# Atomic number, mass number and isotopes

> IB Chemistry SL · IB Diploma Programme Chemistry SL
> Source: https://www.owlsprep.com/study/ib-chemistry-sl-u1-atomic-number-mass-number-and/

This sub-topic explains the fundamental properties of atomic nuclei, covering definitions of atomic number, mass number, nuclide notation, and isotopes. You will also learn to calculate relative atomic mass from isotopic abundance data, a common IB exam question.

**Prerequisites:** [Basic structure of the atom (protons, neutrons, electrons)](https://www.owlsprep.com/study/ib-chemistry-sl-u1-introduction-to-the-atom/)

## Learning objectives

- Distinguish between atomic number, mass number and relative atomic mass
- Write and interpret nuclide notation for different isotopes
- Calculate relative atomic mass from isotopic abundance data
- Explain why isotopes have similar chemical properties

## Atomic Number and Mass Number

**Atomic Number** — The number of protons in the nucleus of an atom of an element, which uniquely identifies the element. All atoms of the same element have the same atomic number, and in neutral atoms, this equals the number of electrons.

*Notation:* $Z$

*Example:* Carbon always has $Z = 6$

**Mass Number** — The total number of protons and neutrons in the nucleus of a specific atom. Since protons and neutrons each have ~1 atomic mass unit, mass number is always a whole number.

*Notation:* $A$

*Example:* A carbon-12 atom has $A = 12$ (6 protons + 6 neutrons)

Standard nuclide notation combines this information as $^A_Z X$, where $X$ is the chemical symbol of the element. To find the number of neutrons in any atom, use the formula $\text{neutrons} = A - Z$.

**Worked example:** How many protons, neutrons and electrons are there in a neutral atom of $^{24}_{12}\text{Mg}$?

1. Step 1: Identify $Z$ (lower number) and $A$ (upper number) from the notation: $Z = 12$, $A = 24$
2. Step 2: Atomic number = number of protons, so number of protons = 12
3. Step 3: The atom is neutral, so number of electrons = number of protons = 12
4. Step 4: Calculate number of neutrons using $A - Z$
5. $$24 - 12 = 12$$
6. Final answer: 12 protons, 12 neutrons, 12 electrons

## Isotopes

**Isotopes** — Atoms of the same element that share the same atomic number (same number of protons) but have different mass numbers (different number of neutrons).

*Example:* Hydrogen has three naturally occurring isotopes: $^1_1\text{H}$ (protium), $^2_1\text{H}$ (deuterium), $^3_1\text{H}$ (tritium)

Because isotopes have the same number of protons, they also have identical electron configurations. This means they have the same chemical properties, only differing in physical properties such as mass, density, and boiling point.

> **info**
>
> Unstable isotopes are called radioisotopes. They have wide applications including radiocarbon dating, cancer treatment, and industrial tracer testing.

**Worked example:** Identify which of the following species are isotopes of the same element: $^{14}_6\text{X}$, $^{12}_7\text{Y}$, $^{14}_7\text{Z}$, $^{12}_6\text{W}$

1. Step 1: Recall that isotopes of the same element must have the same atomic number ($Z$)
2. Step 2: Group species by their $Z$ value: $Z=6$: X and W; $Z=7$: Y and Z
3. Step 3: X and W have the same $Z$ (same element) but different mass numbers, so they are isotopes. Y and Z also share the same $Z$ so they are isotopes of a second element.

## Calculating Relative Atomic Mass

**Relative Atomic Mass** — The weighted average of the mass numbers of all naturally occurring isotopes of an element, weighted by their relative abundance. This is the value shown for each element on the IB periodic table.

*Notation:* $A_r$

For percentage abundance data, the formula for relative atomic mass is:

$$A_r = \frac{(A_1 \times \%_1) + (A_2 \times \%_2) + ...}{100}$$

Where $A_1$ and $A_2$ are the mass numbers of each isotope. If abundances are given as decimal fractions, you do not need to divide by 100.

**Worked example:** Chlorine has two naturally occurring isotopes: 75.77% $^{35}\text{Cl}$ and 24.23% $^{37}\text{Cl}$. Calculate the relative atomic mass of chlorine.

1. Step 1: Substitute values into the formula:
2. $$A_r = \frac{(35 \times 75.77) + (37 \times 24.23)}{100}$$
3. Step 2: Calculate the numerator:
4. $$(35 \times 75.77) = 2651.95; \quad (37 \times 24.23) = 896.51; \quad \text{Total} = 3548.46$$
5. Step 3: Divide by 100 to get the final result:
6. $$A_r = 35.48 \approx 35.5$$

**Check your understanding**

Check your understanding:

1. Neon has two isotopes: 90% $^{20}\text{Ne}$ and 10% $^{22}\text{Ne}$. What is the relative atomic mass of neon?

   - 20.0
   - 20.2
   - 21.0
   - 22.0

   *Answer:* 20.2

   *Why:* Correct calculation: $(20 \times 0.9) + (22 \times 0.1) = 18 + 2.2 = 20.2$

## Common pitfalls

- **Wrong:** Using the relative atomic mass from the periodic table to calculate neutrons
  - Why it fails: Relative atomic mass is a weighted average of all isotopes, not the mass number of an individual atom, so it is usually a decimal and cannot be used directly
  - Correct: Always use the mass number given in the nuclide notation to calculate neutrons as $A - Z$
- **Wrong:** Swapping the positions of $Z$ and $A$ in nuclide notation
  - Why it fails: Mixing up the lower and upper positions leads to wrong counts of protons and neutrons
  - Correct: Remember: A for mass number is Above the element symbol, Z for atomic number is at the Zero (bottom)
- **Wrong:** Claiming isotopes have different chemical properties
  - Why it fails: Chemical reactivity depends on electron configuration, which is identical for all isotopes of an element
  - Correct: Only physical properties (mass, density, boiling point) differ between isotopes
- **Wrong:** Forgetting to divide by 100 when using percentage abundances
  - Why it fails: Percentages add up to 100, so the sum of mass × percentage will be 100 times larger than the correct result
  - Correct: Always divide by 100 for percentage abundances, or convert percentages to decimals before adding

## Cheatsheet

| Term | Symbol | Key Definition | Formula |
| --- | --- | --- | --- |
| Atomic Number | $Z$ | Number of protons in nucleus |  |
| Mass Number | $A$ | Total protons + neutrons | $\text{Neutrons} = A - Z$ |
| Isotopes |  | Same $Z$, different $A$ |  |
| Relative Atomic Mass | $A_r$ | Weighted average of isotopes | $A_r = \frac{\sum (A_i \times \%_i)}{100}$ |
| Nuclide Notation | $^A_Z X$ | Standard notation for atoms |  |

## What's next

This sub-topic is the foundation for all further study of atomic structure and the periodic table in IB Chemistry SL. Understanding the properties of isotopes and how to calculate relative atomic mass is essential for upcoming topics including mass spectrometry, stoichiometric calculations, and nuclear chemistry. Mastery of these basic definitions and simple calculations will help you secure easy marks in both Paper 1 and Paper 2 of your final exam, and builds the core knowledge you need for more advanced concepts.

- [Mass Spectrometry & Isotope Abundance](https://www.owlsprep.com/study/ib-chemistry-sl-u1-mass-spectrometry/)
- [Basic electron arrangement in atoms](https://www.owlsprep.com/study/ib-chemistry-sl-u1-basic-electron-arrangement-in-atoms/)
- [Structure 2: Electron Configuration](https://www.owlsprep.com/study/ib-chemistry-sl-u2-overview/)

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