Fig. 1 shows an emission line in the spectrum of a distant galaxy recorded using a telescope and an oscilloscope display. The line is produced by hydrogen. ...
Question 1 Report
Fig. 1 shows an emission line in the spectrum of a distant galaxy recorded using a telescope and an oscilloscope display. The line is produced by hydrogen. In a laboratory on Earth, the same line has a wavelength of 656.3 nm. The wavelength scale is shown in nanometres, nm.
Fig. 1
(a) State the SI unit of wavelength. [1]
(b) Describe the change in wavelength between the laboratory line and the galaxy line. [2]
(c) Calculate the change in wavelength in nm. [2]
(d) Convert your answer to part (c) into metres, in standard form. [2]
(e) Calculate the red-shift, z, using z = change in wavelength ÷ laboratory wavelength. [3]
(f) Calculate the galaxy’s recessional speed using speed = zc, where c = 3.00 × 108 m s-1. [3]
(g) Explain why the observed wavelength is greater when the galaxy is moving away from Earth. [1]
Answer Details
(a) The SI unit of wavelength is the metre, m. [1]
(b) The observed line has a greater wavelength than the laboratory line. It is shifted towards the red end of the spectrum, so it is red-shifted. [2]
(c)
\[721.9-656.3=65.6\text{ nm}\]
The wavelength change is 65.6 nm. [2]
(d)
\[65.6\text{ nm}=65.6\times10^{-9}\text{ m}=6.56\times10^{-8}\text{ m}\]
The change is \(6.56\times10^{-8}\text{ m}\). [2]
(e)
\[z=\frac{65.6}{656.3}=0.09995\ldots\]
\[z=0.100\]
The red-shift is 0.100. [3]
(f)
\[v=zc=0.09995\ldots\times3.00\times10^8=2.998\ldots\times10^7\text{ m s}^{-1}\]
\[v=3.00\times10^7\text{ m s}^{-1}\]
The recessional speed is \(3.00\times10^7\text{ m s}^{-1}\). [3]
(g) As the galaxy moves away, its light waves are stretched. The observed wavelength is therefore longer. [1]
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