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

Cambridge A-Level Physics 9702 – Atoms, Nuclei and Radiation: Notation $^{A}_{Z}\text{X}$

Notation $^{A}_{Z}\text{X}$ for Nuclides

Learning Objective

By the end of this lesson you should be able to read, write and interpret the nuclide notation $^{A}_{Z}\text{X}$ and use it confidently in calculations involving nuclear reactions.

1. What the Symbols Represent

  • $\text{X}$ – chemical symbol of the element (e.g., C for carbon, U for uranium).
  • $Z$ – atomic number, the number of protons in the nucleus.
  • $A$ – mass number, the total number of nucleons (protons + neutrons) in the nucleus.
  • $N$ – number of neutrons, given by $N = A - Z$.

2. Reading the Notation

The standard format is $^{A}_{Z}\text{X}$, where the mass number $A$ is placed as a superscript to the left of the element symbol and the atomic number $Z$ as a subscript. Example:

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

means a carbon nucleus with $A=14$ (total nucleons) and $Z=6$ (protons). The number of neutrons is $N = 14 - 6 = 8$.

3. Writing the Notation

  1. Identify the element and write its chemical symbol $\text{X}$.
  2. Determine the atomic number $Z$ (from the periodic table).
  3. Determine the mass number $A$ (from the problem statement or by adding protons and neutrons).
  4. Place $A$ as a superscript and $Z$ as a subscript to the left of $\text{X}$: $^{A}_{Z}\text{X}$.

4. Example Nuclides

Nuclide (symbol) Element (X) Atomic number (Z) Mass number (A) Neutrons (N = A‑Z) Common use
$^{1}_{1}\text{H}$ H 1 1 0 Protium, hydrogen fuel
$^{2}_{1}\text{H}$ H 1 2 1 Deuterium, heavy water
$^{14}_{6}\text{C}$ C 6 14 8 Radiocarbon dating
$^{235}_{92}\text{U}$ U 92 235 143 Fissile material in reactors
$^{238}_{92}\text{U}$ U 92 238 146 Natural uranium, fertile material

5. Nuclide Notation in Nuclear Reactions

When writing nuclear equations, each reactant and product is expressed in nuclide notation. Conservation of mass number ($A$) and atomic number ($Z$) must be satisfied.

Example – Alpha decay of $^{238}_{92}\text{U}$:

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

Check:

  • Mass numbers: $238 = 4 + 234$
  • Atomic numbers: $92 = 2 + 90$

6. Practice Questions

  1. Write the nuclide notation for a nitrogen atom with 7 protons and 8 neutrons.
  2. Identify $Z$, $A$ and $N$ for $^{131}_{53}\text{I}$.
  3. Balance the following beta‑minus decay and write the products in nuclide notation:
    $^{14}_{6}\text{C} \;\rightarrow\; ?$
  4. In a nuclear reaction $^{3}_{1}\text{H} + ^{2}_{1}\text{H} \rightarrow ^{4}_{2}\text{He} + n$, verify that $A$ and $Z$ are conserved.

7. Summary Table

Symbol Element (X) $Z$ (protons) $A$ (mass number) $N$ (neutrons) Typical decay mode
$^{3}_{1}\text{H}$ H 1 3 2 Beta‑minus
$^{60}_{27}\text{Co}$ Co 27 60 33 Beta‑minus
$^{222}_{86}\text{Rn}$ Rn 86 222 136 Alpha
$^{131}_{53}\text{I}$ I 53 131 78 Beta‑minus
Suggested diagram: A schematic showing a nucleus with $Z$ protons (red) and $N$ neutrons (blue), labelled with $^{A}_{Z}\text{X}$.