Mini Physics
Part of Mini EducationSwitch subject
Search

Binding Energy

Key idea: Define nuclear binding energy, relate it to mass defect using E_b = Δm c^2, and use it to compare nuclear stability (A Level Physics).

  • GCE A-Level H2 Physics 2027
On this page

Learning objectives

  • Use mass-energy equivalence, mass defect and binding energy.

1. Definitions (Must Know)

A. Nuclear binding energy, E_b

The nuclear binding energy, E_b, is the energy required to separate a nucleus completely into its individual nucleons (protons and neutrons).

B. Relationship with mass defect

If a nucleus has mass defect Δ m, then: E_b = Δ m c²

Equivalently (energy conservation form): m_nucleusc² + E_b = (sum of nucleon rest energies)

2. Key Ideas (What Earns Marks)

  • Binding energy is a measure of how strongly nucleons are bound in the nucleus.
  • Mass defect exists because energy is released when the nucleus forms: E_b = Δ m c²
  • Larger binding energy per nucleon usually means greater stability (handled in the next lesson).
Mark-scheme phrasing

“Binding energy is the energy needed to separate the nucleus into its nucleons.”

3. Detailed Explanations

A. Why bound nuclei have smaller mass

When nucleons bind, energy is released. The system’s mass decreases by Δ m so that mass–energy is conserved: E_b = Δ m c²

B. What binding energy tells you physically

A larger binding energy means you must do more work against the strong nuclear force to pull the nucleus apart.

4. Common Mistakes

  • Defining binding energy as “energy released in decay” (it is the energy to separate the nucleus).
  • Mixing up binding energy (total) with binding energy per nucleon (average).
  • Using Δ m with the wrong sign (use Δ m = m_separated-m_bound).

5. Exam Tips

  • In calculations: find Δ m first, then multiply by c².
  • Keep units consistent: u → kg before using c in SI, or use 1u c² ≈ 931 MeV (if allowed/given).
  • If asked about stability: mention “binding energy per nucleon”, not total binding energy.

6. Worked Examples

Modelled example 1

Binding energy from a mass defect (in u)

Core

Problem

A nucleus has mass defect Δ m = 0.0150 u. Find the binding energy in joules. Take 1u = 1.66 × 10⁻²⁷ kg and c = 3.00 × 10⁸ m s⁻¹.
Study the worked solution

  1. Convert mass to SI

    Method

    Δ m = 2.49 × 10⁻²⁹ kg.

    Reason

    The SI form E = mc² returns joules only when mass is in kilograms.

    Working

    Δ m = 0.0150(1.66 × 10⁻²⁷) = 2.49 × 10⁻²⁹ kg

  2. Apply mass–energy equivalence

    Method

    E_b = 2.24 × 10⁻¹² J.

    Reason

    The mass defect is the energy equivalent of nuclear binding.

    Working

    E_b = (2.49 × 10⁻²⁹)(3.00 × 10⁸)² = 2.24 × 10⁻¹² J

Guided practice 2

Meaning question

About 3 min

Problem

What does a larger total binding energy tell you about a given nucleus?

Try this before viewing the solution

Physical meaning

Hints

Hint 1: return to the definition
Ask what operation the binding energy quantifies.
View solution step by step

  1. State the interpretation

    Method

    The nucleons are more strongly bound: more energy is required to separate the nucleus completely.

    Reason

    Binding energy is defined as separation energy for that nucleus.

    Working

    larger E_b → more separation work

  2. Limit the comparison

    Method

    For nuclei with different nucleon numbers, stability comparisons should use binding energy per nucleon.

    Reason

    A larger nucleus can have greater total binding energy simply because it contains more nucleons.

    Working

    stability comparison: E_b/A

Common misconception 3

Binding energy using the u to MeV shortcut

Find and correct the mistake

Learner claim

A nucleus has Δ m = 0.025 u. A learner divides by 931 to convert the mass defect to energy. Diagnose the direction of conversion and estimate E_b. Use 1u c² = 931 MeV.

Try this before viewing the solution

Unit: MeV

View solution step by step

  1. Read the conversion factor

    Method

    Multiply mass in u by 931 MeV per u.

    Reason

    The factor states the energy equivalent of one atomic mass unit.

    Working

    E_b = (0.025 u)(931 MeV/u)

  2. Evaluate

    Method

    E_b = 23.3 MeV.

    Reason

    The atomic-mass unit cancels, leaving energy.

    Working

    E_b = 0.025(931) = 23.3 MeV

Examiner practice 4

Mass defect from binding energy

2 marks

Examination question

A nucleus has binding energy E_b = 28.0 MeV. Find the mass defect in u. Use 1u c² = 931 MeV. [2 marks]

Try this before viewing the solution

View solution step by step

  1. Reverse the conversion

    1 mark

    Method

    Δ m = E_b/(931 MeV/u).

    Reason

    Energy is being converted back to its mass equivalent.

    Working

    Δ m = 28.0/931 u

  2. Evaluate

    1 mark

    Method

    Δ m = 3.01 × 10⁻² u ≈ 0.030 u.

    Reason

    The result is a mass expressed in atomic mass units.

    Working

    Δ m = 3.01 × 10⁻² u

Challenge 5

Comparing stability (binding energy per nucleon)

Minimal support

Independent transfer

Nucleus X has E_b = 92 MeV and A = 12. Nucleus Y has E_b = 120 MeV and A = 16. Compare their stability using binding energy per nucleon.

Try this before viewing the solution

Hints

Hint 1: normalise each total
Calculate E_b/A for each nucleus before comparing.
View solution step by step

  1. Calculate X average

    Method

    For X, E_b/A = 7.67 MeV per nucleon.

    Reason

    Divide the whole-nucleus energy by its 12 nucleons.

    Working

    (E_b/A)_X = 92/12 = 7.67 MeV

  2. Calculate Y average

    Method

    For Y, E_b/A = 7.50 MeV per nucleon.

    Reason

    Use the same average for a fair comparison.

    Working

    (E_b/A)_Y = 120/16 = 7.50 MeV

  3. Compare stability

    Method

    X is slightly more tightly bound by this measure.

    Reason

    Its binding energy per nucleon is larger even though its total binding energy is smaller.

    Working

    7.67 > 7.50

7. Mind Stretchers

Mind stretcher 1: Why can a nucleus release energy if it forms from nucleons?Extension

Show Answer

Because the bound nucleus has lower total energy (and lower mass) than the separated nucleons. The difference is released (often as kinetic energy and gamma radiation) when the nucleus forms.

Mind stretcher 2: Why is binding energy not “stored chemical energy”?Extension

Explain why nuclear binding energy is much larger than chemical bond energies, even though both involve “binding”.

Show Answer

Chemical bonds involve electromagnetic interactions between electrons and nuclei, with energy scales typically eV per bond.

Nuclear binding energy comes from the strong nuclear force acting at femtometre distances between nucleons, giving MeV-scale energy changes per nucleon, which is much larger.

Continue with the next resource in this course.

Course and syllabus information
Course
GCE A-Level H2 Physics
Edition
GCE A-Level H2 Physics 2027