Atoms are very small, having a radius of about 1 × 10⁻¹⁰ metres.

The idea

Atoms are the smallest particles of an element that retain its chemical identity. The radius of a typical atom is about 1 × 10⁻¹⁰ m, which is 0.0000000001 m, or one ten-billionth of a metre. This is roughly a million times smaller than the width of a human hair. Because atoms are so small, a single grain of sand contains an enormous number of them. The value is an order-of-magnitude figure: atoms vary slightly in size, but 1 × 10⁻¹⁰ m is a useful benchmark. When comparing atomic size with the nucleus, the radius of the nucleus is less than 1/10 000 of the radius of the atom (about 1 × 10⁻¹⁴ m), so most of an atom is empty space.

What earns the marks

• States that the radius of an atom is about 1 × 10⁻¹⁰ m.
• Recognises that this is a typical or approximate value, not an exact size for every atom.
• Converts 1 × 10⁻¹⁰ m into ordinary decimal form as 0.0000000001 m.
• Explains that atoms are mostly empty space because the radius of the nucleus is less than 1/10 000 of the radius of the atom.
• States that the radius of a nucleus is about 1 × 10⁻¹⁴ m.

Common mistakes and how to put them right

• Writing the radius as 1 × 10¹⁰ m instead of 1 × 10⁻¹⁰ m.

  Put it right: The negative exponent is essential because atoms are extremely small.

• Treating 1 × 10⁻¹⁰ m as the exact radius of every atom.

  Put it right: It is a typical value and atoms of different elements vary slightly.

• Confusing the atomic radius with the nuclear radius.

  Put it right: The radius of the nucleus is less than 1/10 000 of the radius of the atom.

Exam tips

• Learn the value 1 × 10⁻¹⁰ m with its negative exponent and be ready to write it in standard form.
• If asked to compare sizes, convert both values to the same form, such as standard form, before dividing.
• Remember that the nuclear radius is less than 1/10 000 of the atomic radius, which is why the atom is mostly empty space.