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Theme E — Nuclear and Quantum Physics

E.3.12 Nuclear Energy Levels — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 29 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.3.12 Nuclear Energy Levels — IB PHYSICS HL notes: Explain gamma emission from excited nuclei, discrete alpha and gamma energies and nuclear energy level diagrams.Excited state — a nucleus can exist in an excited state in the same way as an electronAfter a decay — the daughter n…

  • Photon emission
  • What the symbols mean
  • Mapping levels
  • Wavelength
  • Fingerprint
  • Gamma spectra

Part 1 of 7Excited nuclei

Excited state
  • Excited state a nucleus can exist in an excited state in the same way as an electron
After a decay
  • After a decay the daughter nucleus may be left with excess energy which is emitted as a gamma photon
Photon emission
  • Photon emission it does not change the number of protons or neutrons, only the energy of the nucleus
Lifetime
  • Lifetime the excited state is usually very short-lived, and the nucleus moves to the ground state directly or via lower excited states

Part 2 of 7Photon energy

Equation
  • E = hf = Ei − Ef
    What the symbols mean: E = energy of one photon (J) · h = Planck constant (6.63 × 10−34 J s) · f = frequency (Hz)
Symbols
  • Symbols h = 6.63 × 10−34 J s, f the photon frequency and Ei, Ef the initial and final level energies
Mapping levels
  • Mapping levels measured gamma energies reveal the level diagram, as atomic spectra reveal atomic levels
Wavelength
  • λ = hc/E, with MeV converted to joules
Fingerprint
  • Fingerprint the gamma energies of a nuclide identify an unknown source

Part 3 of 7Discrete energies of alpha and gamma

Gamma spectra
  • Gamma spectra sharp lines rather than a smooth distribution
Alpha spectra
  • Alpha spectra a single emitter commonly emits alpha particles at a few discrete energies, such as 5.49 and 5.44 MeV for americium-241
Reason
  • Reason each alpha energy corresponds to decay to a different level of the daughter
  • The faster alpha leaves the daughter in the ground state
Two-body decay
  • Two-body decay alpha decay involves just two bodies, so energy and momentum fix the energies
Beta
  • Beta the spectrum is continuous because the decay energy is shared among three bodies

Part 4 of 7Metastable technetium-99m

Origin
  • Origin a technetium-99 nucleus in an excited state, formed from molybdenum-99 beta decay
Decays
  • 9942Mo → 99m43Tc + e− + antineutrino, then 99m43Tc → 9943Tc + γ
Metastable
  • Metastable the m means a particularly long-lived excited state
Use
  • Use a source for medical diagnosis, with gamma energy about 140 keV

Part 5 of 7Energy level diagrams

Ground state
  • Ground state a horizontal line at the bottom, often at 0
Excited states
  • Excited states horizontal lines stacked above in ascending energy
Decay mode
  • Decay mode a diagonal line, usually for alpha or beta decay
Transitions
  • Transitions vertical arrows for gamma photons
Cobalt-60
  • Cobalt-60 beta decay to excited nickel-60 followed by gamma photons of 1.17 MeV and 1.33 MeV
Number of lines
  • Number of lines n levels can give n(n − 1)/2 transitions between them

Part 6 of 7Comparison with atomic levels

Similarity
  • Similarity both have discrete levels and transitions that emit photons
Spacing
  • Spacing nuclear levels are separated by keV to MeV and atomic levels by eV
Forces
  • Forces strong and electromagnetic interactions determine nuclear levels
Evidence
  • Evidence the levels are inferred from the energies of emitted radiation
Maximum beta energy
  • Maximum beta energy the maximum kinetic energy of the beta particle is the total decay energy minus the energy of the excited state populated

Part 7 of 7More from the specification

1Radioactive Half-Life and Decay Constant
  • The half-life (t_½) of a radioactive isotope is related to its decay constant λ by t_½ = ln(2) / λ, representing the time for activity to halve.
2Sample Activity Measurement
  • Activity is measured in becquerels (Bq), corresponding to one nuclear disintegration per second recorded on a count meter.
    • (A = -ΔN/Δt = λN)
3Radioactive Dating Using Long-Lived Isotopes
  • Measuring the ratio of parent radioisotopes to daughter isotopes in geological rock samples allows determination of age spanning millions of years.
4Nuclear Energy State De-excitation
  • Like atomic electron orbitals, atomic nuclei possess discrete quantum energy states;
    • transitions between nuclear levels emit gamma rays of exact energies.
5Ionising radiation
  • Radiation with enough energy to remove electrons from atoms
6Penetrating power
  • How far radiation travels through a material.
7Radioactive
  • Describes a nucleus that decays spontaneously and randomly.
8Activity
  • Number of decays per second of a sample.
9Half-life
  • Time for half the nuclei of an isotope to decay.
10Isotope
  • Atom of the same element with a different number of neutrons.
11Isotopes
  • Nuclei with the same proton number but different neutron numbers.
12Binding energy
  • The minimum energy required to separate the nucleons of a nucleus to infinity.
13Radioactive decay
  • Natural process in which unstable nuclei release energy.
14Background radiation
  • Radiation that is always present in the environment.

Key terms

TermMeaning
Excited nucleusA nucleus with more energy than its ground state.
Gamma photonA photon emitted when a nucleus drops to a lower energy level.
Metastable stateA long-lived excited state such as technetium-99m.
Nuclear energy levelOne of the discrete energies a nucleus can have.
Energy level diagramA diagram of horizontal lines for levels and arrows for decays and transitions.

Avoid these mistakes

1
Thinking nuclear levels are the same as atomic electron levels — nuclear energies are far larger.
2
Assuming beta particles show discrete lines — their spectrum is continuous.
3
Using the energy of the nucleus as the photon energy instead of the difference between levels.
4
Forgetting to convert MeV to joules when finding wavelength.
5
Believing gamma emission changes the proton or nucleon numbers.

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