Theme E · Nuclear and Quantum Physics · SL + HL · 6 hours

E.5 Fusion and Stars

What powers the stars, and how do we read their history from their light?

Stars are fusion reactors held together by gravity. In their cores, temperatures exceed 10 million Kelvin — high enough for hydrogen nuclei (protons) to overcome electrostatic repulsion and fuse into helium, releasing energy because helium-4 has greater binding energy per nucleon than the hydrogen nuclei. Our Sun converts about 600 million tonnes of hydrogen to helium every second; the "missing mass" emerges as the sunlight that sustains all life on Earth.

The Hertzsprung-Russell (HR) diagram is the central tool of stellar physics. Plot luminosity against surface temperature (or spectral class) and most stars fall on the main sequence — a diagonal band where stars spend the bulk of their lives fusing hydrogen. The position on the main sequence is determined by mass: massive stars are hotter, bluer, more luminous, and short-lived (millions of years); low-mass stars are cooler, redder, dimmer, and can last trillions of years. When hydrogen in the core is exhausted, a star leaves the main sequence: it expands into a red giant (or red supergiant), then ends as a white dwarf (low mass), neutron star, or black hole (high mass). The path on the HR diagram tells the entire life story.

Star X has luminosity 100L☉ and surface temperature 10,000 K. Star Y has luminosity 0.01L☉ and temperature 4,000 K. Identify their types on the HR diagram. Which star has the longer main-sequence lifetime, and why? (Stefan-Boltzmann: L = 4πR²σT⁴)

Key equations and facts

Stellar luminosity: L = 4πR²σT⁴ (Stefan-Boltzmann)
Wien's law: λmaxT = 2.9 × 10⁻³ m K (peak wavelength → temperature)
Apparent brightness: b = L / (4πd²) (inverse-square law)
HL Stellar parallax: d (parsecs) = 1 / p (arcseconds); 1 pc = 3.26 ly
HL Distance modulus: m − M = 5 log₁₀(d/10) (d in parsecs)

What students must understand

Linking questions

Video Support

Michel van Biezen
Physics - Nuclear Physics (16 of 22) What is Nuclear Fusion?
Astronomy - The Sun (3 of 16) Nuclear Fusion