The Sun's energy – nuclear fusion, hydrostatic equilibrium and energy output
PhysicsGravitation & AstronomyAges 17–18
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Sign in to playStep through the proton–proton chain (or the CNO cycle) in the Sun's core with protons, neutrons, positrons, neutrinos and gamma-ray photons, and work out the mass defect of 4 ¹H → ⁴He (26.73 MeV) and the mass the Sun loses each second, Δm/t = L/c² ≈ 4.3 × 10⁹ kg/s. The Inside the Sun screen lets you set the core temperature and density to compare gas and radiation pressure with gravity (hydrostatic equilibrium) and shows why protons must tunnel through the Coulomb barrier (the Gamow peak). The Energy output screen splits the Sun's spectrum into UV, visible and infrared, traces the Sun's path on the H–R diagram and estimates its lifetime.
Lesson: Nuclear fusion in the Sun, mass defect and E = Δmc², hydrostatic equilibrium and the life of the Sun
What it shows
The Sun shines because hydrogen nuclei in its core fuse into helium. Four hydrogen atoms have slightly more mass than one helium atom; this mass defect of 0.0287 u is released as 26.7 MeV, so the Sun converts about 4.3 billion kilograms of mass into energy every second. Fusion needs a temperature of about 15 million K and a high density, and even then protons only fuse by quantum tunnelling through their electrical repulsion. Gas pressure from the hot core balances gravity, and this equilibrium keeps the Sun stable for about 10 billion years.
How to use
On Fusion in the core, choose the Proton–proton chain or the CNO cycle and press Play or Next step to watch each reaction and the energy bar fill up to 26.73 MeV. On Inside the Sun, drag Core temperature T and Core density ρ and compare the pressure bars and the Gamow peak; press Sun's centre to go back. On Energy output, drag Age of the Sun or press a Jump to button and change Fraction of mass fused f.
Parameters you can change
- Screen Fusion in the core, Inside the Sun, Energy output
- Reaction sequence Proton–proton chain, CNO cycle
- Core temperature 5–40 million K
- Core density 10–300 10³ kg/m³
- Age of the Sun 0–12.5 billion years
- Fraction of the Sun's mass that is fused 1–100 %
Questions to explore
- How many kilograms of mass does the Sun lose each second, and where does that mass go?
- Why can two protons fuse when their average kinetic energy is hundreds of times smaller than the Coulomb barrier?
- If the Sun's core contracted slightly, how would its temperature, fusion rate and pressure change?
