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

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

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