# Isotopes

> CIE A-Level Physics · AS Particle Physics (Unit 11)
> Source: https://www.owlsprep.com/study/cie-9702-u11-isotopes/

This module introduces the definition of isotopes, how to use standard nuclide notation, and how to count subatomic particles for any isotope. We also cover common exam pitfalls.

**Prerequisites:** [Atomic structure and subatomic particles](https://www.owlsprep.com/study/cie-9702-u11-atomic-structure/)

## Learning objectives

- Define isotopes and distinguish between their physical and chemical properties
- Write and interpret standard nuclide notation for isotopes
- Calculate the number of protons, neutrons, and electrons for any isotope

## Definition and Key Properties of Isotopes

**Isotopes** — Isotopes are nuclides of the same chemical element, meaning they have the same number of protons in the nucleus, but different numbers of neutrons.

*Example:* Carbon has two common isotopes: carbon-12 (6 protons, 6 neutrons) and carbon-14 (6 protons, 8 neutrons).

Chemical reactions involve interactions between an atom's electrons. For neutral atoms, electron number equals proton number, so isotopes have identical chemical properties. They can only be separated by physical methods that exploit their different masses, not chemical reactions.

> **info**
>
> Isotopes of the same element always have different physical properties, including different mass, density, and stability. Many isotopes are radioactive, while others are stable.

**Worked example:** Neutral chlorine has two common isotopes: chlorine-35 and chlorine-37. Compare the number of protons, neutrons, and electrons in each.

1. Chlorine is element 17, so proton number $Z=17$ for all chlorine isotopes. Proton number defines the element, so proton count is identical:

   $$\text{Number of protons} = 17 \text{ for both}$$
2. Nucleon (mass) number $A = \text{protons} + \text{neutrons}$, so rearrange to get neutrons = $A - Z$
3. Calculate for chlorine-35 ($A=35$):

   $$\text{Neutrons} = 35 - 17 = 18$$
4. Calculate for chlorine-37 ($A=37$):

   $$\text{Neutrons} = 37 - 17 = 20$$
5. For neutral atoms, electron number equals proton number:

   $$\text{Electrons} = 17 \text{ for both}$$

## Nuclide Notation for Isotopes

CIE exams always use standard nuclide notation to represent isotopes, so you must be able to interpret and write this notation correctly.

**Standard Nuclide Notation** — The standard format for isotopes: $A$ = total nucleon number (protons + neutrons), $Z$ = proton number, $X$ = chemical symbol of the element.

*Notation:* ^A_ZX

**Worked example:** Write the nuclide notation for an oxygen isotope with 10 neutrons.

1. Oxygen always has a proton number $Z=8$, so that is our bottom number.
2. Calculate nucleon number: $A = Z + \text{neutrons} = 8 + 10 = 18$, this is our top number.
3. Oxygen's chemical symbol is O, so the full notation is:

   $$^{18}_{8}\text{O}$$

**Check your understanding**

Test your understanding of notation:

1. What do $^A_ZX$ and $^B_ZX$ represent?

   - Different elements with the same number of neutrons
   - Isotopes of the same element
   - Different elements with different mass numbers
   - The same nuclide written differently

   *Answer:* Isotopes of the same element

   *Why:* Same element symbol X means same proton number Z, different top numbers mean different mass, so these are isotopes.

## Common Uses of Isotopes

Isotopes have many practical applications that are often used as context for exam questions. Key examples you should recognize include: carbon-14 for radiocarbon dating, cobalt-60 for cancer radiotherapy, and uranium-235 for nuclear power fuel.

> **tip**
>
> For context questions, you only need to remember that isotopes have identical chemistry so they behave the same in biological/chemical processes, which is why they can be used as tracers.

**Worked example:** Explain why plants absorb both carbon-12 and carbon-14 from the atmosphere during photosynthesis.

1. Photosynthesis is a chemical reaction that depends on the chemical properties of carbon.
2. Chemical properties are determined by electron arrangement, which depends on proton number. Both carbon isotopes have the same number of protons, so identical chemical properties.
3. Places cannot distinguish between the two isotopes, so both are absorbed and incorporated into plant tissue during photosynthesis.

## Common pitfalls

- **Wrong:** Mixing up A and Z, counting the bottom number as neutrons instead of protons
  - Why it fails: Students often forget which number goes where in standard nuclide notation
  - Correct: Remember: the larger number (nucleon count) is always at the top, smaller number (proton count) at the bottom. Neutrons = top number minus bottom number.
- **Wrong:** Claiming isotopes of the same element have different chemical properties
  - Why it fails: Students confuse differences in physical properties with chemical properties
  - Correct: Chemical properties depend on electron arrangement, which matches proton number, so isotopes have identical chemical properties. Only physical properties differ.
- **Wrong:** Assuming electron number always equals proton number for isotopes
  - Why it fails: Questions often ask about ions, not just neutral atoms
  - Correct: For an ion with charge $+n$, electrons = $Z - n$. For charge $-n$, electrons = $Z + n$.
- **Wrong:** Thinking different isotopes occupy different positions in the periodic table
  - Why it fails: The periodic table is ordered by mass number in many student memory models
  - Correct: The periodic table is ordered by proton number, so all isotopes of an element share the same position.

## Cheatsheet

| Property | For isotopes of the same element |
| --- | --- |
| Proton number (Z) | Same |
| Number of protons | Same |
| Number of neutrons | Different |
| Nucleon number (A) | Different |
| Electrons (neutral atom) | Same |
| Chemical properties | Identical |
| Mass / Density | Different |
| Periodic table position | Same |

## What's next

Understanding isotopes is the foundational concept for all further topics in nuclear physics, including radioactive decay, nuclear reactions, and mass defect and binding energy. You will also apply this knowledge when solving half-life problems, interpreting nuclear reaction equations, and even calculating relative atomic mass in chemistry. This sub-topic almost always appears as an easy 1-2 mark question in your AS exam, so mastering it guarantees you those easy marks. Next, explore the core topics below to build out your nuclear physics knowledge.

- [Alpha, beta and gamma radiation](https://www.owlsprep.com/study/cie-9702-u11-alpha-beta-and-gamma-radiation/)
- [Radioactive decay](https://www.owlsprep.com/study/cie-9702-u11-radioactive-decay/)

---

From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/cie-9702-u11-isotopes/