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.
\$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
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}\$.