Students should be able to relate size and scale of atoms to objects in…

The idea

The radius of an atom is approximately 1 × 10⁻¹⁰ m (0.1 nm), making its diameter roughly 2 × 10⁻¹⁰ m (0.2 nm). To relate this to everyday objects, convert both sizes to the same unit, such as metres, and divide the object's size by the atom's size. For example, a human hair (10⁻⁴ m) is roughly 500,000 atoms wide. Because atoms are so incredibly small, they cannot be seen with the naked eye or even a standard light microscope. A grain of sand contains around 10¹⁸ atoms, and a single water droplet holds more atoms than there are stars in many galaxies. This immense difference in scale explains why atoms were not seen directly until highly advanced electron microscopes were developed.

What earns the marks

• The radius of an atom is approximately 1 × 10⁻¹⁰ m, or 0.1 nm.
• The diameter of an atom is approximately 2 × 10⁻¹⁰ m, or 0.2 nm.
• When comparing the scale of atoms to physical objects, both measurements must be converted to consistent units, such as metres.
• Dividing the object size by the atom size gives the number of atoms across the object.
• The very small size of atoms explains why indirect evidence and advanced microscopes are needed.

Common mistakes and how to put them right

• Comparing sizes without converting to the same unit.

  Put it right: Convert both to metres or both to nanometres first.

• Treating the atomic radius as the diameter.

  Put it right: The radius is 1 × 10⁻¹⁰ m and diameter is 2 × 10⁻¹⁰ m.

• Saying atoms are visible under a light microscope.

  Put it right: State that atoms are far smaller than the wavelength of visible light.

Exam tips

• Convert all lengths to metres before dividing to avoid unit errors.
• Use standard form consistently when writing very small or very large numbers.