# A star is observed from Earth. The light detected from the star shows that a particular spectral line is shifted towards longer wavelengths compared with the same line measured in a laboratory on Earth. Explain what this observation reveals about the motion of the star relative to Earth, and outline how the magnitude of the relative velocity could be determined from this measurement.

> IB DP Physics Standard Level (2023 syllabus) — C.5 Doppler effect · Explain · 4 marks

## Mark scheme (4 marks)

1. The spectral line is red-shifted (shifted to longer wavelength / lower frequency), indicating the star is moving away from Earth.
2. As the star moves away, successive wavefronts are emitted from positions progressively further from the observer, so the observed wavelength is stretched / the received wavelength is greater than the emitted wavelength.
3. The fractional change in wavelength (Δλ/λ₀) equals the ratio of the recessional speed to the wave speed (v_s/c for light).
4. The known (laboratory) rest wavelength of the spectral line is used as the reference value, so that the magnitude of the shift Δλ can be precisely quantified and the speed calculated.

## Key terms

- [spectral line](https://www.gradenine.co.uk/glossary/spectral-line)

## Related

- [Revision notes for IB DP Physics Standard Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
- [Practice this with AI marking (free)](https://www.gradenine.co.uk/start)

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Source: [GradeNine](https://www.gradenine.co.uk/q/a-star-is-observed-from-earth-1977af36) · Published by Druglandscape Ltd.