The nuclear atom and mass spectrometry

IB Chemistry HL· S1.2 The nuclear atom· 15 min read

1. 1. Structure of the Nuclear Atom★★☆☆☆⏱ 15 min

Ernest Rutherford's gold foil experiment disproved the earlier 'plum pudding model' of the atom, leading to the nuclear model that is accepted today.

📘 Definition

Nuclear atom

A model where most of the atom's mass and all its positive charge is concentrated in a small dense nucleus, surrounded by negatively charged electrons that occupy most of the atom's volume.

Example:

A neutral carbon-12 atom has a 6-proton, 6-neutron nucleus, with 6 electrons orbiting outside.

Subatomic Particle	Relative Charge	Relative Mass	Location
Proton	$+ 1$	$1$	Nucleus
Neutron	$0$	$1$	Nucleus
Electron	$- 1$	$\approx 1/1836$	Electron cloud outside nucleus

📐 Worked Example

State the number of protons, neutrons and electrons in the ion $\ce_{13}^{27} A l^{3} +$

1
The lower value $Z$ (atomic number) equals the number of protons, so:
2
$\text{Protons} = Z = 13$
3
The upper value $A$ (mass number) is protons + neutrons, so calculate neutrons:
4
$\text{Neutrons} = A - Z = 27 - 13 = 14$
5
The $3 +$ charge means 3 electrons are lost from the neutral atom, so:
6
$\text{Electrons} = 13 - 3 = 10$

Exam tip:

Proton number always defines the element, only electron count changes for ions.

2. 2. Isotopes★★☆☆☆⏱ 10 min

📘 Definition

Isotopes

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

Example:

Chlorine has two naturally occurring stable isotopes: $\ce^{35} C l$ and $\ce^{37} C l$ .

Isotopes have identical chemical properties because they have the same electron configuration, which governs chemical bonding and reactivity. They differ in physical properties such as mass, density, melting point and rate of diffusion, due to their different masses.

📐 Worked Example

Boron has atomic number 5. Compare the atomic structure and reactivity of boron-10 and boron-11.

1
Both isotopes are boron, so they have the same number of protons:
2
$\text{Protons for both} = 5$
3
Calculate neutrons for each isotope:
4
Boron-10: $10 - 5 = 5$ neutrons; Boron-11: $11 - 5 = 6$ neutrons
5
Neutral atoms of both have 5 electrons, so electron configuration is identical.
6
Conclusion: They have different nuclear composition but identical chemical reactivity.

3. 3. Mass Spectrometry and Relative Atomic Mass Calculation★★★☆☆⏱ 20 min

✓ Calculator OK

Mass spectrometry separates ions of different mass based on their mass-to-charge ratio ( $m / z$ ). The resulting mass spectrum plots relative abundance of each isotope against $m / z$ , which is equal to the isotopic mass for ions with charge +1 (the most common case).

📘 Definition

Relative atomic mass ($A_r$)

The weighted average mass of a naturally occurring sample of an element, relative to $\frac{1}{12}$ the mass of a single carbon-12 atom.

📐 Worked Example

Chlorine has two isotopes with peaks at $m / z = 35$ (75.77% abundance) and $m / z = 37$ (24.23% abundance). Calculate the relative atomic mass of chlorine.

1
Multiply each isotopic mass by its decimal abundance:
2
$(35 \times 0.7577) + (37 \times 0.2423)$
3
Calculate the sum of the products:
4
$26.5195 + 8.9651 = 35.4846$
5
Round to 3 significant figures per IB conventions:
6
$A_r(\text{Cl}) = 35.5$

✓ Quick check

Test your calculation skill:

An element has two isotopes: 10X (20% abundance) and 11X (80% abundance). What is its relative atomic mass?
- 10.0
- 10.2
- 10.8
- 11.0
Reveal answer
10.8 —
Correct! $(10 \times 0.2) + (11 \times 0.8) = 10.8$

4. Common Pitfalls

Wrong move:

Counting electrons in an ion as equal to the proton number regardless of charge

Why:

Only neutral atoms have equal numbers of protons and electrons; ions gain or lose electrons

Correct move:

Subtract positive charge from proton number, add negative charge to get the number of electrons

Wrong move:

Claiming isotopes have different chemical properties

Why:

Chemical reactivity depends entirely on electron arrangement, which is identical for isotopes

Correct move:

State that isotopes have identical chemical properties and different physical properties

Wrong move:

Forgetting to convert percentage abundances to decimals before calculation

Why:

This results in a final value 100 times larger than the correct answer

Correct move:

Divide all percentage abundances by 100, or divide the final sum by 100

Wrong move:

Using whole number mass numbers when the question gives actual isotopic masses

Why:

Actual isotopic masses are slightly different from whole numbers, leading to small calculation errors

Correct move:

Always use the $m / z$ values given in the question's mass spectrum

5. Quick Reference Cheatsheet

Key Concept	Formula / Rule
Atomic number ( $Z$ )	Number of protons = defines the element
Mass number ( $A$ )	$A = Z + number of neutrons$
Electrons in ion	Electrons = $Z - charge$
Isotopes	Same $Z$ , different $A$ , same chemical properties
Relative atomic mass	$A_{r} = \frac{\sum ( isotopic mass \times abundance )}{\sum abundance}$
Subatomic particle charges	Proton $+ 1$ , Neutron $0$ , Electron $- 1$

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2025 · 1
Calculate relative atomic mass from spectrum
2024 · 2
Count subatomic particles in an ion
2023 · 1
Identify properties of isotopes

Going deeper

simulationIB Mass Spectrum SimulationInteractive practice calculating average atomic mass

What's Next

The nuclear atom and mass spectrometry is the foundation for all further chemistry study. The concept of relative atomic mass is core to stoichiometry, the basis of all quantitative chemistry calculations that you will explore next. Isotopic composition also connects to nuclear chemistry, where you will learn about radioactivity and nuclear reactions later in the IB HL syllabus. Mass spectrometry is also extended in organic chemistry, where it is used to identify molecular mass and structure of organic compounds.