What mistakes do students make with The nuclear atom?

Using the proton number Z instead of the nucleon number A in the equation. Forgetting to take the cube root of A and instead multiplying r₀ by A. Confusing the constant r₀ with the nuclear radius R. r₀ is approximately 1.2 × 10⁻¹⁵ m, while R depends on A.

What are the exam tips for The nuclear atom in Physics OCR A-Level?

Write down the equation R = r₀A^(1/3) and substitute values carefully, keeping units consistent. Check whether the question gives A or asks you to find it from the notation. Remember that r₀ is approximately 1.2 × 10⁻¹⁵ m unless another value is given.

OCR · A-Level · Physics

Course version: H556 · Version from Sept 2015

(f) radius of nuclei; R = r₀A^(1/3) where r₀ is a constant and A is the…

Full specification wording

The nuclear atom: (f) radius of nuclei; R = r₀A^(1/3) where r₀ is a constant and A is the nucleon number

The radius R of a nucleus is related to its nucleon number A by R = r₀A^(1/3), where r₀ is an empirical constant approximately equal to 1.2 × 10⁻¹⁵ m.

Checked against the OCR H556 specification (opens in a new tab) on 10 November 2026.

Point 6 of 7
2 key terms

Study notes

From the checked teaching notes for this specification point.

The idea

For example: For A = 64, A^(1/3) = 4, so R = 4r₀ ≈ 4.8 × 10⁻¹⁵ m.

What earns the marks

The nuclear radius R is given by R = r₀A^(1/3), where A is the nucleon number.
r₀ is a constant approximately equal to 1.2 × 10⁻¹⁵ m.
The equation implies that nuclear volume is proportional to A, since volume ∝ R³.
A is the total number of nucleons (protons plus neutrons), not the proton number.
To calculate R, evaluate the cube root of A and multiply by r₀.
For example, for A = 64, R = 4r₀ ≈ 4.8 × 10⁻¹⁵ m.

Common mistakes and how to put them right

Using the proton number Z instead of the nucleon number A in the equation.
Forgetting to take the cube root of A and instead multiplying r₀ by A.
Confusing the constant r₀ with the nuclear radius R.
Put it right: r₀ is approximately 1.2 × 10⁻¹⁵ m, while R depends on A.
Assuming nuclear volume is proportional to A^(1/3) rather than to A; since R ∝ A^(1/3), volume ∝ R³ ∝ A.

Exam tips

Write down the equation R = r₀A^(1/3) and substitute values carefully, keeping units consistent.
Check whether the question gives A or asks you to find it from the notation.
Remember that r₀ is approximately 1.2 × 10⁻¹⁵ m unless another value is given.

Try the lesson

The start of the The nuclear atom: (f) radius of nuclei; R = r₀A^(1/3) where r₀ is a constant and A is the nucleon number lesson, made from checked teaching notes for this specification point.

Listen

The radius R of a nucleus is related to its nucleon number A by R = r₀A^(1/3), where r₀ is an empirical constant approximately equal to 1.2 × 10⁻¹⁵ m. This equation shows that nuclear volume is proportional to A, because volume depends on R³ and R³ = r₀³A. The constant r₀ represents the approximate radius of a single nucleon. To use the equation, substitute the nucleon number and evaluate A^(1/3), then multiply by r₀. For example, for A = 64, A^(1/3) = 4, so R = 4r₀ ≈ 4.8 × 10⁻¹⁵ m. A strong answer earns marks for these points. The nuclear radius R is given by R = r₀A^(1/3), where A is the nucleon number. r₀ is a constant approximately equal to 1.2 × 10⁻¹⁵ m. The equation implies that nuclear volume is proportional to A, since volume ∝ R³. A is the total number of nucleons (protons plus neutrons), not the proton number. Exam tip: Write down the equation R = r₀A^(1/3) and substitute values carefully, keeping units consistent.

See it

A top-down flowchart with six nodes. The first node, 'Nucleon number A', points to 'Evaluate cube root of A', which points to 'Multiply by r₀', which points to 'Nuclear radius R = r₀A^(1/3)'. That node points to 'Volume ∝ R³', which points to the final node 'Volume ∝ A'. — Shows the steps for calculating nuclear radius from the nucleon number using R = r₀A^(1/3), and how this leads to nuclear volume being proportional to A.

Put it in order

Put these steps in the order they happen.

1. Multiply by r₀
2. Evaluate cube root of A
3. Nucleon number A
4. Volume ∝ A
5. Volume ∝ R³
6. Nuclear radius R = r₀A^(1/3)

Key words

Say what each word means before you turn the card.

Nuclear radius

Try answering aloud or in your head before turning the card.

Nucleon number

Try answering aloud or in your head before turning the card.

See every definition

Nuclear radius: The radius R of a nucleus, given by R = r₀A^(1/3), where A is the nucleon number.
Nucleon number: The total number of nucleons (protons plus neutrons), not the proton number.

Label the diagram

Some boxes have lost their names. Pick the right name for each number.

The diagram again, with 3 boxes numbered instead of named. A top-down flowchart with six nodes. The first node, 'Nucleon number A', points to 'Evaluate cube root of A', which points to 'Multiply by r₀', which points to 'Nuclear radius R = r₀A^(1/3)'. That node points to 'Volume ∝ R³', which points to the final node 'Volume ∝ A'.

1Box 1
2Box 2
3Box 3

0 of 3 labelled

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