25.3 Hubble's Law and the Big Bang Theory

2026 Syllabus Objectives

By the end of these notes, you should be able to:

  1. Understand that spectral lines from distant objects show an increase in wavelength compared to their known values.
  2. Use the redshift formula: ∆λ / λ ≈ ∆f / f ≈ v / c
  3. Explain why redshift leads to the idea that the Universe is expanding.
  4. Recall and use Hubble's Law: v ≈ H₀d, and explain how it leads to the Big Bang theory.

Main Content

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1. Emission and Absorption Spectra — A Quick Recap

When atoms in a star or galaxy absorb or release energy, they produce specific patterns of coloured lines called spectral lines. Think of these lines like a unique fingerprint — every element (like hydrogen or helium) produces the exact same pattern of lines, no matter where in the universe it is found.

  • An emission spectrum shows bright coloured lines on a dark background — these are the wavelengths of light given out by an element.
  • An absorption spectrum shows dark lines on a rainbow background — these are the wavelengths of light absorbed by an element.

Because we know exactly what pattern each element produces (measured in a laboratory on Earth), we can compare these known patterns to the light coming from distant stars and galaxies.

2. Redshift — What It Is and What We Observe

What is redshift?

When astronomers study light from very distant galaxies, they notice something strange: the spectral lines are still in the same pattern, so the element can still be identified. However, all the lines have shifted slightly towards the red end of the spectrum — meaning towards longer wavelengths.

This shift is called redshift.

🔑 Redshift = the increase in the observed wavelength (and decrease in the observed frequency) of light from a source that is moving away from the observer.

In simple terms: the light is being "stretched out" as it travels towards us, making the wavelength longer (and the colour appear more red).

What about blueshift?

If a source is moving towards the observer, the opposite happens — wavelengths get shorter and shift towards the blue end. This is called blueshift. However, almost all distant galaxies show redshift, meaning they are moving away from us.

Why do the lines shift?

This is caused by the Doppler effect — a change in the observed wavelength or frequency of a wave because the source and the observer are moving relative to each other.

You have probably heard the Doppler effect with sound: when an ambulance drives towards you, its siren sounds higher-pitched (shorter wavelength), and as it drives away, the pitch drops (longer wavelength). Exactly the same thing happens with light from stars and galaxies.

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