The Big Bang theory says the universe began:

Very hot and dense, and has been expanding and cooling since

The cosmic microwave background is:

Radiation left over from the early universe

Light from the Sun reflected by planets

Heat from the Milky Way's centre

Origins of the Elements | HSC Physics Module 8

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:

Energy turned into matter. Using $E = m c^{2}$ in reverse, radiation produced particles and antiparticles. A tiny excess of matter survived.
Quarks joined to make protons and neutrons.
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.
After about 380 000 years, it was cool enough for electrons to join nuclei and make atoms. Light could then travel freely.
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.

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: $E = m c^{2}$ . 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.

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 12Life 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: $\frac{70}{3.086 \times 1 0 ^{19}} = 2.27 \times 1 0^{- 18}$ s⁻¹, so $\frac{1}{H _{0}} = 4.4 \times 1 0^{17}$ s, about 14 billion years. A smaller $H_{0}$ means a slower expansion, so an older universe.

Distance from a redshift. First $v = c \frac{Δ λ}{λ}$ , then $d = \frac{v}{H _{0}}$ .

Mass and power. A star losing mass at rate $\frac{Δ m}{t}$ gives out power $P = \frac{Δ m}{t} c^{2}$ , so the Sun's $3.85 \times 1 0^{26}$ W means $4.3 \times 1 0^{9}$ kg every second. Reactions per second $= \frac{P}{energy per reaction}$ , with the energy in joules ( $1 MeV = 1.602 \times 1 0^{- 13}$ 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 ( $L \propto R^{2} T^{4}$ ). 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 ( $E = m c^{2}$ ).
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.

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Try 3 questions now

The Big Bang theory says the universe began:
1. A As a cold, empty space
2. B Very hot and dense, and has been expanding and cooling since
3. C About 6000 years ago
4. D With fully formed stars
Show 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.
Light from distant galaxies is redshifted. This shows that galaxies are:
1. A Getting hotter
2. B Moving away from us
3. C Moving towards us
4. D Made of hydrogen
Show answer
B: Moving away from us
A redshift means the source is moving away.
The cosmic microwave background is:
1. A Radiation left over from the early universe
2. B Light from the Sun reflected by planets
3. C Radio signals from Earth
4. D Heat from the Milky Way's centre
Show answer
A: Radiation left over from the early universe
It is light from when the first atoms formed, now stretched into microwaves.