Notation $^{A}_{Z}\text{X}$ for Nuclides – Cambridge International AS & A Level Physics (9702)
1. Where this topic sits in the syllabus
Syllabus Section
Relevant 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
Identify the element and write its symbol $\text{X}$.
Find the atomic number $Z$ from the periodic table.
Determine the mass number $A$ (given, or by adding protons + neutrons).
Place $A$ as a superscript and $Z$ as a subscript to the left of $\text{X}$: $^{A}_{Z}\text{X}$.
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 type
Particle emitted
Charge (subscript)
Δ$A$
Δ$Z$
α‑decay
$^{4}_{2}\text{He}$ (or $^{4}_{2}\alpha$)
+2
–4
–2
β⁻‑decay
$^{0}_{-1}e$ (electron)
–1
0
+1
β⁺‑decay
$^{0}_{+1}e$ (positron)
+1
0
–1
Electron capture (EC)
$^{0}_{0}e$ (inner‑shell electron captured)
0
0
–1
γ‑radiation
$^{0}_{0}\gamma$
0
0
0
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.
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
Nuclide
Element (X)
$Z$
$A$
$N$
Typical use / decay mode
$^{1}_{1}\text{H}$
H
1
1
0
Protium – stable
$^{2}_{1}\text{H}$
H
1
2
1
Deuterium – heavy water
$^{14}_{6}\text{C}$
C
6
14
8
Radiocarbon dating (β⁻ decay)
$^{235}_{92}\text{U}$
U
92
235
143
Fissile material (α/β/γ series)
$^{238}_{92}\text{U}$
U
92
238
146
Natural uranium – fertile
10. Practice Questions
Write the nuclide notation for a nitrogen atom that has 7 protons and 8 neutrons.
Identify $Z$, $A$ and $N$ for $^{131}_{53}\text{I}$.
Balance the following β⁻‑decay and write the products in nuclide notation:
$$^{14}_{6}\text{C} \;\longrightarrow\; \; ?$$
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 $n = ^{1}_{0}\text{n}$.)
Write the nuclear equation for the positron emission of $^{22}_{11}\text{Na}$ and state the change in $Z$.
11. Summary Table (quick reference)
Nuclide
Element (X)
$Z$
$A$
$N$
Typical decay mode
$^{3}_{1}\text{H}$
H
1
3
2
β⁻
$^{60}_{27}\text{Co}$
Co
27
60
33
β⁻
$^{222}_{86}\text{Rn}$
Rn
86
222
136
α
$^{131}_{53}\text{I}$
I
53
131
78
β⁻
Suggested diagram: a schematic nucleus showing $Z$ protons (red) and $N$ neutrons (blue) with the label $^{A}_{Z}\text{X}$.