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.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Model answer (4 marks)
The line is red‑shifted, i.e. its wavelength is longer than the laboratory value, so the star is receding from Earth.
Because the star is moving away, each successive wave crest is emitted from a position further from the observer; the distance between crests when they reach Earth is therefore larger, giving a longer observed wavelength.
The fractional change in wavelength is Δλ/λ₀ = v_s/c, where λ₀ is the rest wavelength measured in the laboratory and v_s is the star’s radial velocity. Thus, by measuring the shift Δλ and using the known λ₀, the recessional speed v_s can be calculated.
Because the star is moving away, each successive wave crest is emitted from a position further from the observer; the distance between crests when they reach Earth is therefore larger, giving a longer observed wavelength.
The fractional change in wavelength is Δλ/λ₀ = v_s/c, where λ₀ is the rest wavelength measured in the laboratory and v_s is the star’s radial velocity. Thus, by measuring the shift Δλ and using the known λ₀, the recessional speed v_s can be calculated.
Examiner tips
- Use the word ‘red‑shifted’ and state the star is moving away. Explain the geometric reason for the wavelength increase. Show the Doppler formula Δλ/λ₀ = v_s/c. Mention that λ₀ comes from laboratory data.
Mark scheme (4 marks)
- The spectral line is red-shifted (shifted to longer wavelength / lower frequency), indicating the star is moving away from Earth.
- 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.
- The fractional change in wavelength (Δλ/λ₀) equals the ratio of the recessional speed to the wave speed (v_s/c for light).
- 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 in this question
Related
- All IB DP Physics Standard Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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