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 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

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 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)

---

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

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

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)

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⁻

---