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Theme E — Nuclear and Quantum Physics

E.3.4 Radioactive Decay Equations — IB Physics HL Revision Notes & Topical Questions

5 min read 12 parts Lesson 21 of 45 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

E.3.4 Radioactive Decay Equations — IB PHYSICS SL notes: Write balanced nuclear equations for alpha, beta, electron capture and gamma decay using conservation of nucleon number and charge.Layout — the parent nuclide is on the left and the daughter and emitted particle are on the …

  • Conserved quantities
  • Particle symbols
  • General equation
  • Typical emitters
  • Chain example
  • Beta-plus process

Part 1 of 10Nuclear equations and conservation

Nuclear equations and conservation
Layout
  • Layout the parent nuclide is on the left and the daughter and emitted particle are on the right
Conserved quantities
  • Conserved quantities the nucleon number A and the charge (sum of bottom numbers)
    • (sum of top numbers)
  • Mass–energy is also conserved, but A and Z are what is balanced.
Neutrinos
  • Neutrinos they have A = 0 and Z = 0, so they do not affect the balance
  • They are still needed for energy, momentum and lepton number.
Particle symbols
  • Particle symbols alpha 42He, electron 0−1e, positron 0+1e, neutron 10n, proton 11p, photon γ with 0 and 0

Part 2 of 10Which decay occurs

Reason for instabilityDecay mode
Too many neutronsBeta-minus emission
Too many protonsBeta-plus emission or electron capture
Too many nucleonsAlpha emission
Too much energyGamma emission

Part 3 of 10Alpha decay

Change
  • Change the parent loses 2 protons and 2 neutrons, so A falls by 4, Z falls by 2 and N falls by 2
General equation
  • AZX → A−4Z−2Y + 42α
Example
  • 23892U → 23490Th + 42He
Typical emitters
  • Typical emitters heavy nuclei, too large to be stable
    • (A above about 200)
Chain example
  • 23994Pu → 23592U + 42α, then 23592U → 23190Th + 42α

Part 4 of 10Beta-minus decay

1Process
  • Process a neutron turns into a proton, an electron and an antineutrino, n → p + e− + antineutrino
2Change
  • A is constant, N falls by 1 and Z rises by 1
3General equation
  • AZX → AZ+1Y + 0−1e + antineutrino
4Example
  • 146C → 147N + 0−1e + antineutrino
5Occurs in
  • Occurs in neutron-rich nuclei

Part 5 of 10Beta-plus decay and electron capture

1
Beta-plus process
  • Beta-plus process a proton turns into a neutron, a positron and a neutrino, p → n + e+ + neutrino
2
Change
  • A is constant, N rises by 1 and Z falls by 1
3
General equation
  • AZX → AZ−1Y + 0+1e + neutrino
4
Example
  • 2211Na → 2210Ne + 0+1e + neutrino
5
Electron capture
  • Electron capture an orbiting electron is taken into the nucleus and combines with a proton to form a neutron and a neutrino
  • AZX + 0−1e → AZ−1Y + neutrino.
6
Occurs in
  • Occurs in proton-rich nuclei
7
Neutrino pairing
  • Neutrino pairing the antineutrino goes with beta-minus and the neutrino with beta-plus

Part 6 of 10Gamma emission

1Cause
  • Cause after alpha or beta decay the daughter is often in an excited state
2Process
  • Process it falls to a lower level by emitting a gamma photon
  • A and Z do not change.
  • The photon energy equals the difference between the nuclear energy levels.
3Notation
  • Notation an excited nucleus is marked with an asterisk, for example 6028Ni* → 6028Ni + γ

Part 7 of 10N–Z graph

N–Z graph
Alpha decay
  • Alpha decay it moves the nuclide down 2 in N and 2 in Z
Beta-minus decay
  • Beta-minus decay it moves the nuclide down 1 in N and up 1 in Z
Beta-plus decay and electron capture
  • Beta-plus decay and electron capture they move it up 1 in N and down 1 in Z

Part 8 of 10Balancing method

1
Write the numbers for each particle.
2
Add the top numbers on each side and make them equal.
3
Add the bottom numbers on each side and make them equal.
4
Identify the unknown element from Z using the periodic table.
5
Write the emitted particle explicitly every time, including the (anti)neutrino.
1Decay chains
  • Decay chains a heavy nuclide such as uranium-238 decays through alpha and beta steps to a stable lead isotope
2Counting steps
  • Counting steps find the number of alphas from the change in A divided by four, then fix the beta count from the net charge change

Part 9 of 10Energy of a decay

Energy released
  • Energy released the mass difference between parent and products times c2
Alpha decay
  • Alpha decay only two bodies share the energy and momentum, so the alpha carries nearly all of it
  • The heavier daughter gets a fraction of about 4/A.
Beta decay
  • Beta decay the energy goes to the electron and neutrino, with a small recoil of the daughter

Part 10 of 10More from the specification

More from the specification
Decay equation balance
  • Decay equation balance equating nucleon and proton numbers across nuclear reactions provides a reliable means to deduce emitted decay products.
Radioactive Decay and Half-Life
  • Radioactive decay is a spontaneous, random breakdown of unstable parent atoms into stable daughter nuclei;
    • the half-life is the time required for half the radioactive atoms in a sample to decay, ranging from fractions of a second to millions of years.
Types of Ionizing Radiation and Penetrating Ability
  • Unstable nuclei emit ionizing radiation: alpha particles, beta particles (high-speed electrons, moderate penetration),
    • (doubly charged, low penetrating power)
  • and gamma rays; recorded experimental activity must always be corrected for background radiation.
    • (highly penetrating photons)
Strong Nuclear Force and Binding Energy
  • The strong nuclear force acts attractively between all nucleons at short ranges (~1 to 3 fm) to balance electrostatic repulsion,
  • and nuclear binding energy represents the total energy needed to completely disassemble a nucleus into its constituent nucleons.
Radioactive Decay and Half-Life
  • Radioactive decay is a spontaneous, random breakdown of unstable parent atoms into stable daughter nuclei;
    • the half-life is the time required for half the radioactive atoms in a sample to decay, ranging from fractions of a second to millions of years.
Types of Ionizing Radiation and Penetrating Ability
  • Unstable nuclei emit ionizing radiation: alpha particles, beta particles (high-speed electrons, moderate penetration),
    • (doubly charged, low penetrating power)
  • and gamma rays; recorded experimental activity must always be corrected for background radiation.
    • (highly penetrating photons)
Strong Nuclear Force and Binding Energy
  • The strong nuclear force acts attractively between all nucleons at short ranges (~1 to 3 fm) to balance electrostatic repulsion,
  • and nuclear binding energy represents the total energy needed to completely disassemble a nucleus into its constituent nucleons.
Radiation
  • Transfer by electromagnetic waves, requiring no medium
Half-life
  • Time for half the nuclei of an isotope to decay.
Source
  • Reservoir at TH providing heat QH
Binding energy
  • The minimum energy required to separate the nucleons of a nucleus to infinity.
Background radiation
  • Radiation that is always present in the environment.
Ionising radiation
  • Radiation with enough energy to remove electrons from atoms
Penetrating power
  • How far radiation travels through a material.

Key terms

TermMeaning
Parent nuclideThe original unstable nuclide.
Daughter nuclideThe product nuclide after decay.
AntineutrinoAntiparticle of the neutrino, emitted in β⁻ decay.
Electron captureA nucleus takes in an orbital electron, turning a proton into a neutron.
Excited stateA nucleus with more energy than its ground state.
Decay chainA series of successive decays ending in a stable nuclide.

Avoid these mistakes

1
Forgetting that A does not change in beta decay.
2
Writing the beta particle with +1 charge for β⁻ — it is −1.
3
Omitting the (anti)neutrino from beta decay equations.
4
Changing A or Z in gamma emission — neither changes.
5
Mixing up which of neutrino and antineutrino goes with β⁻ (antineutrino) and β⁺ (neutrino).

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