# Atomic nucleus and isotopes

> CIE A-Level Chemistry · Unit 2: Atomic Structure
> Source: https://www.owlsprep.com/study/cie-9701-u2-atomic-nucleus-and-isotopes/

This sub-topic covers the basic structure of the atomic nucleus, standard nuclide notation, the definition and properties of isotopes, and the core skill of calculating relative atomic mass from isotopic abundance data, regularly tested in exams.

**Prerequisites:** [Basic IGCSE-level atomic structure](https://www.owlsprep.com/study/cie-9701-igcse-basic-atomic-structure/)

## Learning objectives

- Describe the structure and composition of the atomic nucleus
- Interpret nuclide notation to find proton, neutron and electron counts
- Define isotopes and compare their chemical and physical properties
- Calculate relative atomic mass from isotopic abundance data

## Nuclide Structure and Notation

**Atomic Nucleus** — The dense, positively charged central core of an atom, made up of protons and neutrons (collectively called nucleons)

*Example:* A neutral carbon-12 atom has a nucleus containing 6 protons and 6 neutrons, with 6 electrons outside the nucleus

| Subatomic Particle | Relative Mass | Relative Charge |
| --- | --- | --- |
| Proton | 1 | +1 |
| Neutron | 1 | 0 |
| Electron | ~1/1836 | -1 |

Standard nuclide notation $^A_Z X$ summarizes key information about a nuclide: the top number $A$ is the total nucleon (proton + neutron) count, the bottom number $Z$ is the proton count, and $X$ is the element's chemical symbol. For neutral atoms, the number of electrons equals $Z$.

**Worked example:** Write the full nuclide notation for a neutral aluminium atom with 13 protons and 14 neutrons.

1. Identify the proton number $Z$ (given):
2. $$Z = 13$$
3. Calculate nucleon number $A$ as sum of protons and neutrons:
4. $$A = 13 + 14 = 27$$
5. Find the chemical symbol for aluminium: Al
6. Write in standard nuclide notation:
7. $$^{27}_{13}Al$$

> **Exam tip:** Always confirm the proton number matches the element on your periodic table — examiners often use mismatched Z/X as a distractor in multiple choice questions.

## Isotopes: Definition and Properties

**Isotopes** — Atoms of the same element that share the same number of protons (same proton number $Z$) but have different numbers of neutrons (different nucleon number $A$)

*Example:* Hydrogen has three isotopes: $^1_1H$ (protium), $^2_1H$ (deuterium), and $^3_1H$ (tritium)

Chemical properties of isotopes are identical: chemical behavior is determined by the number and arrangement of electrons, which is the same for all isotopes of an element. Physical properties (mass, density, boiling point, melting point) differ because of the different mass of the nucleus.

**Worked example:** Three particles have the following composition: P (17p, 18n, 17e), Q (16p, 18n, 16e), R (17p, 20n, 17e). Identify which pair are isotopes of the same element.

1. Recall that isotopes have the same proton number $Z$:
2. Particle P has $Z=17$, particle Q has $Z=16$, particle R has $Z=17$
3. Since P and R share the same proton number, they are isotopes of the same element (chlorine)

## Calculating Relative Atomic Mass

**Relative Atomic Mass ($A_r$)** — The weighted average mass of one atom of an element, accounting for the relative abundance of each of its naturally occurring isotopes, measured on a scale where an atom of carbon-12 has a mass of exactly 12

The general formula for relative atomic mass is:

$$A_r = \frac{\sum (\text{isotopic mass} \times \text{relative abundance})}{\sum \text{relative abundance}}$$

**Worked example:** Bromine has two naturally occurring isotopes: $^{79}Br$ (abundance 50.7%) and $^{81}Br$ (abundance 49.3%). Calculate the relative atomic mass of bromine.

1. Multiply each isotopic mass by its percent abundance:
2. $$(79 \times 50.7) + (81 \times 49.3) = 4005.3 + 3993.3 = 7998.6$$
3. Divide by the sum of percent abundances (100 for percent data):
4. $$A_r = \frac{7998.6}{100} = 79.99$$
5. Final result: $A_r$ of bromine ≈ 80.0

**Check your understanding**

Test your calculation skill: A sample of magnesium has three isotopes with the following data: $^{24}Mg$ (78.6%), $^{25}Mg$ (10.1%), $^{26}Mg$ (11.3%). What is the correct relative atomic mass?

1. Calculate $A_r$ for magnesium

   - 24.00
   - 24.33
   - 25.00
   - 24.10

   *Why:* Correct: $(24×78.6)+(25×10.1)+(26×11.3) = 2432.7$, divided by 100 = 24.33

## Common pitfalls

- **Wrong:** Mixing up nucleon and proton number in nuclide notation
  - Why it fails: The order of numbers in notation is easy to reverse when reading quickly
  - Correct: Remember: A (top) = All nucleons, Z (bottom) = number of Protons
- **Wrong:** Claiming isotopes have different chemical properties
  - Why it fails: Different masses lead to different physical properties, but chemistry depends on electrons
  - Correct: All isotopes of the same element have identical chemical behavior
- **Wrong:** Calculating a simple average of isotopic masses, ignoring abundance weighting
  - Why it fails: Simple averages only work if all isotopes are equally abundant, which is rare
  - Correct: Always multiply each mass by its abundance before summing and dividing
- **Wrong:** Claiming neutral isotopes have different numbers of electrons
  - Why it fails: Isotopes only differ in neutron count for neutral atoms
  - Correct: Neutral isotopes have equal numbers of protons and electrons, so electron counts are identical

## Cheatsheet

| Term | Key Information |
| --- | --- |
| Proton | Relative mass 1, charge +1 |
| Neutron | Relative mass 1, charge 0 |
| Proton number (Z) | Number of protons, defines the element |
| Nucleon number (A) | Total protons + neutrons |
| Neutron count | $A - Z$ |
| Isotopes | Same Z, different A |
| Relative Atomic Mass | $\frac{\sum (\text{mass} \times \text{abundance})}{\sum \text{abundance}}$ |

## What's next

Mastery of the atomic nucleus and isotopes is the foundation for all subsequent topics in chemistry. This knowledge underpins the study of electron configuration, which explains how elements bond and react, and is essential for understanding mass spectrometry, a key technique used to identify isotopes and organic compounds. Calculating relative atomic mass is also a core skill required for all mole and stoichiometry calculations, which appear throughout the CIE A-Level Chemistry syllabus. This topic also introduces the concepts you will need for the further study of radioactivity in nuclear chemistry later in the course.

- [Electron orbitals and configuration](https://www.owlsprep.com/study/cie-9701-u2-electron-orbitals-and-configuration/)
- [Ionisation energies](https://www.owlsprep.com/study/cie-9701-u2-ionisation-energies/)
- [Chemical bonding](https://www.owlsprep.com/study/cie-9701-u3-overview/)

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