10.2 Red-shift and the Big Bang — Practise

Work through these on your own. Keep your working neat: the method matters as much as the answer.

Both the questions and the answers below come from a set that is checked by computer every time the book is built.

Explain what is meant by the red-shift of light from a galaxy.
Describe how the red-shift of a galaxy changes as the galaxy gets further away.
Explain how red-shift provides evidence that the universe is expanding.
Explain how red-shift supports the Big Bang model of the universe.
Explain how scientists use observations to decide whether a model, such as the Big Bang model, is a good one.
State one piece of evidence, other than red-shift, that supports the Big Bang model. Explain what it shows.
A distant galaxy is $2.4 \times 10^{25}\,\text{m}$ from the Earth. Light travels at $3.0 \times 10^{8}\,\text{m/s}$ . Say which equation you will use, then calculate how long the light has taken to reach the Earth. Give your answer in seconds to 2 significant figures.
The Andromeda galaxy is $2.4 \times 10^{22}\,\text{m}$ from the Earth. A pupil says that the light we see from Andromeda left it 2.5 million years ago. Check the pupil claim by calculating the time for the light to travel that distance.
Explain why looking at a very distant galaxy is like looking back in time.
Since 1998, observations of distant supernovae suggest that the expansion of the universe is speeding up. Explain why scientists say that the universe is still not fully understood.
Two models of the universe were once considered: the Steady State model and the Big Bang model. Explain why the Big Bang model is the one accepted today.
A line in a laboratory spectrum has a wavelength of 500 nm. The same line in the light from a galaxy has a wavelength of 550 nm. State whether the galaxy is moving towards the Earth or away from it, and explain your answer.
The light from a galaxy has a frequency of $5.0 \times 10^{14}\,\text{Hz}$ and a wavelength of $6.0 \times 10^{-7}\,\text{m}$ . Say which equation you will use, then calculate the speed of the light. Give your answer to 2 significant figures.

Answers and concise solutions

1. What red-shift means

The wavelength of the light is longer than the wavelength of the same light measured in a laboratory.
The dark lines in the galaxy spectrum are moved towards the red end of the spectrum, where the wavelengths are longer.
This happens because the galaxy is moving away from the Earth.

2. Red-shift and distance

The further away a galaxy is, the bigger its red-shift.
A bigger red-shift means the galaxy is moving away from us faster.

3. Red-shift and the expanding universe

The red-shift shows that most galaxies are moving away from us.
The further away a galaxy is, the faster it is moving away.
This pattern is what we expect if space itself is expanding, so the galaxies are carried apart as space grows.

4. Red-shift and the Big Bang model

The Big Bang model says the universe began from a very small region that was extremely hot and dense.
The model predicts that the universe has been expanding ever since.
Red-shift shows that the universe is expanding, so it is evidence that supports the model.

5. How observations are used to test a model

A model makes predictions that can be checked against observations.
Scientists collect many observations and check whether they match the predictions.
If new evidence does not fit the model, the model is changed or replaced.

6. Another piece of evidence for the Big Bang

The cosmic microwave background radiation is a faint microwave signal that comes from every direction in space.
It is left over from the hot, dense early universe, so it matches a prediction of the Big Bang model.

7. Time for the light from a distant galaxy

Answer: Use $\text{time} = \dfrac{\text{distance}}{\text{speed}}$ . $t = \dfrac{2.4 \times 10^{25}}{3.0 \times 10^{8}} = 8.0 \times 10^{16}\,\text{s}$ . Taking one year as $3.15 \times 10^{7}\,\text{s}$ , this is about $2.5 \times 10^{9}$ years, so the light set out about 2.5 billion years ago.

8. Checking the light-travel time from Andromeda

Answer: $t = \dfrac{d}{v} = \dfrac{2.4 \times 10^{22}}{3.0 \times 10^{8}} = 8.0 \times 10^{13}\,\text{s}$ . Taking one year as $3.15 \times 10^{7}\,\text{s}$ , this is $2.5 \times 10^{6}$ years. The pupil is right.

9. Why a distant galaxy is seen as it was

Light takes a very long time to travel from the galaxy to us, because the distance is enormous.
The light we see now set out from the galaxy billions of years ago.
So we see the galaxy as it was then, not as it is now.

10. Why the universe is not fully understood

The distant supernovae are further away than expected, so the expansion of the universe seems to be getting faster.
The cause of the speeding up is not known. It is called dark energy, and dark matter is also not understood.

11. Why the Big Bang model is accepted

Both models can explain the red-shift of the galaxies.
The Steady State model does not explain the cosmic microwave background radiation. That radiation fits a hot, dense beginning.
More evidence supports the Big Bang model, so it is the accepted model for the origin of the universe.

12. The direction the galaxy is moving

The wavelength in the galaxy light, 550 nm, is longer than the laboratory wavelength of 500 nm.
The galaxy is moving away from the Earth.
A longer wavelength, shifted towards the red end, is the red-shift caused by a source that is receding.

13. Speed of the light

Answer: Use the wave equation $v = f\lambda = 5.0 \times 10^{14} \times 6.0 \times 10^{-7} = 3.0 \times 10^{8}\,\text{m/s}$ . This is the speed of light in a vacuum, which is what we expect for light.