Life Cycle of a Star – Cambridge IGCSE Physics (0625)
Learning objective (0625 – 2.2.2):
Describe the main stages in the life of a star, from formation in an interstellar cloud to its final end‑state, and link each stage to the core physics concepts required by the IGCSE syllabus (motion, forces & energy; thermal physics; waves; electricity & magnetism; nuclear physics; space physics).
1. Core Physics Topics that Support the Stellar Life‑Cycle
| IGCSE Topic | Key ideas (relevant formulas) | How it relates to stars |
|---|
| Motion, Forces & Energy | - Vectors, resultant force, torque → τ = r × F
- Newton’s II law → F = ma
- Gravitational force → F = G m₁m₂/r²
- Work = F·s, power = work/t
- Energy–mass equivalence → E = mc²
| - Collapse of a nebula (gravity, vectors, torque if the cloud rotates)
- Hydrostatic equilibrium (pressure gradient balances gravity)
- Energy released by gravitational contraction (work done by gravity)
- Orbital motion of planets around a star (centripetal force, Kepler’s 3rd law)
|
| Thermal Physics | - Specific heat capacity → c = ΔQ/(m ΔT)
- Thermal expansion → ΔL = α L₀ ΔT
- Heat‑transfer modes: conduction, convection, radiation
- Stefan‑Boltzmann law → L = 4πR²σT⁴
| - Heating of a protostar by conversion of gravitational potential energy
- Expansion of a red‑giant envelope (thermal expansion)
- Radiative and convective zones inside stars
- Luminosity calculations for different stages
|
| Waves | - Wave speed → v = f λ
- Electromagnetic spectrum, frequency & wavelength
- Diffraction & spectral line broadening
| - Starlight is electromagnetic radiation; colour ↔ surface temperature (Wien’s law)
- Diffraction gratings used in classroom to view stellar spectra
- Broadening of spectral lines by thermal motion (Doppler) and pressure
|
| Electricity & Magnetism | - Charge, current I, potential difference V, resistance R (Ohm’s law)
- Magnetic field B, right‑hand rule, magnetic flux Φ
- Electromagnetic induction (Faraday’s law)
| - Ionised gas (plasma) in nebulae carries charge
- Solar magnetic activity: sunspots, flares, coronal mass ejections
- Stellar winds as a flow of charged particles guided by magnetic fields
|
| Nuclear Physics | - Radioactive decay equations (α, β⁻, β⁺, γ)
- Half‑life t½ = ln 2 / λ
- Mass defect Δm and binding energy E = Δm c²
- Fusion reactions (p‑p chain, CNO cycle)
| - Hydrogen → helium fusion in main‑sequence stars
- Energy released per kilogram of H fuel (≈ 6 × 10¹⁴ J kg⁻¹)
- Supernova nucleosynthesis and production of heavy elements
- Radioactive isotopes (e.g., ⁵⁶Co) used to date supernova remnants
|
| Space Physics | - Kepler’s laws, orbital period T = 2π√(r³/GM)
- Gravitational field strength g = GM/r²
- Escape velocity vₑ = √(2GM/r)
| - Planets orbiting a star – use of Kepler’s 3rd law
- Escape of gas from a supernova or planetary nebula
- Binding of planetary systems to a newly formed star
|
Each stage of the stellar life cycle (Section 2) is linked to one or more of the concepts above. The “Concept‑Check” boxes after each stage show the relevant AO1 (knowledge), AO2 (application) and AO3 (practical) points.
2. The Life Cycle of a Star (IGCSE level)
2.1 Formation – Interstellar Cloud (Nebula)
- Large clouds of gas (≈ 90 % hydrogen) and dust are called nebulae.
- Typical temperature: 10–30 K; particles move randomly → low kinetic energy.
- Gravity pulls every particle toward every other particle. The resultant force is a vector sum; if the cloud rotates, a torque τ = r × F acts, slowing the collapse.
- When the inward gravitational force exceeds internal pressure, the cloud begins to contract.
Concept‑Check (AO1‑AO3)
AO1: State that a nebula is a mixture of gas (mainly H) and dust.
AO2: Use \(F = G\frac{m1m2}{r^2}\) to show why the net force on a small mass element points toward the centre. Sketch a vector diagram.
AO3: Practical idea: Model a collapsing cloud with a ball of sand on a stretched rubber sheet; place a heavy weight in the centre to represent gravity and observe the resulting “potential‑energy well”.
2.2 Protostar – Gravitational Collapse
Concept‑Check (AO1‑AO3)
AO1: Define a protostar and explain why its temperature rises during contraction.
AO2: Given M = 2 × 10³⁰ kg, Ri = 5 × 10¹³ m and Rf = 2 × 10¹³ m, calculate the work done by gravity (use the formula above).
AO3: Investigation: Use a small calorimeter with water; drop a known mass from a height h onto the water to mimic gravitational heating. Measure ΔT and compare with the calculated W.
2.3 Main‑Sequence Star – Stable Hydrogen Fusion
- When the core temperature reaches ≈ 1 × 10⁷ K, the proton‑proton (p‑p) chain begins:
\[
4p \;\rightarrow\; ^4\!He \;+\; 2e^{+} \;+\; 2\nu \;+\; 26.7\;\text{MeV}.
\]
- Energy per kilogram of hydrogen fused:
\[
E = \frac{26.7\;\text{MeV}}{4\,mp}\times NA \approx 6.3\times10^{14}\;\text{J kg}^{-1}.
\]
- Radiation pressure + gas pressure balances gravity → hydrostatic equilibrium (dP/dr = – GρM(r)/r²).
- Star remains on the main‑sequence for millions to billions of years, depending on mass.
Concept‑Check (AO1‑AO3)
AO1: State the basic hydrogen‑fusion reaction and the energy released.
AO2: Using E = mc², calculate the energy released when 1 kg of H is converted to He (assume 0.7 % mass loss).
AO3: Practical idea: Compare the energy density of a chemical reaction (e.g., vinegar + baking soda) with the nuclear value calculated above; discuss why nuclear fusion powers stars.
2.4 Red Giant (Low‑Mass) – Shell Hydrogen Burning
- Core H is exhausted → core contracts, temperature rises to ≈ 1 × 10⁸ K.
- Hydrogen now fuses in a thin shell surrounding the inert He core. The extra energy inflates the outer layers.
- Thermal expansion: ΔR = α R₀ ΔT (α ≈ 10⁻⁴ K⁻¹ for stellar gas). The radius can increase by a factor of 100 while the surface temperature drops to ≈ 3 000 K → the star appears red.
- Luminosity stays high because L = 4πR²σT⁴; the large R compensates for the lower T.
Concept‑Check (AO1‑AO3)
AO1: Explain why the surface cools while the core gets hotter.
AO2: Show qualitatively, using the Stefan‑Boltzmann law, how a 100‑fold increase in radius can keep the luminosity roughly constant when T falls from 6 000 K to 3 000 K.
AO3: Investigation: Use a dimmable lamp with a coloured filter to model a star that becomes larger and redder but retains similar brightness.
2.5 Red Supergiant – Advanced Fusion (Mass > 8 M☉)
- Massive stars continue fusing heavier elements: He → C, O, Ne, Si … up to iron (Fe).
- Each stage releases energy until iron is reached; iron has the highest binding energy per nucleon, so further fusion is endothermic.
- When the iron core reaches the Chandrasekhar limit (≈ 1.4 M☉) it can no longer support itself → catastrophic collapse.
Concept‑Check (AO1‑AO3)
AO1: State why fusion stops at iron.
AO2: Sketch a binding‑energy‑per‑nucleon curve and identify the peak at iron.
AO3: Practical idea: Use a spring‑loaded “exploding” model to illustrate the sudden release of stored energy during core collapse.
2.6 End‑states
Low‑Mass Stars (≤ 8 M☉)
- Outer envelope is gently expelled → planetary nebula (glowing shell of ionised gas).
- Core remains as a white dwarf: radius ≈ Earth’s, mass ≤ 1.4 M☉, supported by electron‑degeneracy pressure.
- White dwarf cools slowly; after ≈ 10¹⁰ yr it becomes a black dwarf (theoretical, not yet observed).
High‑Mass Stars (> 8 M☉)
- Core collapse triggers a core‑collapse supernova (Type II). The shock wave ejects the outer layers at ≈ 10⁴ km s⁻¹.
- Remnant depends on core mass after collapse:
- ≤ 3 M☉ → neutron star (supported by neutron‑degeneracy pressure).
- > 3 M☉ → black hole (escape velocity > c).
Concept‑Check (AO1‑AO3)
AO1: Identify the two possible remnants of massive stars (neutron star, black hole).
AO2: Explain, using the binding‑energy curve, why iron cannot release energy by fusion and why the core collapses.
AO3: Investigation: Analyse a high‑speed video of a balloon popping; discuss the analogy with the rapid energy release of a supernova.
2.7 Recycling of Material – New Star‑Forming Regions
- Planetary nebulae and supernova remnants enrich the interstellar medium with elements heavier than helium (C, O, Fe, …).
- Enriched gas cools, fragments under its own gravity, and the cycle begins again.
- Typical time‑scale for a nebula to collapse into a new star: 10⁵ – 10⁶ yr (order‑of‑magnitude estimate).
Concept‑Check (AO1‑AO3)
AO1: State that supernovae and planetary nebulae provide the heavy elements found in later‑generation stars.
AO2: Estimate the collapse time using the free‑fall time formula
\[
t_{\text{ff}} \approx \sqrt{\frac{3\pi}{32G\rho}}.
\]
Assume ρ ≈ 10⁻¹⁸ kg m⁻³ for a typical molecular cloud.
AO3: Investigation: Mix sand and water in a tray; let it dry and observe the formation of clumps that mimic fragmentation of a cooling nebula.
3. Summary Table – Stellar Life Cycle (IGCSE level)
| Stage | Key Process | Typical Mass Range | Final Remnant | Relevant IGCSE Topics |
|---|
| Interstellar Cloud (Nebula) | Gravitational collapse (vectors, torque) | — | — | Motion & Forces, Thermal Physics |
| Protostar | Heating by gravitational contraction (specific heat, work) | — | — | Thermal Physics, Motion & Forces |
| Main‑Sequence Star | Core H → He fusion (p‑p chain) | 0.08 – 50 M☉ | — | Nuclear Physics, Waves, Space Physics |
| Red Giant (≤ 8 M☉) | Shell H burning, core He accumulation, envelope expansion | ≤ 8 M☉ | White dwarf → (theoretical) black dwarf | Thermal Physics, Motion & Forces, Waves |
| Red Supergiant (> 8 M☉) | Fusion up to Fe, core collapse | > 8 M☉ | Neutron star or Black hole | Nuclear Physics, Motion & Forces, Space Physics |
| Planetary Nebula | Envelope ejection, ionised gas emission | ≤ 8 M☉ | White dwarf | Waves (spectra), Chemistry of gases |
| Supernova Remnant | Explosive nucleosynthesis, shock‑wave expansion | > 8 M☉ | Neutron star or Black hole | Nuclear Physics, Energy, Space Physics |
| New Star‑Forming Region | Cooling, fragmentation, collapse of enriched gas | — | — | All core topics revisited |
4. Suggested Classroom Activities (AO3)
- Gravity‑collapse demonstration: Place a heavy ball on a stretched fabric (representing spacetime). Add smaller masses around it to show how they move toward the centre, illustrating vectors and the resultant gravitational force.
- Energy‑release comparison: Perform a chemical reaction (e.g., vinegar + baking soda). Measure the temperature rise, calculate the energy per gram, then compare with the nuclear energy per kilogram calculated for H‑fusion.
- Stellar spectrum experiment: Shine a white LED through a diffraction grating. Measure the wavelengths of the visible lines and use \(v = f\lambda\) (with v = c) to find the frequencies. Relate the observed colours to surface temperatures of different star types.
- Orbit simulation: Use a string and a small weight to model a planet orbiting a central “star”. Measure the orbital period for different radii and verify Kepler’s 3rd law, \(T^2 \propto r^3\).
- Radioactivity half‑life activity: Use an online simulation to plot decay curves for isotopes produced in supernovae (e.g., ⁵⁶Co). Calculate the half‑life from the graph and discuss its relevance to supernova light curves.
- Magnetic‑field mapping: Place iron filings around a bar magnet to visualise field lines. Discuss how similar magnetic structures exist on the Sun and affect solar wind particles.
5. Quick Revision Checklist
- Identify the six IGCSE physics topic blocks illustrated by the stellar life cycle.
- Explain why a protostar heats up as it contracts (gravitational potential → thermal energy; use c = ΔQ/(m ΔT)).
- State the basic hydrogen‑fusion reaction and calculate the energy released per kilogram of H.
- Distinguish between the end‑states of low‑mass (white dwarf) and high‑mass (neutron star or black hole) stars.
- Describe how supernovae and planetary nebulae enrich the interstellar medium with heavy elements.
- Connect at least one practical activity to each stage of the cycle.
- Use the formulas \(F = Gm1m2/r^2\), \(L = 4\pi R^2\sigma T^4\), \(E = mc^2\), \(t_{\text{ff}} = \sqrt{3\pi/(32G\rho)}\) in relevant calculations.