Knowledge of typical values for nuclear radius.

The idea

Nuclear radii are of the order of 10⁻¹⁵ m to 10⁻¹⁴ m, commonly quoted in femtometres where 1 fm = 10⁻¹⁵ m. A typical nucleus has R ≈ 1.2 × 10⁻¹⁵ m × A^(1/3), so a single nucleon radius constant R₀ ≈ 1.2 fm and the radius grows as the cube root of the nucleon number A. For example, A = 64 gives R ≈ 4.8 fm, while A = 197 gives R ≈ 7.0 fm. This means nuclear volume is proportional to A, so nuclear density is roughly constant for all nuclei, unlike atomic radii which are about 10⁻¹⁰ m.

What earns the marks

• States that nuclear radii are of the order of 10⁻¹⁵ m to 10⁻¹⁴ m, or 1 fm to 10 fm.
• Recalls the relationship R = R₀A^(1/3) with R₀ approximately 1.2 fm.
• Uses the relationship to calculate a typical radius for a given nucleon number A.
• Explains that radius increases with the cube root of nucleon number, so volume is proportional to A.
• Deduces that nuclear density is approximately constant across different nuclei because mass and volume both scale with A.
• Compares nuclear size with atomic size, noting that nuclear radii are about 10⁻⁵ to 10⁻⁴ times atomic radii.

Common mistakes and how to put them right

• Writing R ∝ A instead of R ∝ A^(1/3).

  Put it right by remembering volume is proportional to A, so radius scales as the cube root.

• Using R₀ = 1.2 × 10⁻¹⁰ m.

  Put it right by using R₀ ≈ 1.2 × 10⁻¹⁵ m.

• Confusing nuclear radius with atomic radius.

  Put it right by noting atomic radii are around 10⁻¹⁰ m, roughly 10⁵ times larger.

Exam tips

• Quote R₀ ≈ 1.2 fm when using R = R₀A^(1/3), as the value may be expected in the answer.
• Check whether the question asks for a value in metres or femtometres and convert consistently.
• Use the cube-root relationship to justify constant nuclear density when asked to explain it.