitfalls (quick reminder)

  • Mixing up \$A\$ (mass number) and \$Z\$ (atomic number). Remember \$A\$ is the total nucleons, \$Z\$ is the protons.

  • For β‑decays, \$A\$ does not change – only \$Z\$ changes.

  • Positron notation: \$^{0}_{+1}e\$ – the “+1” is the positive charge of the emitted particle, not a change in \$A\$.

  • When writing a nuclear equation, always verify both \$A\$ and \$Z\$ on the left‑hand side equal those on the right‑hand side.

  • Electron capture does not emit a particle that appears in the equation; the captured electron is shown as \$^{0}_{0}e\$ on the product side to indicate the loss of one positive charge.

7. Writing nuclear equations

Every reactant and product must be expressed in nuclide form. The equation must obey:

  • Conservation of mass number \$A\$: total nucleons before = total nucleons after.

  • Conservation of atomic number \$Z\$: total charge (protons) before = total charge after.

Worked examples

Example 1 – α‑decay of \$^{238}_{92}\text{U}\$

\$^{238}{92}\text{U} \;\longrightarrow\; ^{4}{2}\text{He}\;+\;^{234}_{90}\text{Th}\$

  • Mass numbers: \$238 = 4 + 234\$

  • Atomic numbers: \$92 = 2 + 90\$

Example 2 – β⁻‑decay of \$^{14}_{6}\text{C}\$

\$^{14}{6}\text{C} \;\longrightarrow\; ^{14}{7}\text{N}\;+\;^{0}_{-1}e\$

  • \$A\$: \$14 = 14 + 0\$

  • \$Z\$: \$6 = 7 - 1\$ (the emitted electron carries –1 charge).

Example 3 – β⁺‑decay of \$^{22}_{11}\text{Na}\$ (positron emission)

\$^{22}{11}\text{Na} \;\longrightarrow\; ^{22}{10}\text{Ne}\;+\;^{0}_{+1}e\$

(The superscript “+1” indicates the positive charge of the emitted positron.)

Example 4 – Electron capture of \$^{55}_{26}\text{Fe}\$

\$^{55}{26}\text{Fe} \;\longrightarrow\; ^{55}{25}\text{Mn}\;+\;^{0}_{0}e\$

  • \$A\$ unchanged (55), \$Z\$ decreases by 1 (26 → 25).

8. Link‑on: Mass‑defect & Binding Energy (Unit 23.1)

Once you can write balanced nuclear equations, you can calculate the energy released using the mass‑defect concept:

  • Mass defect \$\Delta m = \bigl(\sum\text{masses of separate nucleons}\bigr) - \bigl(\text{mass of the nucleus}\bigr)\$.

  • Binding energy \$E_{\text{b}} = \Delta m \, c^{2}\$.

Preview example: The binding energy of \$^{4}_{2}\text{He}\$ is obtained from the mass defect between two protons, two neutrons and the helium nucleus.

9. Example Nuclides

NuclideElement (X)\$Z\$\$A\$\$N\$Typical use / decay mode
\$^{1}_{1}\text{H}\$H110Protium – stable
\$^{2}_{1}\text{H}\$H121Deuterium – heavy water
\$^{14}_{6}\text{C}\$C6148Radiocarbon dating (β⁻ decay)
\$^{235}_{92}\text{U}\$U92235143Fissile material (α/β/γ series)
\$^{238}_{92}\text{U}\$U92238146Natural uranium – fertile

10. Practice Questions

  1. Write the nuclide notation for a nitrogen atom that has 7 protons and 8 neutrons.

  2. Identify \$Z\$, \$A\$ and \$N\$ for \$^{131}_{53}\text{I}\$.

  3. Balance the following β⁻‑decay and write the products in nuclide notation:

    \$^{14}_{6}\text{C} \;\longrightarrow\; \; ?\$

  4. In the reaction \$^{3}{1}\text{H} + ^{2}{1}\text{H} \;\longrightarrow\; ^{4}{2}\text{He} + n\$, verify that both \$A\$ and \$Z\$ are conserved. (Recall \$n = ^{1}{0}\text{n}\$.)

  5. Write the nuclear equation for the positron emission of \$^{22}_{11}\text{Na}\$ and state the change in \$Z\$.

11. Summary Table (quick reference)

NuclideElement (X)\$Z\$\$A\$\$N\$Typical decay mode
\$^{3}_{1}\text{H}\$H132β⁻
\$^{60}_{27}\text{Co}\$Co276033β⁻
\$^{222}_{86}\text{Rn}\$Rn86222136α
\$^{131}_{53}\text{I}\$I5313178β⁻

Suggested diagram: a schematic nucleus showing \$Z\$ protons (red) and \$N\$ neutrons (blue) with the label \$^{A}_{Z}\text{X}\$.