OxfordAQA International GCSE Physics: Life cycle of a star (9203)

This study guide follows the OxfordAQA International GCSE Physics (9203) specification, for exams May/June 2018 onwards, section 3.8.1 (Life cycle of a star), statements a to i. The qualification is untiered, so this content applies to all candidates. Use it with the revision notes and the practice questions. The course page is the OxfordAQA IGCSE Physics hub, the printable checklist lists every outcome, and the 10-minute diagnostics show where to start. For the energy ideas behind this topic see OxfordAQA IGCSE Physics: Energy.

What this unit covers

Spec	You must be able to
3.8.1 a	Explain how stars (and planets) form from dust and gas pulled together by gravity
3.8.1 b	Describe the main sequence: hydrogen fuses to helium in the core and the forces inside the star are balanced
3.8.1 c, d	Say where fusion happens, and how mass sets core temperature and the heaviest nuclei made
3.8.1 e, f	Explain that stars have a life cycle set by their mass, and what happens when hydrogen runs out
3.8.1 g	Describe the route for a larger star: red supergiant, supernova, then neutron star or black hole
3.8.1 h	Describe the route for a smaller star like the Sun: red giant, white dwarf, black dwarf
3.8.1 i	Explain the origin of the elements, why stars last millions of years, and where elements heavier than iron come from

You should also be able to work with charts showing the stages of different stars. The specification does not ask for the term radiation pressure, so it is not used here.

Birth of a star (3.8.1 a)

Space contains clouds of dust and gas. They are mainly hydrogen and helium. Every particle attracts every other particle through gravity. If a cloud is dense enough and has enough mass, gravity pulls it together. As the material falls inwards, the cloud becomes denser and its temperature rises. A star forms when enough material has gathered.

Not everything falls into the middle. Smaller clumps of material can form and be attracted by the larger mass. These can become planets. If a clump is large enough it may become a star in its own right.

Key idea: the start of a star is a gravity story. Gravity pulls, the material heats up as it is squeezed, and the star is born once the core is hot and dense enough for fusion to start.

The main sequence (3.8.1 b, c)

Most of a star’s life is spent on the main sequence. Two facts define it.

1. Energy is released by nuclear fusion. Hydrogen nuclei fuse to make helium nuclei in the core.
2. The star is stable, because the forces acting inside it cancel out.

Think about the two opposing effects. Gravity pulls the star’s material towards the centre. The very hot gas pushes outwards. If the star shrank, the core would get hotter and fusion would speed up, pushing the outer layers back out. If it expanded, the core would cool a little, fusion would slow, and gravity would pull it back. The star settles at a steady size. The inward force of gravity equals the outward force from the hot gas.

The core is the centre of the star. It has the greatest temperature and the greatest density, and most of the fusion happens there. Fusion needs extreme conditions because nuclei carry positive charge and repel each other. They only fuse when they are moving fast enough and close enough together.

During fusion, some mass is converted to energy. That energy leaves the star as light and heat. A main sequence star is therefore a nuclear reactor held together by its own gravity.

Why stars last millions of years (3.8.1 i)

The specification asks you to explain how a star keeps up its energy output for millions of years. There are two linked reasons.

• Fusion releases an enormous amount of energy for every kilogram of hydrogen used.
• A star contains a huge mass of hydrogen, and the balance between gravity and the outward push keeps the core at a steady rate of fusion rather than burning the fuel all at once.

The next worked example shows the scale. It is not a required calculation, but it makes the idea concrete.

Worked example 1: how long can a star-sized fuel supply last?

Data supplied: the Sun gives out 3.8 × 10²⁶ J every second. Fusing 1 kg of hydrogen releases about 6.4 × 10¹⁴ J. The Sun’s mass is 2.0 × 10³⁰ kg. Assume that 7% of the Sun’s mass (hydrogen in the core region) is available as fuel. One year is 3.156 × 10⁷ s.

Step 1, the mass of hydrogen fused each second. mass per second = power ÷ energy per kg = 3.8 × 10²⁶ ÷ 6.4 × 10¹⁴ = 5.9 × 10¹¹ kg per second.

Step 2, the fuel available. fuel = 0.07 × 2.0 × 10³⁰ = 1.4 × 10²⁹ kg.

Step 3, the time the fuel lasts. time = 1.4 × 10²⁹ ÷ 5.9 × 10¹¹ = 2.4 × 10¹⁷ s. In years: 2.4 × 10¹⁷ ÷ 3.156 × 10⁷ = 7.5 × 10⁹ years.

Conclusion: about 7.5 billion years. Fusing nearly 600 billion kilograms of hydrogen every second still leaves a supply that lasts billions of years, because the fuel mass is so large. That is why a star’s energy output can continue for millions of years.

Mass decides everything (3.8.1 d, e, f)

A star’s mass fixes its whole life cycle. Two links to remember.

• The more massive a star, the greater the gravitational squeeze on its core, so the hotter its core is.
• The hotter the core, the heavier the nuclei that fusion can build.

A massive star has more fuel, but it uses it up far faster. A hotter core fuses faster, so a large star is short-lived. A small star burns its fuel slowly and lasts longest.

Worked example 2: more fuel but a shorter life

Data supplied for three main sequence stars:

Star	Mass (Sun = 1)	Time on main sequence
P	1	10 billion years
Q	5	100 million years
R	20	8 million years

(a) How many times longer does P last than Q? 10 billion ÷ 100 million = 10 000 million ÷ 100 million = 100 times.

(b) Star Q has 5 times the fuel of P. How many times faster does Q use its fuel? Fuel is proportional to mass, so rate of use = fuel ÷ time. Q’s rate ÷ P’s rate = (5 ÷ 1) × (10 billion ÷ 100 million) = 5 × 100 = 500 times faster.

(c) Do the same for R. R’s lifetime is 10 000 million ÷ 8 million = 1250 times shorter than P’s. R’s rate ÷ P’s rate = 20 × 1250 = 25 000 times faster.

Conclusion: the more massive the star, the faster it uses its hydrogen, so a larger star has a shorter life even though it has more fuel.

When the hydrogen in the core runs out, the main sequence ends. What happens next depends on mass (statement f). There are two routes.

Route 1: a larger star (3.8.1 g)

1. The star swells to become a red supergiant. It expands and its surface cools, so it looks red.
2. Helium nuclei fuse to form carbon. Further fusion makes heavier nuclei such as nitrogen and oxygen.
3. The outer layers are blasted away in a supernova, which is a huge explosion.
4. The core collapses. Mass settles whether the core ends as a neutron star or a black hole.

The more massive the collapsing core, the more likely it is to end as a black hole. A neutron star is the smaller remnant.

Route 2: a smaller star like the Sun (3.8.1 h)

1. The star swells to become a red giant.
2. It sheds its outer layers of gas. This exposes the core, which is a white dwarf.
3. The white dwarf slowly cools and fades to become a black dwarf.

The Sun is a medium-sized star and follows this route, with no supernova. A black dwarf is a final stage that the universe has not yet had time to produce, because cooling takes so long.

Reading a life-cycle chart

Life-cycle charts are usually drawn as two branches from a common start.

Dust and gas (gravity pulls together)
        |
   Main sequence star
     /            \
 smaller star     larger star
     |                 |
 Red giant       Red supergiant
     |                 |
 White dwarf        Supernova
     |               /      \
 Black dwarf  Neutron star  Black hole

Check three things when you read or draw one: the start is the same for both, the split depends on mass, and the supernova belongs only to the larger-star branch.

Where the elements come from (3.8.1 i)

The early universe contained only hydrogen. The specification wording is “only hydrogen”; if you want to add detail, a little helium also formed, but hydrogen is the key point. Fusion in stars is the source of energy and produces all the naturally occurring elements.

• On the main sequence, hydrogen fuses to helium.
• In red giants and red supergiants, helium fuses to carbon, then heavier nuclei such as nitrogen and oxygen form.
• The most massive stars have the hottest cores and so make the heaviest nuclei.
• Any element heavier than iron comes from a supernova.

The elements are spread through the universe when a massive star explodes as a supernova at the end of its life. The ejected material can later become part of new stars and planets. That is why the variety of elements now in the universe, and in the Earth, was made inside earlier stars.

Worked example 3: a full explanation

Question: Explain how the universe has come to hold many different elements when the early universe held only hydrogen. (4 marks)

Model answer, one point per step:

1. The early universe had only hydrogen; there were no other elements yet.
2. Stars formed from the hydrogen and fusion in their cores made helium and then heavier nuclei.
3. Any element heavier than iron comes from a supernova.
4. A supernova explosion distributes the elements through the universe.

Common errors

• Saying a star like the Sun explodes as a supernova. Only the larger-star route has a supernova.
• Putting a white dwarf after a supernova. A white dwarf comes from the smaller-star route.
• Saying a star is stable because fusion stops. Fusion continues; the forces are balanced.
• Claiming supernovae make every element. Fusion during a star’s life builds nuclei up to iron; only those heavier than iron come from a supernova.
• Saying a larger star lasts longer because it has more fuel. It uses fuel much faster.
• Writing that the red supergiant “turns blue”. It expands, cools and turns red.

Next steps

Work through the revision notes, then try the practice questions. Tick off 3.8.1 on the checklist when you can write both routes from memory, and take the diagnostics to check your recall.

Official syllabus

OxfordAQA International GCSE Physics (9203), specification version 5.2, for exams May/June 2018 onwards, published by OxfordAQA. Section 3.8.1, Life cycle of a star.