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Physics · 9. Nuclear physics and radioactivity

Atomic nucleus, binding energy and radioactive decay

Investigate mass defect, binding energy per nucleon, exponential radioactive decay law and nuclear reactions.

40 minutesContent version: 2.1
Start the interactive pathwayOpen the virtual experiment

Driving question

Why is the combined rest mass of separated protons and neutrons always strictly greater than the bound nucleus they form?

Curriculum coverage

Vietnam 2018 Physics 12 (Nuclear physics); Cambridge A-Level Physics 9702 Topic 23; AP Physics 2.

Model scope and limitations

Covers spontaneous radioactivity and standard nuclear reactions; omits non-perturbative quantum chromodynamics.

Learning objectives

  • Calculate mass defect Δm and binding energy E = Δm·c²; evaluate nuclear stability via binding energy per nucleon.
  • Apply radioactive decay laws N(t) = N0·2^(-t/T) = N0·e^(-λt) and evaluate half-life T.
  • Formulate alpha, beta-, beta+, and gamma decay equations, distinguishing fission from nuclear fusion.

Prerequisite knowledge

  • Atomic structure (mass number A, atomic number Z, neutron count N = A − Z).
  • Einstein mass-energy equivalence E = mc² and atomic mass unit conversion (1 u ≈ 931.5 MeV/c²).

Core knowledge

Mass defect and binding energy

Mass defect Δm = (Z·mp + N·mn) − m_nucleus converts into binding energy E = Δm·c². Binding energy per nucleon peaks near iron-56 (≈ 8.8 MeV/nucleon), identifying the most stable nuclei.

Exponential decay law

Undecayed nuclei diminish exponentially: N(t) = N0 e^(-λt) with decay constant λ = ln 2 / T. Activity H(t) = λN is measured in Becquerels (1 Bq = 1 decay per second).

Radiation types

Alpha is helium-4 nuclei (+2e); beta- is high-energy electrons; beta+ is positrons; gamma is ultra-high-energy photons with highest penetrating ability and zero charge.

Worked example

Iodine-131 has half-life T = 8 days. After 24 days (t = 3T), the remaining fraction is N/N0 = (1/2)³ = 1/8 = 12.5%. The fraction decayed into daughter nuclei is 100% − 12.5% = 87.5%.

Misconceptions to avoid

  • Half-life is an intrinsic nuclear property, completely invariant to temperature, chemical state, pressure, or magnetic fields.
  • Nuclear stability is governed exclusively by binding energy per nucleon (E/A), not by total raw binding energy E.

Virtual experiment procedure: Radioactive decay and half-life

  1. Launch the Geiger counter simulation, initialising radioactive source with N0 = 10,000 nuclei.
  2. Advance time steps and record remaining parent nuclei at t = T, 2T, 3T, 4T intervals.
  3. Plot N versus t on Cartesian coordinates, and verify the linearised plot ln(N) vs t whose slope equals −λ.

Safety and cautions

  • Ionising radiation carries cellular damage risks; in wet facilities, adhere strictly to ALARA principles (time, distance, lead shielding).

Evidence to collect

  • Data table tracking elapsed time t, undecayed nuclei count N, and instantaneous activity H.
  • Semi-logarithmic decay curve yielding experimental decay constant λ and half-life T.
Open the virtual experiment
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Diagnostic check

1. Which quantity dictates the stability of an atomic nucleus?

  1. Binding energy per nucleon (E/A)
  2. Total binding energy
  3. Mass number A
Show answer and explanation

Correct answer: Binding energy per nucleon (E/A)

Binding energy per nucleon measures the energy required to remove each nucleon; higher values signify greater stability.

2. In beta-minus (β-) decay, the nucleus emits an electron and which accompanying particle?

  1. Antineutrino
  2. Neutrino
  3. Positron
Show answer and explanation

Correct answer: Antineutrino

To conserve lepton number and spin, beta-minus decay (n → p + e- + ν̄_e) emits an electron antineutrino.

Application practice

1. A radionuclide has half-life T = 10 days. From an initial 80 g, how much remains after 30 days?

  1. 10 g
  2. 20 g
  3. 40 g
Show answer and explanation

Correct answer: 10 g

30 days corresponds to 3 half-lives: m = 80 × (1/2)³ = 10 g.

2. The mass defect of helium He-4 is Δm = 0.0304 u (1 u = 931.5 MeV/c²). What is its total binding energy?

  1. 28.3 MeV
  2. 7.08 MeV
  3. 113 MeV
Show answer and explanation

Correct answer: 28.3 MeV

E = 0.0304 × 931.5 ≈ 28.32 MeV (giving ≈ 7.1 MeV per nucleon).

3. Uranium-238 emits an alpha particle (He-4) to become Thorium (Th). What are Thorium’s A and Z?

  1. A = 234, Z = 90
  2. A = 236, Z = 91
  3. A = 234, Z = 92
Show answer and explanation

Correct answer: A = 234, Z = 90

Alpha emission reduces mass number by 4 (238 - 4 = 234) and proton number by 2 (92 - 2 = 90).

Academic references

  1. Cambridge IGCSE Physics 0625 — official syllabus and resources
  2. Cambridge AS & A Level Physics 9702 — official syllabus
  3. OpenStax Physics — peer-reviewed high-school physics
  4. BIPM — SI Brochure, 9th edition

This lesson is maintained against the cited sources below. Simulations are learning models and do not replace supervised physical-laboratory safety procedures.

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WebLab STEM
Technical maintainer
Đức Tiến — Control & Automation Engineer