Redshift, Hubble's law and the Big Bang Edexcel International A Level Physics revision
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In plain words
The light from distant galaxies arrives stretched: every line in their spectra sits at a longer wavelength than it should. They are rushing away from us, and the further away they are, the faster they go. Run that film backwards and everything starts out in the same place.
4 things to know
- Redshift: the lines in the spectra of distant galaxies are at longer wavelengths than the same lines measured on Earth. A source moving away from an observer has its waves stretched: this is the Doppler effect.
- For speeds much less than the speed of light: z = Δλ ÷ λ ≈ Δf ÷ f ≈ v ÷ c.
- Hubble's law: v ≈ H₀d. The speed at which a galaxy is moving away is proportional to its distance. H₀ is the Hubble constant.
- Nearly every galaxy is moving away, and the further ones faster. So the Universe is expanding, and in the past everything was closer together. That is the basis of the Big Bang theory: the Universe began in a very hot, dense state and has been expanding ever since.
Worked example
A spectral line with a wavelength of 656.3 nm in the laboratory is seen at 662.9 nm in the light from a galaxy. Find the speed of the galaxy and its distance. (H₀ = 2.2 × 10⁻¹⁸ s⁻¹.)
- Δλ = 662.9 − 656.3 = 6.6 nm, so z = 6.6 ÷ 656.3 = 0.0101.
- v = zc = 0.0101 × 3.00 × 10⁸ = 3.0 × 10⁶ m/s.
- d = v ÷ H₀ = 3.0 × 10⁶ ÷ 2.2 × 10⁻¹⁸ = 1.4 × 10²⁴ m.
Tips and tricks
- Put the laboratory wavelength, not the observed one, on the bottom of Δλ ÷ λ.
- Redshift does not mean the galaxy looks red. It means every wavelength has been shifted towards the red end of the spectrum.
It lands in your notebook with its questions as flashcards.
Redshift, Hubble's law and the Big Bang: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What does the redshift of a galaxy's light show?
Its light waves have been stretched.
What does Hubble's law say?
v ≈ H₀d.
A galaxy has a redshift z of 0.10. How fast is it moving away?
v = zc.
What does the redshift of nearly all distant galaxies suggest?
Every galaxy sees the others moving away.
Galaxy B is twice as far away as galaxy A. How do their speeds away from us compare?
Speed is proportional to distance.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 7 marks. Write your answers on paper, then check them.
Redshift, Hubble's law and the Big Bang
Edexcel International A Level Physics WPH · 7 marks · papermunch.org
Name ______________________________ Date ______________
A galaxy is moving away at 1.5 × 10⁷ m/s. Find its redshift z, and the wavelength at which a 500 nm line is observed.[2]
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z = 0.050, and 525 nm.
Use Hubble's law to find the speed of a galaxy 3.0 × 10²⁴ m away. (H₀ = 2.2 × 10⁻¹⁸ s⁻¹.)[2]
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6.6 × 10⁶ m/s.
Explain how Hubble's law supports the Big Bang theory.[3]
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The light from distant galaxies is redshifted, so they are moving away from us, and the further away a galaxy is the faster it is moving. This shows the Universe is expanding. So in the past the galaxies were closer together, and the Universe must have begun in a very small, hot, dense state.
Answers: Redshift, Hubble's law and the Big Bang
- 1. z = 0.050, and 525 nm.
- 2. 6.6 × 10⁶ m/s.
- 3. The light from distant galaxies is redshifted, so they are moving away from us, and the further away a galaxy is the faster it is moving. This shows the Universe is expanding. So in the past the galaxies were closer together, and the Universe must have begun in a very small, hot, dense state.