# Origins of the Elements

> The Big Bang, the expanding universe, how stars make energy and new elements, and how to read a Hertzsprung-Russell diagram.

From HSC Physics on WhizzNotes, free study notes for NSW students: https://whizznotes.com/physics/origins-of-the-elements/. Updated 2 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: You are made of stars
Hold up your hand. The hydrogen in the water inside it was made in the first few minutes of the universe, 13.8 billion years ago.

The carbon in your skin, the oxygen you breathe and the calcium in your bones were not around then. They were cooked inside stars, by fusing lighter atoms together. When those stars died, some exploded and scattered these atoms across space. Clouds of that dust later collapsed to form the Sun, Earth and, eventually, you.

The astronomer Carl Sagan put it simply: we are made of star-stuff. This chapter explains how.

**In short:** The universe began about 13.8 billion years ago in the Big Bang and has been expanding and cooling ever since, which made hydrogen and helium. Heavier elements are made later by nuclear fusion inside stars, and elements heavier than iron are made in supernovae.

## The Big Bang

About **13.8 billion years ago**, the universe was extremely **hot and dense**. Since then it has been **expanding and cooling**. This is the **Big Bang theory**. It was not an explosion into empty space: space itself has been stretching.

As the universe cooled:

1. **Energy turned into matter.** Using $E = mc^2$ in reverse, radiation produced particles and antiparticles. A tiny excess of matter survived.
2. **Quarks** joined to make **protons** and **neutrons**.
3. In the first few minutes, some protons and neutrons fused into **helium** nuclei and a little **lithium**. The universe was then about 75% hydrogen and 25% helium by mass.
4. After about 380 000 years, it was cool enough for electrons to join nuclei and make **atoms**. Light could then travel freely.
5. Gravity pulled gas into clumps that became **stars** and **galaxies**.

## Evidence for the Big Bang

- **Expansion (Hubble's law):** Edwin Hubble found that distant galaxies are all **redshifted**, so they are moving away from us. The further away a galaxy is, the faster it recedes:

$$v = H_0 d$$

where $H_0$ is the **Hubble constant**.

- **Cosmic microwave background (CMB):** faint microwave radiation from every direction in the sky, at about 2.7 K. It is light released when atoms first formed, stretched by the expansion.
- **Abundance of light elements:** the measured amounts of hydrogen, helium and lithium match what the Big Bang predicts.

### Worked example: The age of the universe
If everything has been moving apart at a steady rate, the time since all galaxies were together is about $\dfrac{1}{H_0}$. With $H_0 = 2.3 \times 10^{-18}$ s⁻¹:

$t = \dfrac{1}{2.3 \times 10^{-18}} = 4.3 \times 10^{17}$ s, which is about 14 billion years.

## How stars make energy

A star is a huge ball of gas, held together by gravity. In its core, the temperature reaches millions of kelvin. Nuclei move fast enough to **fuse** together despite their positive charges repelling.

In fusion, the products have **less mass** than what went in. The missing mass becomes energy: $E = mc^2$. The Sun turns about 4 million tonnes of mass into energy every second.

**Main sequence stars fuse hydrogen into helium** in their cores, in one of two ways:

- **Proton-proton chain**: protons fuse step by step to make helium. This is the main process in stars like the Sun and smaller.
- **CNO cycle**: carbon, nitrogen and oxygen act as helpers (catalysts) to turn hydrogen into helium. It needs a hotter core, so it is the main process in stars more massive than the Sun.

## After the main sequence

When a star runs out of hydrogen in its core, the core shrinks and heats up while the outer layers swell. It becomes a **red giant**.

- The core gets hot enough to fuse **helium into carbon** (the **triple-alpha process**: three helium-4 nuclei make one carbon-12).
- Massive stars go on to fuse heavier elements, up to **iron**.
- Elements heavier than iron are made in **supernova** explosions and when neutron stars collide.

## The Hertzsprung-Russell diagram

An **H-R diagram** plots stars by **luminosity** (how much light they give out, up the side) against **surface temperature** (along the bottom). The temperature axis runs **backwards**: hot stars on the left, cool on the right.

| Region | Where on the diagram | What the stars are like |
|---|---|---|
| **Main sequence** | Diagonal band, top left to bottom right | Fusing hydrogen in their core. Most stars, including the Sun. |
| **Red giants** | Top right | Cool but very bright, because they are huge |
| **Supergiants** | Very top | The biggest, brightest stars |
| **White dwarfs** | Bottom left | Hot but dim, because they are tiny. Dead cores of stars like the Sun. |

On the main sequence, **more massive** stars are **hotter, brighter and bluer**, but they burn their fuel much faster and have **shorter lives**.

**Mind map**

```text
Origins of the Elements
  Big Bang
    Hot, dense start
    Expanding and cooling
    Energy to matter
  Evidence
    Hubble: v = H₀d
    Redshift of galaxies
    CMB at 2.7 K
    H and He amounts
  Stars make energy
    Fusion in the core
    Mass lost: E = mc²
    p-p chain: Sun-like
    CNO: hotter, bigger
  Later life
    Red giant
    Helium to carbon
    Supernova: heavy elements
  H-R diagram
    Luminosity vs temperature
    Main sequence
    Giants, white dwarfs
```

### Year 11: Reading a star's colour
A star's colour tells you its surface temperature. Red stars are about 3000 K, yellow stars like the Sun about 5800 K, and blue-white stars over 10 000 K. You can find the exact value from the peak of its spectrum with Wien's law (see Light: the Quantum Model).

Two stars at the same temperature but very different luminosities must be very different sizes. A red giant and a red dwarf can be the same colour, but the giant is thousands of times brighter because its surface is so much larger.

### Year 12: Life story of a star on the H-R diagram
**A Sun-like star:** forms from a gas cloud, then joins the main sequence and stays there for about 10 billion years. When core hydrogen runs out, it moves **up and to the right** to become a red giant. It later throws off its outer layers, leaving its core as a white dwarf in the **bottom left**.

**A massive star:** starts at the **top left** of the main sequence, stays there only millions of years, becomes a red supergiant, then explodes as a supernova. It leaves a neutron star or a black hole.

**Ages of star clusters.** All stars in a cluster formed at about the same time. The most massive ones leave the main sequence first, so the main sequence "peels away" from the top. A cluster with only cool, dim main sequence stars left is **old**. One that still has hot, bright blue main sequence stars is **young**.

**Hubble's law in units.** $H_0$ is often given in km/s per megaparsec. A galaxy 100 Mpc away with $H_0 = 70$ km/s/Mpc recedes at 7000 km/s. For the age, change $H_0$ into s⁻¹: $\dfrac{70}{3.086 \times 10^{19}} = 2.27 \times 10^{-18}$ s⁻¹, so $\dfrac{1}{H_0} = 4.4 \times 10^{17}$ s, about 14 billion years. A **smaller** $H_0$ means a slower expansion, so an **older** universe.

**Distance from a redshift.** First $v = c\dfrac{\Delta\lambda}{\lambda}$, then $d = \dfrac{v}{H_0}$.

**Mass and power.** A star losing mass at rate $\dfrac{\Delta m}{t}$ gives out power $P = \dfrac{\Delta m}{t}c^2$, so the Sun's $3.85 \times 10^{26}$ W means $4.3 \times 10^9$ kg every second. Reactions per second $= \dfrac{P}{\text{energy per reaction}}$, with the energy in joules ($1 \text{ MeV} = 1.602 \times 10^{-13}$ J).

**Energy from a reaction.** Find the mass lost in atomic mass units and multiply by 931.5 MeV per u. For three helium-4 nuclei (4.002603 u each) forming carbon-12 (12.000000 u): mass lost $= 0.007809$ u, so 7.27 MeV is released.

**Matter over antimatter.** Equal amounts would have annihilated into radiation. A tiny excess of matter (about one extra particle in a billion) was left over, and everything we see is made of it.

**The iron limit.** Iron-56 has about the highest binding energy per nucleon. Fusing iron with anything **uses** energy instead of releasing it, so stars cannot make heavier elements by core fusion. Those form in supernovae and neutron star mergers.

**Size from brightness and temperature.** Luminosity grows with surface area and very strongly with temperature ($L \propto R^2T^4$). Two stars with the same luminosity but different temperatures must be different sizes: the hot one is much smaller.

## Quick summary

- The universe began about 13.8 billion years ago in a hot, dense state and has been expanding and cooling.
- Evidence: redshifted galaxies ($v = H_0 d$), the cosmic microwave background, and the amounts of H, He and Li.
- Stars release energy by fusion. The mass lost becomes energy ($E = mc^2$).
- Main sequence stars fuse hydrogen to helium: the proton-proton chain in Sun-like stars, the CNO cycle in hotter, heavier stars.
- Heavier elements form in red giants and supergiants (up to iron) and in supernovae (beyond iron).
- The H-R diagram plots luminosity against temperature: main sequence, giants and white dwarfs.

## Quiz

Try these questions from the chapter quiz.

1. The Big Bang theory says the universe began:
   - A. As a cold, empty space
   - B. Very hot and dense, and has been expanding and cooling since
   - C. About 6000 years ago
   - D. With fully formed stars
   - Answer: B. Very hot and dense, and has been expanding and cooling since. The universe started hot and dense about 13.8 billion years ago.

2. Light from distant galaxies is redshifted. This shows that galaxies are:
   - A. Getting hotter
   - B. Moving away from us
   - C. Moving towards us
   - D. Made of hydrogen
   - Answer: B. Moving away from us. A redshift means the source is moving away.

3. The cosmic microwave background is:
   - A. Radiation left over from the early universe
   - B. Light from the Sun reflected by planets
   - C. Radio signals from Earth
   - D. Heat from the Milky Way's centre
   - Answer: A. Radiation left over from the early universe. It is light from when the first atoms formed, now stretched into microwaves.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/physics/origins-of-the-elements/#quiz