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Atoms are small. Everyone knows that. But “small” doesn’t really capture it. The numbers are so extreme that our brains, which evolved to judge the size of fruit and the distance to a tree, have no natural feel for them. This article uses real figures and comparisons to give you a sense of atomic scale, and explains how scientists measure things that no light microscope can ever show.
The size of an atom in numbers
Atoms don’t have hard edges, because their electrons are spread out in fuzzy regions. So chemists define atomic size in several ways, such as half the distance between the nuclei of two bonded atoms (the covalent radius). Typical atomic radii are between about 30 and 300 picometres.
A picometre (pm) is one trillionth of a metre: 10⁻¹² m. Another common unit is the ångström (Å), equal to 100 pm (10⁻¹⁰ m). A typical atom is roughly 1–3 Å across.
| Atom | Approximate radius | Approximate diameter |
|---|---|---|
| Hydrogen | about 30–50 pm (depending on definition) | about 0.1 nm |
| Carbon | about 70 pm | about 0.15 nm |
| Oxygen | about 60–70 pm | about 0.13 nm |
| Gold | about 140 pm | about 0.3 nm |
| Caesium | about 250–300 pm | about 0.5–0.6 nm |
(Values vary with the definition used, which is why ranges are given. See atomic radius trend and largest and smallest atoms.)
So even the biggest atoms are only about half a nanometre across, and a nanometre is a millionth of a millimetre.
Comparisons that help
Across a human hair
A human hair is roughly 0.07 mm (70,000 nm) thick. A carbon atom is about 0.15 nm across. So you could line up about half a million carbon atoms across the width of a single hair.
Across a full stop
The full stop at the end of this sentence is perhaps 0.3 mm across. That’s roughly 2 million atoms side by side.
Scaling up an apple
If you enlarged an apple to the size of the Earth, the atoms in it would be roughly the size of the original apple. That’s the scale difference between your everyday world and the atomic world.
Counting atoms in a drop of water
One drop of water (about 0.05 cm³) has a mass of about 0.05 g. Water’s molar mass is 18 g/mol, so:
- moles of water = 0.05 ÷ 18 ≈ 0.0028 mol
- molecules = 0.0028 × 6.02 × 10²³ ≈ 1.7 × 10²¹ molecules
- atoms (3 per molecule) ≈ 5 × 10²¹ atoms
If every person on Earth (about 8 billion) counted one atom per second, it would take them roughly 20,000 years to count the atoms in that single drop. See Avogadro’s number and how to convert grams to moles.
The mass of an atom
Atoms are light as well as small. Masses of individual atoms are measured in atomic mass units (u, also called daltons, Da), where 1 u is one-twelfth of the mass of a carbon-12 atom:
1 u ≈ 1.66 × 10⁻²⁷ kg
| Atom | Mass (u) | Mass (kg) |
|---|---|---|
| Hydrogen-1 | about 1.008 | 1.67 × 10⁻²⁷ |
| Carbon-12 | 12 (exactly, by definition) | 1.99 × 10⁻²⁶ |
| Gold-197 | about 197 | 3.27 × 10⁻²⁵ |
A gold atom has a mass of about 0.0000000000000000000000003 kg. It would take about 3 × 10²¹ gold atoms to make one gram of gold. See atomic mass vs mass number vs molar mass.
The nucleus: smaller still
The nucleus is where nearly all an atom’s mass sits, yet it’s tiny compared with the atom itself.
- A typical nucleus has a radius of a few femtometres (1 fm = 10⁻¹⁵ m).
- An atom is roughly 10,000 to 100,000 times wider than its nucleus.
The stadium analogy: if an atom were the size of a large sports stadium, the nucleus would be about the size of a pea or a marble at the centre spot. The electrons would be spread thinly through the whole stadium.
Because the nucleus is so small and so massive, it’s incredibly dense: about 2 × 10¹⁷ kg/m³. A teaspoon of pure nuclear matter would weigh hundreds of millions of tonnes. Neutron stars are made of matter at roughly this density.
Atoms are mostly empty space, so why are things solid?
If atoms are mostly empty, why can’t you walk through walls? Because the electrons of the atoms in your body and in the wall repel each other electrically, and quantum rules prevent electrons from crowding into the same states (the Pauli exclusion principle). These forces make matter resist being pushed together, even though the particles themselves take up almost none of the space.
How many atoms are in a human body?
An adult human is made of roughly 7 × 10²⁷ atoms, most of them hydrogen, oxygen and carbon. See elements in the human body. That number is larger than the number of stars estimated in the observable universe (often quoted as around 10²² to 10²⁴).
How can we measure something so small?
Light can’t show individual atoms, because visible light has wavelengths of 400–700 nm, thousands of times larger than an atom. Scientists use other methods:
- X-ray crystallography: X-rays have wavelengths close to atomic spacings. When they pass through a crystal, the regular arrangement of atoms produces a diffraction pattern, from which distances between atoms can be calculated precisely.
- Scanning tunnelling microscopy (STM): an extremely sharp tip scans across a conducting surface. A tiny current flows between the tip and the surface, and it changes sharply with distance, allowing individual atoms to be mapped.
- Atomic force microscopy (AFM): a tip on a tiny cantilever “feels” the forces from surface atoms.
- Electron microscopy: beams of electrons, with much shorter wavelengths than light, can image atomic columns in thin samples.
- Calculations from density: knowing the density and molar mass of a substance, together with Avogadro’s constant, gives the volume available to each atom.
Worked example: estimating the size of a gold atom
- Density of gold ≈ 19.3 g/cm³; molar mass ≈ 197 g/mol.
- Volume of one mole = 197 ÷ 19.3 ≈ 10.2 cm³.
- Volume per atom = 10.2 ÷ 6.02 × 10²³ ≈ 1.7 × 10⁻²³ cm³ = 1.7 × 10⁻²⁹ m³.
- Treating each atom as occupying a small cube, side = ∛(1.7 × 10⁻²⁹) ≈ 2.6 × 10⁻¹⁰ m = 0.26 nm.
That’s close to measured values (gold atoms are about 0.29 nm apart in the metal). A simple calculation with everyday data gives an atomic size to within about 10%. See density calculations.
Key takeaways
- Atoms are roughly 0.1–0.5 nm across; you could fit about half a million carbon atoms across a hair.
- A single atom’s mass is around 10⁻²⁷ to 10⁻²⁵ kg; 1 u ≈ 1.66 × 10⁻²⁷ kg.
- The nucleus is 10,000–100,000 times smaller than the atom but holds almost all its mass.
- A drop of water contains about 5 × 10²¹ atoms.
- Atoms are measured with X-ray diffraction, scanning probe microscopes and electron microscopes, or estimated from density. See what is an atom?
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