E.5 Fusion and stars

UNIT SYLLABUS

SL/HL 6 hours

Stars are fusion reactors held together by their own gravity. A star is stable while outward radiation pressure balances inward gravitational pull — a truce that lasts as long as the fuel does. Fusion requires brutal conditions (tens of millions of kelvin, enormous densities) so nuclei can tunnel through their Coulomb repulsion; the payoff is the largest energy-per-nucleon gains on the binding-energy curve. The Hertzsprung–Russell diagram maps every star's biography — main sequence, red giants, white dwarfs — and stellar mass decides the ending: gentle white dwarf or spectacular supernova. Parallax gives the distances; Wien and Stefan–Boltzmann, applied to starlight, give temperatures and radii.

Guiding Questions

? What keeps a star stable, and what happens when the balance fails?
? How can we measure the properties of objects thousands of light-years away?

✓ What the IB expects you to master

Explain stellar stability as equilibrium between outward radiation pressure and inward gravitation.
Describe fusion as the energy source of stars, and the density and temperature conditions it requires.
Explain how stellar mass determines a star's evolution and eventual fate.
Identify the main regions of the Hertzsprung–Russell diagram — main sequence, red giants, supergiants, white dwarfs — and the properties of stars in each.
Use stellar parallax to find distances: $d(\text{parsec}) = \frac{1}{p(\text{arc-second})}$ .
Determine stellar radii from luminosity and temperature via $L = 4\pi R^2\sigma T^4$ (with $T$ from Wien's law and $L$ from apparent brightness and distance).

1 Key Formulas

Stellar parallax

d(\text{parsec}) = \frac{1}{p(\text{arc-second})}

Stellar luminosity

L = 4\pi R^{2}\sigma T^{4}

Apparent brightness

b = \frac{L}{4\pi d^{2}}

Wien's law

\lambda_{\text{max}} T = 2.9 \times 10^{-3}\ \text{m K}

2 Exam Preparation & Topic Explanations

The astrophysics measurement chain

Exam questions walk the chain: parallax → distance; spectrum peak + Wien → temperature; apparent brightness + distance → luminosity; luminosity + temperature + Stefan–Boltzmann → radius. Practise the full sequence from raw data to stellar radius — it is the unit's signature calculation.

On the HR diagram, know the axes (luminosity up, temperature INCREASING LEFTWARD) and be able to place the Sun, giants, supergiants and white dwarfs.

Pro Exam Strategy

The HR temperature axis runs backwards — hottest stars on the left. Label it or lose the mark.
Parsec, light-year and AU: know the definitions; parallax works only for nearby stars.
Mass decides destiny: low-mass → red giant → white dwarf; high-mass → supergiant → supernova → neutron star or black hole.
Fusion vs fission energy comparison lives on the gradient of the binding-energy curve — steep left, shallow right.

3 MCQ Practice

Q1. Fusion in stellar cores requires extremely high temperatures because:

Nuclei must overcome their mutual electrostatic repulsion to get within range of the strong force
The strong force only operates at high temperatures
Photons must have enough energy to split nuclei
Electrons must be removed from the atoms first

Q2. A star has parallax 0.040 arc-seconds. Its distance is:

25 pc
40 pc
0.04 pc
2.5 pc

Q3. On the HR diagram, white dwarfs lie below the main sequence because they are:

Cool and large
Hot but very small, hence dim
Cool and very small
Hot and very large

4 Short Answer Questions

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