Galactic Redshift (AQA A Level Physics): Revision Note

The spectra below show dark absorption lines against a continuous visible spectrum.

A particular line in the spectrum of light from a source in the laboratory has a frequency of 4.570 × 10¹⁴ Hz.

The same line in the spectrum of light from a distant galaxy is observed to have a frequency of 4.547 × 10¹⁴ Hz.

Calculate the speed of the distant galaxy, and state whether it is moving towards or away from the Earth.

[3]

Answer:

Step 1: Write down the known quantities

• Observed frequency, $f\text{'}=4.547\times {10}^{14}\mathrm{Hz}$

• Original frequency, $f=4.570\times {10}^{14}\mathrm{Hz}$

• Change in frequency, $∆f=4.547\times {10}^{14}-4.570\times {10}^{14}=-2.3\times {10}^{12}\mathrm{Hz}$

• Speed of light, $c=3.0\times {10}^8\mathrm{m}{\mathrm{s}}^{-1}$

Step 2: Write down the Doppler redshift equation

$\frac{∆f}{f}=\frac{v}{c}$

Step 3: Rearrange for speed v, and calculate

$v=\frac{c∆f}{f}$

$v=\frac{\left(3.0\times {10}^8\right)\times \left(-2.3\times {10}^{12}\right)}{4.570\times {10}^{14}}$ [1 mark]

$v=-1.51\times {10}^6\mathrm{m}{\mathrm{s}}^{-1}\left(3\mathrm{s}.\mathrm{f}.\right)$ [1 mark]

Step 4: Write a concluding sentence

• The relative velocity is negative, so the source is moving away from the Earth [1 mark]

OR 

• The observed frequency is less than the emitted frequency (the light from a laboratory source), therefore, the source is receding, or moving away, from the Earth at 1.5 × 10⁶ m s^–1 [1 mark]

Keep track of the minus signs in your calculation, as this gives you information about whether the object is moving away or towards the observer.

The speed of light is given in your data booklet, you will not need to memorise this value.