How Small Are Particles?

Introduction

Particles are small — but how small? It is hard to imagine anything so tiny that a single drop of water contains more particles than there are grains of sand on all the beaches on Earth. This page uses measurements and simple arithmetic to show just how small atoms and molecules are, and introduces the units and number notation chemists use to describe them.

Core explanation

The nanometre. Atoms and molecules are measured in nanometres (nm) . One nanometre is one-billionth of a metre, or one-millionth of a millimetre. Typical sizes: - a hydrogen atom: about 0.1 nm across; - most atoms: 0.1–0.5 nm; - a water molecule: about 0.3 nm; - a sugar (sucrose) molecule: about 1 nm; - a human hair: about 80 000 nm wide.

About three million water molecules lined up side by side would stretch only 1 mm.

Standard form. Such numbers are easier to write in standard form : 0.3 nm = 3 × 10⁻¹⁰ m. Large numbers are handled the same way: 1 700 000 000 000 000 000 000 = 1.7 × 10²¹.

How many molecules in a drop? A drop of water has a volume of about 0.05 cm³ and a mass of about 0.05 g. Chemists know (from the mole concept, which you will learn later) that 18 g of water contains about 6.0 × 10²³ molecules. So a 0.05 g drop contains:

(0.05 ÷ 18) × 6.0 × 10²³ ≈ 1.7 × 10²¹ molecules

— about 1 700 billion billion molecules.

Comparing with everyday numbers. The world population is about 8 × 10⁹ people. If every person on Earth counted one molecule per second from that drop, it would take them roughly 7000 years to count them all.

Seeing atoms. Ordinary light microscopes cannot show atoms, because atoms are much smaller than the wavelength of visible light (about 400–700 nm). Scanning tunnelling microscopes and electron microscopes, invented in the twentieth century, can produce images in which individual atoms appear as bumps on a surface.

Why this matters. The tiny size and enormous number of particles explain why matter looks continuous, why a small crystal can colour a whole beaker of water (page 68), and why chemists need a special counting unit, the mole, to work with particles in practical amounts.

Step-by-step reasoning

To estimate how many water molecules fit across 1 mm:

1. Convert 1 mm to nanometres: 1 mm = 1 000 000 nm. 2. Size of one water molecule ≈ 0.3 nm. 3. Number = 1 000 000 ÷ 0.3. 4. ≈ 3 300 000, or about 3 × 10⁶ molecules.

Visual explanation

A "powers of ten" scale bar runs from 1 m (a person's arm span) through 1 mm (a grain of sand), 0.1 mm (a hair's width), 1 µm (a bacterium), 100 nm (a virus), 1 nm (a sugar molecule) and 0.1 nm (a single atom), each step ten or a hundred times smaller. Beside it, an image of a scanning tunnelling microscope picture shows atoms as a regular pattern of bumps.

Real-world analogy

If an apple were magnified to the size of the Earth, each of its atoms would be roughly the size of the original apple. That comparison gives a sense of how many atoms are packed into everyday objects.

Real-world example

Modern computer chips contain transistors with features only a few tens of nanometres across — just a hundred or so atoms wide. Engineers designing these chips must think about individual atoms, which is why nanotechnology has become an important branch of chemistry and materials science.

Why?

Why can light microscopes not see atoms? A microscope cannot clearly show details much smaller than about half the wavelength of the light it uses. Visible light has wavelengths of 400–700 nm, a thousand times larger than an atom, so atoms are far below what light can resolve.

Common misconception

"Atoms are tiny, but a few thousand of them would make a speck you could see." A speck just visible to the eye, about 0.1 mm across, contains roughly 10¹⁷ to 10¹⁸ atoms — hundreds of thousands of trillions. The numbers involved are far beyond everyday experience.

Worked example

Question: Estimate how many sugar molecules (1 nm long) would fit along the width of a human hair (80 000 nm).

Reasoning: Number = 80 000 ÷ 1.

Answer: About 80 000 (8 × 10⁴) sugar molecules.

Quick check

1. How many nanometres are in 1 millimetre? Answer: 1 000 000 (10⁶) nm.

Exam focus

You may be asked to convert between m, mm and nm and to use standard form. Show the working and keep track of powers of ten. Remember typical atomic sizes (about 0.1 nm) as a sense check.

Advanced insight

The number 6.022 × 10²³, called the Avogadro constant, links the particle scale to the laboratory scale: it is the number of particles in one mole of any substance. It was first estimated from measurements such as Perrin's work on Brownian motion, and it is now fixed exactly by definition in the SI system.

Summary

Atoms and molecules are extremely small — about 0.1–0.5 nm for most atoms and 0.3 nm for a water molecule. Standard form and the nanometre help express such sizes. A single drop of water contains about 1.7 × 10²¹ molecules. Atoms are too small for light microscopes but can be imaged with scanning tunnelling and electron microscopes.

Practice questions

1. Write 0.000 000 000 3 m in standard form. Answer: 3 × 10⁻¹⁰ m. 2. Roughly how many water molecules are in a 0.05 g drop of water? Answer: About 1.7 × 10²¹. 3. Why can atoms not be seen with a light microscope? Answer: They are much smaller than the wavelength of visible light, which limits the detail a light microscope can show. 4. A molecule is 2 nm long. How many would fit end to end across 1 mm? Answer: 1 000 000 ÷ 2 = 500 000 (5 × 10⁵).