14. Stellar Astrophysics & Nucleosynthesis
CollegeEvery atom of iron in your blood and calcium in your bones was forged inside a star. This chapter derives how, and why fusion stops at iron.
Stellar structure and fusion chains
A star's interior obeys the equation of hydrostatic equilibrium, balancing the inward pull of gravity against the outward gradient of pressure at every radius: dP/dr = −G M(r) ρ(r) / r². Energy generated by fusion in the core is transported outward by radiation and/or convection, ultimately escaping as the star's luminosity.
Sun-like stars fuse hydrogen via the proton-proton chain: four protons combine, through several steps, into one helium-4 nucleus, releasing energy from the resulting mass deficit. More massive, hotter stars additionally (or primarily) use the CNO cycle, where carbon, nitrogen and oxygen act as catalysts to fuse hydrogen into helium faster at high temperature. As stars evolve, cores fuse progressively heavier elements — helium into carbon, then up through neon, oxygen, and silicon — each stage shorter and hotter than the last.
Why fusion stops at iron
Nuclear binding energy per nucleon peaks at iron-56 — fusing lighter elements together releases energy (exothermic), but fusing iron with anything else absorbs energy (endothermic) rather than releasing it. A massive star's core therefore fuses its way up to iron and then stalls: with no further energy source to resist gravity, the core collapses catastrophically in milliseconds, triggering a core-collapse supernova.
Worked example — energy from hydrogen fusion
Four protons (mass 1.6726×10⁻²⁷ kg each) fuse into one helium-4 nucleus (mass 6.6447×10⁻²⁷ kg). Find the energy released per fusion event using E = Δmc².
- Mass of 4 protons: 4 × 1.6726×10⁻²⁷ = 6.6904×10⁻²⁷ kg.
- Mass deficit: Δm = 6.6904×10⁻²⁷ − 6.6447×10⁻²⁷ = 4.57×10⁻²⁻⁵ kg.
- Apply E = Δmc² with c² = 9.00×10¹⁶ m²s⁻²: E = 4.57×10⁻²⁻⁵ × 9.00×10¹⁶ ≈ 4.11×10⁻¹² J.
- About 0.7% of the original mass converts to energy — the source of a star's entire luminous output over billions of years.
Answer: roughly 4.1×10⁻¹² J per fusion event — a tiny amount per reaction, but multiplied by roughly 10³⁶ such reactions per second in the Sun's core, it powers the entire Solar System.
Test your understanding
Why does fusion release energy for light elements but not for iron and beyond?
Because nuclear binding energy per nucleon increases with mass number up to iron-56, then decreases. Fusing elements lighter than iron moves nucleons toward the more tightly-bound iron peak, releasing the difference as energy. Fusing iron or heavier elements would move away from that peak, requiring an energy input rather than releasing one.
What is the CNO cycle, and when does it dominate over the proton-proton chain?
The CNO cycle fuses hydrogen into helium using carbon, nitrogen, and oxygen nuclei as catalysts (they are regenerated, not consumed). It dominates in stars more massive and hotter than the Sun (roughly above 1.3 solar masses), because its reaction rate is far more sensitive to temperature than the proton-proton chain.
Where do elements heavier than iron, like gold, come from?
Not from ordinary stellar fusion, which stops being energetically favourable at iron. Heavy elements form via rapid neutron capture (the r-process) in extreme events like core-collapse supernovae and neutron-star mergers, where free neutrons are abundant enough to build up heavy nuclei before they decay.
What triggers a core-collapse supernova?
Once a massive star's core has fused its way to iron, no further fusion stage releases net energy, so the core loses its outward pressure support. Gravity then collapses the core in a fraction of a second, and the resulting rebound and shockwave blast the star's outer layers into space as a supernova.
How the ideas connect
Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.
The process, step by step
Worked problems, step by step
Follow each solution line by line, then try to reproduce it on paper before moving on.
Example 1Fusing hydrogen to helium converts about 0.7% of the mass to energy. How much energy from 1 kg of hydrogen?
- Mass converted = 0.007 x 1 kg = 0.007 kg
- E = mc^2 = 0.007 x (3e8)^2
- E = 0.007 x 9e16 = ~6.3e14 J
Example 2Why does fusion stop producing energy at iron?
- Fusion releases energy only when it raises binding energy per nucleon
- Iron sits at the peak of binding energy per nucleon
- Fusing beyond iron absorbs energy instead of releasing it
Now you try
Work each one out first, then tap to reveal the worked answer.