Theme E — Nuclear and Quantum Physics
E.5.2 Energy Released in Fusion Reactions — IB Physics HL Revision Notes & Topical Questions
5 min read 10 parts Lesson 39 of 45 1 quiz
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.
Lesson summary
E.5.2 Energy Released in Fusion Reactions — IB PHYSICS SL notes: Calculate the energy released in fusion from mass differences or binding energies and compare fusion with fission.The larger nucleus formed has a higher binding energy per nucleon than the original nuclei.There is a…
- There is a mass defect between the original nuclei and the new nucleus
- In the hot core of a star fusion begins with two protons forming deuterium
- Alternative
- Use atomic masses or nuclear masses consistently
- With nuclear masses the mass defect is about 0.0265 u
- The positrons annihilate with two electrons
Part 1 of 8Why fusion releases energy
1
The larger nucleus formed has a higher binding energy per nucleon than the original nuclei.
2There is a mass defect between the original nuclei and the new nucleus
- There is a mass defect between the original nuclei and the new nucleus the difference in binding energy is released.
3Example
- Example two deuterium nuclei fusing to helium-4: helium has about 28 MeV, the deuterons about 4 MeV, so about 24 MeV is released.
4In the hot core of a star fusion begins with two protons forming deuterium
- In the hot core of a star fusion begins with two protons forming deuterium then helium forms and the star keeps burning.
Part 2 of 8Calculating the energy released
Calculating the energy released
Write the reaction and check that nucleon number and charge balance.
List the masses and find Δm = Σmreactants − Σmproducts.
Q (MeV) = Δm (u) × 931.5, or in joules Q = Δm c2.
Calculating the energy released
Alternative
- Q = Σ binding energy of products − Σ binding energy of reactants.
- Free protons and neutrons have zero binding energy.
Use atomic masses or nuclear masses consistently
- Use atomic masses or nuclear masses consistently so the electrons balance on both sides.
A positron emission step brings two extra electron masses into the balance.
Part 3 of 8Hydrogen to helium in the Sun
Hydrogen to helium in the Sun
Overall
- 4 11H gives 42He + 2e+ + 2 neutrinos.
With nuclear masses the mass defect is about 0.0265 u
- With nuclear masses the mass defect is about 0.0265 u about 24.7 MeV.
The positrons annihilate with two electrons
- The positrons annihilate with two electrons releasing a further 2 × 1.02 MeV, so the total is about 26.7 MeV.
- Neutrinos escape with about 2% of the energy.
Using atomic masses, 4(1.007825 u) − 4.002603 u
0.028697 u — about 4.3 × 10-12 J per reaction.
This is about 0.7% of the rest-mass energy of the hydrogen consumed.
Part 4 of 8Deuterium-tritium reaction
1
21H + 31H gives 42He + 10n, releasing 17.6 MeV.
- The neutron carries about 14.1 MeV and the helium nucleus about 3.5 MeV.
2It has the lowest ignition temperature, about 108 K
- It has the lowest ignition temperature, about 108 K so it is the most promising fusion reaction on Earth.
3Deuterium is abundant in seawater
- Deuterium is abundant in seawater tritium is radioactive and must be bred from lithium using the neutrons.
- (half-life 12.3 years)
4
The neutron's energy is captured as heat in a surrounding blanket.
Part 5 of 8Fusion compared with fission
| Feature | Fusion | Fission |
|---|---|---|
| Energy per nucleon | About 3.5 to 6 MeV (hydrogen isotopes to helium) | About 0.85 MeV (uranium) |
| Energy per kilogram | About 6 × 1014 J for hydrogen to helium, roughly 8 times uranium-235 | About 8 × 1013 J for uranium-235 |
| Reason | Binding energy curve is steeper for light nuclei | Curve is shallow for heavy nuclei |
| Initial energy input | Greater | Smaller |
| Waste | Helium, not radioactive; neutrons activate the structure | Radioactive fission products |
1Both reactions have products of slightly less mass than the reactants
- Both reactions have products of slightly less mass than the reactants the mass defect equals the energy released.
2Fusion plasma cannot run away
- Fusion plasma cannot run away if conditions fail the reaction simply stops.
Part 6 of 8Power of the Sun
Power of the Sun
The Sun radiates 3.83 × 1026 W.
Mass lost per second
P / c2 — about 4.3 × 109 kg s-1, roughly four million tonnes.
About 6 × 1011 kg of hydrogen fuses every second
- About 6 × 1011 kg of hydrogen fuses every second a tiny fraction of the Sun's mass of 2.0 × 1030 kg.
So the Sun can keep its output for billions of years.
Worked check
- Worked check the reactions per second equal divided by energy per reaction.
- (power minus neutrino share)
Part 7 of 8Fusion power on Earth
Fusion power on Earth
Net power needs ignition temperature, high enough density and long enough confinement time (the Lawson criterion).
Magnetic confinement (tokamaks and stellarators)
- Magnetic confinement (tokamaks and stellarators) holds hot plasma away from the walls with strong magnetic fields.
Inertial confinement
- Inertial confinement lasers compress a tiny fuel pellet.
Difficulties
- Difficulties heating plasma to 108 K, preventing instabilities and building walls that withstand neutron bombardment.
Energy appears as kinetic energy of the products
- Energy appears as kinetic energy of the products shared by momentum conservation, so the lighter product carries the larger share.
Part 8 of 8More from the specification
Transitions in nuclear energy levels
- Transitions in nuclear energy levels mass differences converted into radiant energy correspond to quantum steps between discrete nuclear energy levels.
Stellar Fusion and Main Sequence Equilibrium
- Main sequence stars generate energy by fusing hydrogen into helium in their cores;
- hydrostatic equilibrium is maintained when outward radiation and thermal pressure balance inward gravitational contraction.
Luminosity and Stefan-Boltzmann Law
- A star's total radiant power output (luminosity L) depends on its surface radius R and surface temperature T according to the Stefan-Boltzmann equation L = 4πR²σT⁴.
Stellar Absorption Spectra and Spectral Classes
- As stellar light passes through cooler outer atmospheres, specific wavelengths are absorbed,
- producing distinctive dark absorption lines that classify stars into spectral types.
- (O, B, A, F, G, K, M)
Stellar Parallax and Cosmic Distance
- Stellar parallax determines the distance d to nearby stars by measuring the apparent angular shift p against background stars as Earth orbits the Sun,
- where distance in parsecs equals d = 1 / p.
Stable main-sequence star
- An equilibrium state where inward gravitational collapse is counteracted by outward thermal pressure generated from sustained nuclear fusion.
White dwarf
- Small, hot, dense core left by a low-mass star.
Surface temperature
- Effective temperature of the star's radiating surface.
Energy level
- A discrete energy an electron in an atom can have
Continuous spectrum
- Spectrum with no gaps between the regions.
Spectrum
- Range of colours in white light.
Luminosity
- The total power of radiation emitted by a star.
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.
Photon
- A quantum of electromagnetic energy, E = hfWhat the symbols mean: E = energy of one photon (J) · h = Planck constant (6.63 × 10−34 J s) · f = frequency (Hz)
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
Key terms
| Term | Meaning |
|---|---|
| Q value | Energy released in a nuclear reaction. |
| D-T reaction | Fusion of deuterium and tritium into helium and a neutron, releasing 17.6 MeV. |
| Tokamak | Magnetic confinement device with a doughnut-shaped plasma. |
| Lawson criterion | Condition on density, temperature and confinement time for net energy gain. |
| Ignition | Fusion that sustains itself with no external heating. |
| Mass defect | Mass lost when nuclei fuse, equivalent to the energy released. |
Avoid these mistakes
1
Using nuclear and atomic masses together without balancing the electrons.
2
Thinking fusion releases less energy per kilogram than fission — it releases more.
3
Forgetting that neutrinos carry away some of the energy in the proton-proton chain.
4
Giving the D-T energy as 17.6 J instead of 17.6 MeV.
5
Believing the Sun's mass is being used up rapidly — it loses a tiny fraction.
Marked practiceQuizzes for this lesson
Last updated:
\n