IB DP Physics · Theme E Nuclear and quantum physics · E.5 · ~6 min read
E.5 Fusion and stars
Fusion and the conditions it needs, stellar equilibrium, the energy source of stars, stellar parallax, the Hertzsprung–Russell diagram, and the evolution of stars into white dwarfs, neutron stars and black holes.
Nuclear fusionConditions for fusionStellar equilibriumParallax & the parsecHR diagramStellar evolutionWhite dwarfs, neutron stars, black holes
RSby Riyaz Sir
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No tag = SL and HLHL ONLY HL students onlyDATA BOOKLET given in the examM1A1 how marks are awardedhighlight = comes up again and againTest yourself at the end
In 30 seconds
- Fusion joins light nuclei into heavier ones. The products have a higher binding energy per nucleon, so energy is released. Stars are powered by fusing hydrogen into helium.
- Fusion needs very high temperature (to overcome the electric repulsion) and high density (so collisions are frequent).
- A main-sequence star is stable because the inward pull of gravity balances the outward radiation and gas pressure from fusion.
- Stars are mapped on the Hertzsprung–Russell diagram (luminosity against temperature). Their mass decides their fate: white dwarf, neutron star or black hole.
- E.5 is the same at SL and HL.
By the end you can
- Explain why fusion releases energy and the conditions it needs.
- Explain the equilibrium of a main-sequence star.
- Measure stellar distances with parallax and the parsec.
- Read and interpret the HR diagram, including using luminosity and temperature to compare radii.
- Describe the evolution of low-mass and high-mass stars and their end points.
1Fusion
4 11H → 42He + 2 0+1e + 2ν + energy
overall result of the proton–proton chain in the Sun (about 26.7 MeV)- Why it releases energy: on the binding-energy curve (E.3) light nuclei sit on the steep rising part, so building them up raises the binding energy per nucleon.
- Conditions: nuclei are positive and repel. They need enough kinetic energy to get within range of the strong force: temperatures of about 107 K, and high density for enough collisions. The Sun's core provides both; on Earth, magnetic confinement (tokamaks) is still experimental.
Worked example
The Sun's luminosity is 3.8 × 1026 W. How much mass does it convert to energy each second?
- Δm = E/c2 = 3.8 × 1026/(3.0 × 108)2 M1
- = 4.2 × 109 kg s−1 A1
2Stellar equilibrium
- If fusion slowed, pressure would drop, the core would contract and heat up, and fusion would speed up again: the balance is self-correcting. When hydrogen in the core runs out, the balance shifts and the star changes stage.
3Distances: parallax
d (parsec) = 1p (arc-second) DATA BOOKLET
1 pc ≈ 3.26 light-years ≈ 3.09 × 1016 mWorked example
A star has a parallax angle of 0.20 arc-seconds. Find its distance.
- d = 1/0.20 = 5.0 pc A1
- = 5.0 × 3.26 = 16 light-years A1
- Limits: parallax angles become too small to measure beyond a few hundred parsecs from the ground (further with satellites such as Gaia).
4The Hertzsprung–Russell diagram
- Axes: luminosity (log scale, often in solar luminosities) against surface temperature, decreasing to the right. Colour runs from blue (hot) on the left to red (cool) on the right.
- Reading radius: L = σ(4πR2)T4 (B.1). Red giants are cool but very luminous, so they must be huge; white dwarfs are hot but dim, so they must be tiny.
Worked example
A red giant has the same surface temperature as a main-sequence star but 10 000 times its luminosity. Compare their radii.
- L ∝ R2T4; same T, so L ∝ R2 M1
- R ratio = √10 000 = 100 A1
Common mistakeReading the temperature axis the wrong way round. On an HR diagram hot stars are on the left.
5Stellar evolution
- Low and medium mass (like the Sun): main sequence (hydrogen fusion) → red giant (helium fusion in the core, outer layers swell) → planetary nebula, leaving a white dwarf that slowly cools.
- High mass: main sequence (much shorter, because they burn fuel fast) → red supergiant (fusion up to iron) → supernova → a neutron star, or a black hole if the remaining core is massive enough.
- Elements: fusion in stars makes elements up to iron; heavier elements form in supernovae and neutron-star mergers. The atoms in your body were made in stars.
Exam tip"Explain why fusion stops at iron": iron-56 has the highest binding energy per nucleon, so fusing it further would absorb energy instead of releasing it.
Linking questionStellar spectra (E.1), redshift (C.5), black-body radiation (B.1) and gravity (D.1) all come together here: astronomy is how physicists test their models on the largest scales.
Idea for your IA / explorationUse public data (for example a star catalogue or Gaia data) to build your own HR diagram for a star cluster and estimate the cluster's age from where its main sequence turns off.
Test yourself — cover the answers first
Quick check
- Why does fusion need high temperatures?
- What keeps a main-sequence star stable?
- Define the parsec.
- Where are the hottest stars on an HR diagram?
- What will the Sun eventually become?
- Why are white dwarfs dim even though they are hot?
Exam-style
- Star A is at 10 pc and star B at 40 pc. They have the same luminosity. Compare their apparent brightness.
- A white dwarf at 20 000 K has luminosity 0.010 L☉. The Sun is at 5800 K. Find its radius in solar radii.
Show answers
- nuclei must move fast enough to overcome their electric repulsion
- gravity inward balanced by radiation and gas pressure outward
- the distance at which a star has a parallax angle of one arc-second
- on the left
- a red giant, then a white dwarf
- they are very small (small surface area)
- b ∝ 1/d2
bA/bB = (40/10)2
A is 16 times brighter - R/R☉ = √(L/L☉) × (T☉/T)2
= √0.010 × (5800/20 000)2
= 0.10 × 0.0841 = 0.0084 R☉ (about the size of the Earth)
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