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Theme E — Nuclear and Quantum Physics

E.5.1 Fusion Reactions in Stars — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 38 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.5.1 Fusion Reactions in Stars — IB PHYSICS SL notes: Explain the conditions needed for fusion and describe how stars release energy by fusing hydrogen into helium.Nuclear fusion = the joining of two small nuclei to produce a larger nucleus.Low-mass nuclei such as hydrogen and h…

  • The product has a higher binding energy per nucleon
  • Both nuclei must have high kinetic energy
  • The strong nuclear force has a very short range
  • Mean kinetic energy of gas particles is (3/2)kT
  • Fusion still occurs
  • High temperature (above about 107 K)

Part 1 of 8What fusion is

What fusion is
Nuclear fusion
Nuclear fusion the joining of two small nuclei to produce a larger nucleus.
  • Low-mass nuclei such as hydrogen and helium fuse and release energy.
The product has a higher binding energy per nucleon
  • The product has a higher binding energy per nucleon so energy equal to Δmc2 is released.
  • The mass of the new nucleus is less than the total mass of the nuclei fused.
Fusion powers the Sun and all main-sequence stars.

Part 2 of 8Overcoming electrostatic repulsion

Overcoming electrostatic repulsion
Both nuclei must have high kinetic energy
  • Both nuclei must have high kinetic energy to overcome the repulsive Coulomb force between protons.
The strong nuclear force has a very short range
  • The strong nuclear force has a very short range so nuclei must get very close, within about 1 fm.
The electrostatic potential energy at 1 fm is about 2 × 10-13 J (around 1.4 MeV).
Mean kinetic energy of gas particles is (3/2)kT
  • Mean kinetic energy of gas particles is (3/2)kT at the Sun's core temperature of 1.5 × 107 K it is only about 2 keV.
Fusion still occurs
  • Fusion still occurs because some particles in the high-energy tail have far more than average, and quantum tunnelling helps.
  • The enormous number of particles makes up for the low probability for each pair.

Part 3 of 8Conditions for fusion

1High temperature (above about 107 K)
  • High temperature (above about 107 K) so nuclei collide with enough energy.
  • The gas is then a plasma of free nuclei and electrons.
2High density and pressure
  • High density and pressure so collisions are frequent enough for a significant reaction rate.
3Confinement for long enough
  • Confinement for long enough in a star gravity holds the plasma together.
  • On Earth, magnetic fields or inertia must do the job.
4
Only the core, about the central 10% of the mass, is hot and dense enough for fusion.

Part 4 of 8Hydrogen fusion in stars

1
In the centre of a star four hydrogen nuclei (11H) fuse to form a helium nucleus (42He).
  • The products are also two positrons, two neutrinos and gamma-ray photons.
2
Proton-proton chain steps.
  • 11H + 11H gives 21H + e+ + electron neutrino, as a proton changes to a neutron by beta-plus decay.
  • 11H + 21H gives 32He + γ.
  • 32He + 32He gives 42He + 2 11H.
3The first step is a very slow weak interaction
  • The first step is a very slow weak interaction so the Sun burns steadily for billions of years.
4Neutrinos escape
  • Neutrinos escape carrying about 2% of the energy released.
5
In stars above about 1.3 solar masses the CNO cycle, with carbon as catalyst, dominates
  • because it depends more strongly on temperature.

Part 5 of 8Energy output and equilibrium

1Mass lost per helium nucleus formed
  • 4 × 1.007825 u − 4.002603 u = 0.028697 u.
  • This is about 4.3 × 10-12 J per reaction, which gives the luminosity of the Sun of 3.85 × 1026 W.
2Radiation pressure from the photons
  • Radiation pressure from the photons balances the inward pull of gravity.
3Self-regulating star
  • Self-regulating star if the core heats up the fusion rate rises, the star expands and cools, and the rate falls.
4Hydrostatic equilibrium
Hydrostatic equilibrium the balance between gravity and internal gas and radiation pressure.

Part 6 of 8Deuterium-tritium fusion on Earth

Deuterium-tritium fusion on Earth
Research on Earth targets the D–T reaction: 21H + 31H gives 42He + 10n.
The helium nucleus has less mass than the individual nucleons
  • The helium nucleus has less mass than the individual nucleons so a large amount of energy is released per unit mass of fuel.
This energy can be harnessed in a fusion reactor
  • This energy can be harnessed in a fusion reactor but the hot, dense conditions must be reproduced.

Part 7 of 8Fusion of heavier elements

1When core hydrogen is exhausted, the core contracts and heats
  • When core hydrogen is exhausted, the core contracts and heats until helium fuses at about 108 K.
  • Triple-alpha process3 42He gives 126C.
2Massive stars fuse carbon, neon, oxygen and silicon in successive stages
  • Massive stars fuse carbon, neon, oxygen and silicon in successive stages building elements up to iron-56.
3Beyond iron fusion no longer releases energy
  • Beyond iron fusion no longer releases energy because iron-56 is at the maximum of the binding energy per nucleon curve.
4
Heavier elements are mostly made by neutron capture in supernovae and neutron-star mergers.

Part 8 of 8More from the specification

Nuclear fusion energy levels
  • Nuclear fusion energy levels overcoming Coulomb repulsion enables light hydrogen nuclei to fuse, populating deeply bound nuclear energy levels.
Stellar Nuclear Fusion
  • Core hydrogen nuclei fuse under extreme gravitational pressure and temperature into helium, releasing thermal energy and sustaining radiation pressure.
Hydrostatic Equilibrium in Stars
  • A stable main-sequence star balances inward gravitational collapse against the outward thermal gas and radiation pressure generated by core nuclear reactions.
Stellar Absorption Spectra
  • Continuous light emerging from a stellar core passes through cooler outer atmospheric gases,
  • producing dark absorption lines corresponding to elemental electron transitions.
Stellar Parallax and Distance
  • The apparent angular shift of a nearby star viewed against background stars over six months allows distance calculation via the trigonometric parallax formula d = 1 / p.
Surface temperature
  • Effective temperature of the star's radiating surface.
Stellar parallax
  • Apparent shift of a nearby star against distant stars as Earth orbits the Sun.
Emission spectrum
  • The set of discrete wavelengths emitted by excited atoms of an element.
Energy level
  • A discrete energy an electron in an atom can have
Spectrum
  • Range of colours in white light.
Absorption
  • The conversion of wave energy to internal energy of the medium.
Parallax
  • Apparent shift between objects caused by viewing from different positions
Distance
  • Total length of path travelled, a scalar.
Radius
  • Distance from the centre to the circular path.
Wavelength
  • Distance between a point on one wave and the same point on the next wave
White dwarf
  • Small, hot, dense core left by a low-mass star.
Absorption spectrum
  • A continuous spectrum crossed by dark lines where a cool gas absorbed specific wavelengths.

Key terms

TermMeaning
FusionJoining of light nuclei to make a heavier nucleus.
PlasmaHot gas of ions and free electrons.
Proton-proton chainSequence converting four protons into helium-4.
Hydrostatic equilibriumBalance between gravity and internal pressure in a star.
Coulomb barrierElectrostatic repulsion between nuclei that must be overcome.
Quantum tunnellingPassing through a barrier that classical mechanics forbids.
Radiation pressureOutward pressure from photons produced by fusion.

Avoid these mistakes

1
Thinking stars burn fuel chemically — they get energy from nuclear fusion.
2
Saying the Sun is hot enough for fusion without tunnelling — the mean energy is far below the barrier.
3
Believing fusion releases energy for all nuclei — beyond iron it needs energy input.
4
Confusing fusion with fission — fusion joins nuclei, fission splits them.
5
Forgetting that gravity provides the confinement in stars.

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