Edexcel IGCSE Physics 8(d) Cosmology — Notes
Written for Pearson Edexcel International GCSE Physics (4PH1), linear and modular. Everything on this page is examined on Paper 2P only.
Which parts do I need?
This whole page is for International GCSE Physics (4PH1 and modular 4XPH1) only. Science Single Award (4SS0) and Science Double Award (4SD0) candidates do not need any of it. Double Award candidates meet the Doppler effect itself in 3(b) Properties of waves.
What this page covers
| Spec | Modular no. | You need to be able to… | Route |
|---|---|---|---|
| 8.13P | 9.13P | outline how the universe has developed since the Big Bang and the main reasons for accepting the theory | Physics only · 2P |
| 8.14P | 9.14P | describe red-shift and the cosmic microwave background (CMB) as evidence for the Big Bang | Physics only · 2P |
| 8.15P | 9.15P | describe how the observed frequency and wavelength change when a wave source moves relative to the observer | Physics only · 2P |
| 8.16P | 9.16P | calculate with change in wavelength ÷ reference wavelength = velocity of galaxy ÷ speed of light | Physics only · 2P |
| 8.17P | 9.17P | describe how the red-shift of light from galaxies depends on their distance from the Earth | Physics only · 2P |
| 8.18P | 9.18P | explain how the red-shift of galaxies shows that the universe is expanding | Physics only · 2P |
Modular candidates: Astrophysics is topic 9 in the modular specification — these are statements 9.13P–9.18P of 4XPH1 Unit 2 (4WPH2). They are not in 4XSD1.
In one minute
- If a wave source moves away from you, you receive a longer wavelength and lower frequency; moving towards you, a shorter wavelength and higher frequency.
- Light from almost all galaxies is red-shifted: the dark lines in their spectra are moved towards the red (long-wavelength) end. So the galaxies are moving away from us.
- \(\dfrac{\Delta\lambda}{\lambda_0}=\dfrac{v}{c}\): the fractional change in wavelength equals the galaxy's speed divided by the speed of light.
- The further away a galaxy is, the greater its red-shift, so the faster it is moving away. This shows the universe is expanding.
- Big Bang theory: the universe began about 13.8 billion years ago from an extremely small, hot, dense state and has been expanding and cooling ever since. Evidence: red-shift and the cosmic microwave background (CMB).
What happens to a wave when its source is moving? Physics only · 2P
A stationary source sends out wavefronts that spread out evenly in all directions. If the source moves, each new wavefront is emitted from a slightly different place.
- The wave speed does not change; only the spacing of the wavefronts reaching the observer changes. Since \(v=f\lambda\), a longer wavelength at the same speed means a lower frequency.
- For sound, you hear this as a change in pitch: a siren sounds higher as it approaches and lower as it moves away.
- For light, a longer wavelength is a shift towards the red end of the spectrum — a red-shift. A source moving towards you gives a blue-shift.
- The faster the source moves, the bigger the change in wavelength.
A star in a nearby galaxy is moving towards the Earth. Describe how the light received on Earth differs from the light the star emits.
The observed wavelength is shorter (1) and the observed frequency is higher (1), so the light is shifted towards the blue end of the spectrum — a blue-shift (1).
What is red-shift in the light from galaxies? Physics only · 2P
Every element absorbs light of particular wavelengths. When light from a star passes through the gases in its outer layers, these wavelengths are missing, so the spectrum shows a pattern of dark lines. The pattern is like a fingerprint: hydrogen always gives lines at the same wavelengths, for example 656.3 nm and 486.1 nm, when measured in a laboratory or in light from the Sun.
- Red-shift: the lines in the spectrum of a galaxy are at longer wavelengths than the same lines measured on Earth — the pattern is moved towards the red end.
- The pattern of lines is still recognisable, so astronomers know which element made them and can measure how far each line has moved.
- Red-shift means the galaxy is moving away from the Earth. Light from almost every galaxy is red-shifted.
How do you use \(\dfrac{\Delta\lambda}{\lambda_0}=\dfrac{v}{c}\)? Physics only · 2P
\[ \frac{\text{change in wavelength}}{\text{reference wavelength}}=\frac{\text{velocity of a galaxy}}{\text{speed of light}}\qquad \frac{\lambda-\lambda_0}{\lambda_0}=\frac{\Delta\lambda}{\lambda_0}=\frac{v}{c} \]- \(\lambda_0\) = reference wavelength: the wavelength of the line measured on Earth (in a laboratory).
- \(\lambda\) = observed wavelength of the same line in light from the galaxy; \(\Delta\lambda=\lambda-\lambda_0\) is the change in wavelength.
- \(v\) = velocity of the galaxy relative to the Earth (m/s); \(c\) = speed of light = 3.0 × 108 m/s (the value is given in the question).
- \(\Delta\lambda\) and \(\lambda_0\) must be in the same unit (both nm is fine), because the units cancel in the ratio.
- The equation is on the Equation List for Paper 2P. A positive \(\Delta\lambda\) means red-shift (moving away); a negative one means blue-shift (moving towards).
A hydrogen line has a wavelength of 656.3 nm in the laboratory. In light from a galaxy, the same line is measured at 662.9 nm. Calculate the speed of the galaxy relative to the Earth. (speed of light = 3.0 × 108 m/s)
\(\Delta\lambda=662.9-656.3=6.6\ \text{nm}\)
\(v=\dfrac{\Delta\lambda}{\lambda_0}\times c=\dfrac{6.6}{656.3}\times3.0\times10^{8}=3.02\times10^{6}\ \text{m/s}\) = 3.0 × 106 m/s, moving away (red-shift).
Common error: dividing by the observed wavelength, 662.9 nm. Always divide by the reference wavelength \(\lambda_0\).
A galaxy is moving away from the Earth at 1.5 × 107 m/s. A hydrogen line has a laboratory wavelength of 486.1 nm. Calculate the wavelength of this line in light received from the galaxy. (speed of light = 3.0 × 108 m/s)
\(\Delta\lambda=\lambda_0\times\dfrac{v}{c}=486.1\times\dfrac{1.5\times10^{7}}{3.0\times10^{8}}=486.1\times0.050=24.3\ \text{nm}\)
Moving away, so the wavelength increases: \(\lambda=486.1+24.3=\) 510.4 nm
The answer 24.3 nm is only the change. The question asks for the observed wavelength, so add it to \(\lambda_0\).
How does red-shift depend on a galaxy's distance? Physics only · 2P
When astronomers measure the red-shift and the distance of many galaxies, they find a clear pattern:
The table shows the observed wavelength of the 656.3 nm hydrogen line in light from three galaxies, and their distances from the Earth. (a) Calculate the speed of each galaxy. (b) Describe the relationship between the speed of a galaxy and its distance. (speed of light = 3.0 × 108 m/s)
| Galaxy | Distance / million light-years | Observed wavelength / nm |
|---|---|---|
| A | 120 | 661.9 |
| B | 250 | 668.1 |
| C | 480 | 678.9 |
(a) A: \(\Delta\lambda=5.6\) nm, \(v=\dfrac{5.6}{656.3}\times3.0\times10^{8}=\) 2.6 × 106 m/s
B: \(\Delta\lambda=11.8\) nm, \(v=\) 5.4 × 106 m/s
C: \(\Delta\lambda=22.6\) nm, \(v=\) 1.03 × 107 m/s
(b) The further away the galaxy, the faster it is moving away. Galaxy C is 4 times as far away as A and moving about 4 times as fast, so the speed is roughly proportional to the distance.
Why red-shift shows that the universe is expanding
- Light from (almost) all distant galaxies is red-shifted, so they are all moving away from us, in every direction.
- The more distant galaxies have bigger red-shifts, so they are moving away faster.
- This is what you would see if the whole universe is expanding: the distances between the galaxies are increasing.
Beyond the specification — not examined
All galaxies moving away from us does not mean the Earth is at the centre of the universe. A common picture is dots on a balloon being blown up: every dot moves away from every other dot, and dots that are further apart separate faster. An observer in any galaxy would see the same pattern of red-shifts, so there is no special centre.
What is the Big Bang theory, and what is the evidence for it? Physics only · 2P
If the galaxies are moving apart now, they must have been closer together in the past. Running the expansion backwards leads to the Big Bang theory.
The past evolution of the universe
- All the matter and energy in the universe started in an extremely small, hot, dense state.
- The universe expanded rapidly and cooled. As it cooled, the first particles and then simple atoms (mainly hydrogen and helium) formed.
- When atoms had formed, the universe became transparent and radiation could travel freely through space. That radiation is still arriving today as the CMB.
- Gravity pulled clouds of gas together to form the first stars and galaxies.
- Much later, our Sun and the Earth formed from a nebula, about 4.6 billion years ago. The universe is still expanding today.
Evidence 1: red-shift
- Light from distant galaxies is red-shifted, and the red-shift is greater for more distant galaxies.
- So the galaxies are moving apart and the universe is expanding. In the past, the galaxies must have been much closer together — consistent with the universe starting from a single, very small region.
Evidence 2: the cosmic microwave background (CMB) radiation
- The CMB is microwave radiation that reaches the Earth from every direction in space, with almost exactly the same intensity everywhere.
- The Big Bang theory explains it as radiation left over from the early universe, when it was very hot. As the universe has expanded, the wavelength of this radiation has been stretched, so it is now in the microwave region.
- The Big Bang theory predicted this radiation before it was discovered (in the 1960s), which is strong support for the theory. No other model has explained it as well.
Explain how observations of the cosmic microwave background radiation and of red-shift support the Big Bang theory. (4 marks)
- light from distant galaxies is red-shifted, so they are moving away from us (1);
- more distant galaxies have a greater red-shift, so the universe is expanding — it must have started from a smaller region (1);
- CMB is microwave radiation detected from all directions in space (1);
- it is the remains of radiation from the hot early universe, stretched to microwave wavelengths by the expansion (1).
Exam tips for 8(d)
Define red-shift as an increase in the observed wavelength (or a decrease in frequency), with the spectral lines moved towards the red end. “The galaxy turns red” or “the light becomes red” is not credited.
In \(\dfrac{\Delta\lambda}{\lambda_0}=\dfrac{v}{c}\), subtract first to find \(\Delta\lambda\), then divide by \(\lambda_0\), the laboratory value. Keep both wavelengths in the same unit.
To explain why red-shift shows expansion, you need both: (1) galaxies are red-shifted, so they are moving away; (2) more distant galaxies are red-shifted more, so they move away faster. Only the second point shows the universe as a whole is expanding.
Say what it is (microwave radiation), where it comes from (all directions), and what it is evidence of (radiation left over from the hot early universe). “Background noise from space” is too vague.
A galaxy's speed calculated from red-shift must be less than 3.0 × 108 m/s. If you get a bigger number, you have probably divided by the change in wavelength instead of multiplying, or forgotten to subtract.
Common misconceptions
| Misconception | Why it is wrong | Correct idea |
|---|---|---|
| Red-shifted galaxies look red. | The whole spectrum shifts a little; most galaxies do not change colour noticeably. | Red-shift is measured from the positions of the spectral lines. |
| The speed of the waves changes when the source moves. | The wave speed depends on the medium, not the source. | Only the observed wavelength and frequency change. |
| Red-shift alone shows the universe is expanding. | One galaxy moving away could just be moving through space. | Red-shift increasing with distance, seen in all directions, shows expansion. |
| The CMB comes from stars or the Sun. | It arrives evenly from every direction, not from particular objects. | It is radiation left over from the early universe. |
Key equations
| Equation | Use it to find | Route | On the Equation List? |
|---|---|---|---|
| \(\dfrac{\text{change in wavelength}}{\text{reference wavelength}}=\dfrac{\text{velocity of a galaxy}}{\text{speed of light}}\), \(\dfrac{\lambda-\lambda_0}{\lambda_0}=\dfrac{\Delta\lambda}{\lambda_0}=\dfrac{v}{c}\) | the speed of a galaxy from its red-shift, or the observed wavelength | Physics only · 2P | yes — Physics 2P only |
The Equation List is printed with the question paper, but you still need to know what each symbol means and which wavelength is the reference wavelength.
Check your understanding
1. A train sounds its horn as it moves away from a listener. State how the frequency and wavelength heard by the listener compare with those emitted. Physics only · 2P
The listener hears a lower frequency and a longer wavelength than emitted.
2. State what is meant by red-shift. Physics only · 2P
The observed wavelength of light from a source moving away is longer than the emitted wavelength (1); spectral lines are shifted towards the red end of the spectrum (1).
3. Name the two pieces of evidence for the Big Bang theory in the specification. Physics only · 2P
Red-shift of light from distant galaxies and the cosmic microwave background (CMB) radiation.
4. A calcium line has a laboratory wavelength of 393.4 nm. In light from a galaxy it is observed at 401.2 nm. Calculate the speed of the galaxy. (c = 3.0 × 108 m/s) Physics only · 2P
\(\Delta\lambda=7.8\) nm (1); \(v=\dfrac{7.8}{393.4}\times3.0\times10^{8}\) (1) \(=\) 5.9 × 106 m/s, moving away (1).
5. The Andromeda galaxy is moving towards the Earth at about 3.0 × 105 m/s. Calculate the observed wavelength of a line emitted at 500.0 nm. (c = 3.0 × 108 m/s) Physics only · 2P
\(\Delta\lambda=500.0\times\dfrac{3.0\times10^{5}}{3.0\times10^{8}}=0.50\) nm (1). Moving towards us, so the wavelength decreases (blue-shift): \(\lambda=500.0-0.50=\) 499.5 nm (1).
6. A galaxy is moving away at one-tenth of the speed of light. A line has a reference wavelength of 600 nm. Determine its observed wavelength. Physics only · 2P
\(\dfrac{\Delta\lambda}{\lambda_0}=\dfrac{v}{c}=0.10\), so \(\Delta\lambda=60\) nm and \(\lambda=\) 660 nm.
7. Explain why the red-shift of galaxies provides evidence that the universe is expanding. Physics only · 2P
Light from distant galaxies is red-shifted, so they are moving away from the Earth (1). More distant galaxies have a greater red-shift (1), so they are moving away faster (1). Galaxies in all directions are moving apart, so the universe is expanding (1).